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2 Financial Assets and Investment Risk

From: The Law of Financial Advice, Investment Management, and Trading

Lodewijk van Setten

From: Oxford Legal Research Library (http://olrl.ouplaw.com). (c) Oxford University Press, 2023. All Rights Reserved. Subscriber: null; date: 06 June 2023

Debt — Derivatives — Equity — Financial stability — Collective investment scheme — Securitization vehicles

(p. 41) Financial Assets and Investment Risk

A.  Financial Assets

1.  What is a financial asset?

2.01  A financial asset is a medium through which the person acquiring that asset provides capital to the real economy in return for a claim on expected future benefits. Bodie et al describe the economic character of financial assets as follows:1

The material wealth of a society is determined ultimately by the productive capacity of its economy, that is, the goods and services its members can create. This capacity is a function of the real assets of the economy: the land, buildings, knowledge, and machines that can be used to produce goods and services. In contrast to real assets are financial assets such as stocks or bonds … [T]hese assets are the means by which individuals in developed economies hold their claims on real assets. Financial assets (p. 42) are claims on the income generated by real assets (or claims on income from the government).

2.02  In economic terms, the holder of a financial asset is a person who provides capital funding to an undertaking, including governments, in return for future payments of income and, if applicable, repayment of capital. In legal terms, the financial asset is constituted by the legal construction that underpins the capital transfer.2 Like other legal constructions, such as the corporation, that exist in abstracto only but have a critical organizational impact on the real economy, financial assets are a truly remarkable feat of societal evolution. The operation of the concept of a financial asset in society enables the allocation of capital (ie monetary means), enables wealth to be stored for future consumption, and enables the collectivization and diversification of funding risk.3

2.03  It follows that money is not a financial asset. Rather, the financial asset creates monetary obligations expressed in a currency and money is the means to satisfy those obligations. Money is a unit of exchange by social convention: one party accepts money as payment in the expectation that others will do so, too.4 An investor’s base currency, meaning the currency in which the investor’s liabilities are expressed, serves as a medium to switch between financial assets or to discharge liabilities. Money is not a commodity.5 A foreign currency, meaning a currency other than the investor’s base currency, is also money and not a commodity. Nevertheless, a foreign currency’s value, unless it is ‘pegged’, fluctuates relative to the value of an investor’s base currency. Indeed, the investor in a financial asset that is denominated or expressed in a foreign currency will be exposed to ‘foreign currency risk’.

2.04  Cryptocurrencies present a new species of exchange value. They are based on ‘blockchain’ technology, that is, a network ledger system in which each transaction is confirmed by the network participants, rather than a central administrator, and in which each network participant has full visibility on the complete blockchained ledger of transactions carried out through the system. Complex mathematics-based confirmation calculations protect the blockchained ledger from fraud. In the case of a cryptocurrency, the blockchained network participants’ confirmation effort is rewarded with certain units of the cryptocurrency, (p. 43) which is called ‘mining’. It is probably an apt description. It conjures the image of precious metals and other commodities that can be used as an alternative means of exchange to money. Where ‘fiat money’, meaning government-issued units of exchange, functions as an asset-backed claim on the issuing government (ie can be said to represent the unitization of the value of the claim of the issuing government on its country’s economy through taxes or otherwise) cryptocurrencies represent nothing but themselves and are not backed up by any value. They are intangible things that tantum valet quantum vendi potest, that is, are worth only for what they can be sold. Although cryptocurrencies undeniably have evolved to serve a payment function in certain parts of the real economy and even a form of fundraising for the issuer of new crypto-coins in so-called initial coin offerings (ICOs), the acceptance as a form of tender is entirely voluntary and therefore speculative in nature.6 Its regulatory status is uncertain.7 Its legal status is yet unknown.8 Accordingly, unless and until its legal status changes and it becomes legal tender, cryptocurrencies are a commodity and not money.

2.  Primary financial assets: equity and debt interests

2.05  Financial assets are constructed so that capital is provided either in the form of equity or in the form of debt. Equity instruments are offered by undertakings with a view to obtaining capital that is at risk in return for some form of ownership-like control by way of a vote in a governing body and a profit share. Accordingly, equity is a form of proprietary interest in the funded undertaking. The profits may be distributed during the life of the funded undertaking as dividend or as a share in the liquidation proceeds in which holders of equity instruments rank last. The common offerors of equity are companies, including financial services companies such as banks and insurance companies. In addition, equity is offered by collective (p. 44) investment schemes, which in turn use the capital obtained to invest in financial assets for the account of the participants in the collective investment scheme.

2.06  Debt, or ‘fixed income’, is a form of in personam claim against the funded undertaking that entitles the holder to fixed or floating rate interest payments and a repayment of capital on maturity. Several variations exist on this principal form of debt as a claim for a stream of interest payments and repayment of capital at maturity. For instance, debt may be structured as a ‘zero coupon’ instrument offered at a value below its face value, so that the interest is recouped over the life time of the debt. Alternatively, debt may be structured as a perpetual instrument, so that no capital repayment date is set, at which point the debt instrument may typically be treated as equity for accounting purposes. Debt instruments are offered by undertakings with a view to obtaining capital that must be repaid at some point and that has no control strings attached, although the funding may be subject to certain covenants and conditions. Some debt is constructed so that its repayment is secured by specified, ring-fenced assets rather than the assets generally of the offeror. The common offerors of debt are governments and governmental agencies, supranational bodies, and companies, including financial services companies. In addition, debt instruments are offered by special purpose or ‘securitization’ vehicles to fund the acquisition of financial assets.

2.07  Equity and debt instruments may be constructed in hybrid form. Equity instruments may be offered as preference shares. Preference shares technically are equity instruments, but typically carry no voting rights and give a preferential right to dividend and liquidation distribution payments in priority over holders of ordinary shares. Usually, holders of preference shares are entitled to a dividend at a fixed rate and, if holding cumulative preference shares, the right to a dividend payment carries over if in any dividend period the undertaking is unable to make the payment. Preference shares may therefore be equated to subordinated debt.

2.08  Equally, debt instruments may be offered as convertible bonds or structured notes. Convertible bonds are debt securities with embedded ‘put and call’ options entitling the holder of the convertible bond to exchange the bond against an ordinary share. Preference shares and convertible bonds both have the legal characteristics of a debt instrument. Nevertheless, their economic value is closely correlated to the value of ordinary shares, and preference shares and convertible bonds are often treated as equity investments in investment risk terms.

2.09  Structured notes are debt-like instruments offered by financial services and commercial companies as an alternative to traditional funding through existing borrowing programmes.9 A structured note may be described as a composite (p. 45) financial asset that permits the combination of debt with options and a payoff structure that is calculated by reference to different reference values.10 In terms of the reference value, the universe of structured notes can be divided into equity, interest rate, or credit-linked and other less common values such as funds, currencies, or commodities.11 In terms of their payoff structure, structured notes can be categorized as capital guaranteed, yield enhancement, or participation products. ‘Capital guaranteed’ products limit the loss potential to the amount of the invested capital while at the same time permitting participation in any upside of a risky reference value, such as equity, foreign exchange, or commodities.12 ‘Yield enhancement’ products offer a higher payoff rate by embedding a short put on a risky asset. The embedded short put implies that although the coupons are guaranteed, the invested capital is not protected.13 ‘Participation’ products are the riskiest. They offer partial or full, potentially leveraged, participation in the return of a risky asset.14 The offeror of the structured note will usually hedge the payoff due under the structured note via a structured swap. The swap provides the offeror a series of payoffs that match the payoffs under structured note, in consideration of which the swap provider will receive its funding cost—that is, a series of floating rate payments based on a published benchmark market cash rate for the relevant currency15—plus a spread—that is, a series of fixed rate payments that reflect the real rate of return demanded by the provider.16

2.10  Structured notes have existed for many years. From the mid-1990s, however, the predominant manner of issuance has been through ‘medium-term note (p. 46) programmes’ (MTNs), which are distributed internationally. The benefit of an MTN programme for issuers is that it serves as a relatively low-cost way to obtain funding. Often the swap counterparty is the dealer that arranges and distributes the notes, that is the arranger. Structured notes have been the instrument of choice for brokers who wish to offer various forms of market exposure to private investors.

3.  Secondary financial assets: collective investment schemes and securitization

2.11  Debt and equity offered by businesses and governments represent the original financial asset, that is, the original claim on the real economy. Debt and equity may also be offered by collective investment schemes and special purpose vehicles (SPVs), which in turn use the capital received to acquire original financial assets, thus removing the financial asset offered by the intermediating vehicle one step from the original financial asset. This type of financial asset may therefore be characterized as a secondary financial asset. The value of the secondary financial assets will be based on the value of the portfolio of original financial assets acquired by these intermediating vehicles.17

2.12  Collective investment schemes, or ‘investment funds’, are undertakings that permit collectively funded acquisition and management of a portfolio of assets of any description, including financial assets, with a view to sharing the profits or income arising from the managed portfolio.18 Accordingly, the interests offered by the collective investment scheme to obtain capital needed to fund the acquisition of the investment portfolio constitute equity instruments. Collective investment schemes may be ‘open-ended’ or ‘closed-ended’. The former allow the holders of interests in the collective investment schemes to redeem their interest at certain intervals against payment of the value of that interest out of the investment portfolio of the collective investment scheme; or permit existing or new holders to acquire additional interests against a contribution of a payment commensurate to the pro rata value in the investment portfolio of the collective investment scheme represented by the offered interests. Closed-ended schemes do not permit redemption until the end of the fixed term of the collective investment scheme. They typically aim at the acquisition of real, illiquid assets, such as real property or privately held companies, or some other form of illiquid portfolio. Collective investment schemes may be constituted as a company (eg a company with variable capital), in contractual form (eg a partnership in which the collective holders become limited partners), or as a unit trust.

(p. 47) 2.13  Securitization or ‘asset backed’ schemes entail the offering of debt instruments called ‘notes’ by an SPV. Securitization is a way for owners of receivables, loans, or other eligible assets, the ‘originators’, to liquidate these assets by selling them to the SPV who raises the capital for the purchase by offering debt instruments to investors.19 The claims on the SPV of the holders of the issued debt instruments are secured by the assets acquired by the SPV from the originator;20 hence the use of the term ‘asset-backed scheme’. This method of financing offers the originator the ability to diversify its funding sources and improve its cash flow. Recital (4) of the Securitization Regulation observes the potential benefits of securitization:

Securitisation is an important element of well-functioning financial markets. Soundly structured securitisation is an important channel for diversifying funding sources and allocating risk more widely within the Union financial system. It allows for a broader distribution of financial-sector risk and can help free up originators’ balance sheets to allow for further lending to the economy. Overall, it can improve efficiencies in the financial system and provide additional investment opportunities. Securitisation can create a bridge between credit institutions and capital markets with an indirect benefit for businesses and citizens (through, for example, less expensive loans and business financing, and credits for immovable property and credit cards).

2.14  A variety of asset-backed schemes has been created and sold in the market over the years. The differences between the programmes stem from the degrees of complexity of the securitized portfolio (the mix of asset classes and the extent of the use of derivatives), the way the securitized portfolio is funded or covered, and the way the obligations of the issuer under the debt securities are secured. In a basic programme, the receivables held by the SPV match the payments due under the notes issued against those assets, so that funding of the payments due under the (p. 48) issued debt securities is covered. These securities are called ‘collateralized loan obligations’ (CLOs), ‘collateralized mortgage obligations’ (CMOs), or ‘collateralized bond obligations’ (CBOs), in each case depending on the type of asset that is securitized through the programme. Where the scheme securitizes liquid assets, such as corporate loans in a CLO, it might appoint an investment manager charged with managing the securitized portfolio of loans in accordance with a certain investment objective.

2.15  Once single-asset-class asset-backed schemes, that is, CLOs, CBOs, and CMOs, became well established, originators moved along the complexity scale by offering schemes that effectively became SPV-of-SPVs, meaning schemes that permit the SPV to invest in a collection of CLOs, CBOs, or CMOs. These layered asset-backed schemes were referred to as collateralized debt obligations (CDOs). From there, it is only a small step to devise schemes that permit the SPV to issue structured notes. At that point, the SPV acquires the payoff due under the notes from a swap provider. The SPV will invest the proceeds of the notes issued in a portfolio of money market securities or other fixed-income investments that deliver a predictable return and use that return to make payments under the total return swap. These structured note schemes are referred to as ‘synthetic’ CDOs.

2.16  In a further development, taking asset-backed schemes away from asset-backed securitization and into a hybrid money-market-fund-cum-banking model, originators structured asset-backed schemes such that the SPV could profit from credit spreads between short-term and long-term debt by issuing short-term—‘money market’—debt against long-term assets that have less liquidity but pay higher yields. These schemes were referred to as ‘structured investment vehicles’ (SIVs). Purchase of long-term portfolios by SIVs was funded not by a single issue, but by the issuance of short-term commercial paper that is continuously renewed or ‘rolled over’. The SIV earned profits on the spread between incoming cash flows, principal and interest payments on the long-term assets in the portfolio—often asset-backed securities issued by standard securitization schemes—and the rates paid in respect of the commercial paper that it issues. In addition, SIVs often borrowed money, that is, leveraged the securitized portfolio, to generate excess returns. Originators managed to obtain high credit ratings for the senior tranche of short-term debt issued by SIVs despite the leverage in the portfolio and despite the liquidity mismatch between the short-maturity funding side of the SIV and the long-maturity investment side. The lowest, or equity, tranche would earn a higher yield, but be subordinated to all the higher tranches. Only the highest ranking tranche obtains the superior credit rating. Because of the excess returns earned from the interest-rate spread and the leverage, an SIV was able to pay a higher rate of interest to the various note-holders.

2.17  At the time, CDOs and SIVs were thought to be quite clever schemes, but in the summer of 2007, when the global housing bubble started to deflate, first in the sub-prime mortgage market in the United States, CDOs turned out to (p. 49) exhibit complex correlations, resulting in uncertainty as to the risk and return prospects and a subsequent collapse in the values of CDOs. Mindful of the potential complexity of the correlations, the Securitization Regulation has restricted re-securitizations to limited circumstances in which it is considered to ‘be useful in preserving the interests of investors’.21 Similarly, the funding risk for SIVs materialized when the short-term credit markets ceased up and no buyers could be found for the SIVs’ roll-over paper. The SIVs’ liquidity crunch was aggravated by the fact that many SIV providers, who considered the risk that the short-term credit markets would become illiquid and disrupt the scheduled roll-overs too small to insure, had decided not to obtain back-up bank-supplied credit lines. When the liquidity crunch materialized and the SIVs could not roll their short-term debt over, the sponsoring banks had to decide whether to support their SIV or walk away and suffer reputational risk.22The chain of value failures in the market for securitized vehicles did not only affect CDOs and SIVs, but also CLOs and other single-asset-class asset-backed schemes that would otherwise have been viable but for a general lack of trust in the financial system.23

4.  Meta-financial assets: derivatives

2.18  The value of financial assets, financial reference rates, and indices based on financial assets or reference rates, may go up as well as down and, consequently, there is a natural economic interest in transactions that offer a notional or ‘synthetic’ form of exposure to or, conversely, hedge against that fluctuation. There are principally two structures that can be used to do so: buy or sell a financial asset, reference rate, or index of financial assets on a forward basis; or buy or sell an option to buy or sell a financial asset, reference rate, or index. Both permit the parties to the transaction to express a view on future fluctuations by locking today’s price or rate in on a non-contingent forward basis or on a contingent option basis. Because forward and option-based transactions offer that economic functionality, they are intrinsic to the universe of financial transactions, both stand-alone and embedded in a swap or other combination transaction.24

(p. 50) 2.19  Forward, option, or combination transactions are commonly referred to as ‘derivatives’ because the contract’s intrinsic value fluctuates based on the fluctuation of the value of another financial asset that is outside of the control of the parties to the contract. It can be said that derivative contracts are bilateral, zero net supply assets. An asset that exists in zero net supply is created by the agreement to establish a short position (the seller) and a long position (the buyer). The sum of all long positions minus the sum of all short positions is always zero.25 It follows that derivatives do not represent a claim on the real economy, but rather represent ‘meta’ financial assets that are based on, and give information about, primary and secondary financial assets. The ability of investors, investment firms, and banks to increase or hedge exposure to a financial asset through the creation of derivative financial assets is of critical importance to the financial system and therefore to economic progress, not dissimilar to the importance of the insurance industry’s ability to collectivize risks in the real economy.

5.  Securities financing and short selling transactions

2.20  Spot transactions in financial assets need to be settled within several days from the trade date, depending on the trading venue. Settlement can be financed. This means that a third party, the liquidity provider or financing party, provides the cash or assets needed to perform the trade by way of a cash loan, a securities loan, or a repurchasing agreement (repo). Securities finance transactions are sometimes referred to as ‘derivatives’, but that would not seem to reconcile with the notion that a derivative is a zero net supply asset. Quite the opposite is true for securities finance transactions: repos, securities loans etc are ‘funded’ transactions, that is, require the underlying financial asset to be supplied at the outset.

2.21  The analyses of the 2007–08 liquidity crunch shed light on the lack of reliable and in-depth data on securities financing transactions. The European Commission considers this data essential to assess ‘risks associated with interconnectedness, excessive leverage and pro-cyclical behaviours’. The Commission also observed that access to such data ‘will permit the identification of risk factors such as excessive recourse to short-term funding to finance long-term assets, high dependence on certain types of collateral and shortcomings in assessing them’. It considered these gaps a concern, ‘particularly in view of the opacity of collateral chains which increases the risk of contagion’.26 The Securities Financing Regulation27 seeks to address this data gap. Recital (7) observes:

(p. 51)

This Regulation responds to the need to enhance the transparency of securities financing markets and thus of the financial system. In order to ensure equivalent conditions of competition and international convergence, this Regulation follows the FSB Policy Framework. It creates a Union framework under which details of [securities financing transactions (SFTs)] can be efficiently reported to trade repositories and information on SFTs and total return swaps is disclosed to investors in collective investment undertakings

2.22  Several financing techniques are used by participants in the financial markets:

  1. (a)  The financing party extends a cash loan to a funded party to finance the purchase of financials assets, also known as a ‘margin lending transaction’.28

  2. (b)  The financing party funds the other party by way of a repurchase agreement (repo). A repo is a bilateral agreement whereby the financing party agrees, depending on the financing needs of the funded party, to transfer cash or financial assets to the funded party in consideration of a certain countervalue in cash or financial assets, and at the same time and as part of the same transaction both parties commit to reverse the transaction at a later date and transfer equivalent financial assets and cash back, adjusted for any variation margin collateral top-ups or draw-downs that may have occurred during the term of the transaction.29 In legal terms, a repo is documented as a sale and purchase of financial assets and simultaneous agreement to sell and buy back equivalent financial assets, coupled with a variation margin obligation. Repos are used either to advance cash against the purchased financial assets as collateral, or to advance financial assets against the cash or other financial assets as collateral. The latter purpose is identical to a securities loan, that is, the repo documentation is used to document a transaction that has the objective of a securities loan.

    The securities financing transaction in the form of a repo can also be structured as a buy-and-sell-back transaction,30 or as a funded total return swap, (p. 52) also known as a ‘synthetic repo’. A sell/buy back is structured as two simultaneous transactions, that is a spot sale or purchase and the reverse on a forward basis.31

    A funded total return swap, or ‘liquidity swap’,32 is documented as a transaction whereby the financing party agrees to pay the funded party for a certain number of intervals the value of a certain reference asset or portfolio of assets, plus or minus the valuation fluctuation as at the end of each interval, in return for payment by the funded party of a rate calculated on the funds received as the value of the reference asset at inception, and a refund of the original funding at expiration of the swap.33 The Securities Financing Regulation also recognizes the funded total return swap as a securities financing instrument. Recital (7) notes that the definition of ‘securities financing transaction’ does not include derivative contracts as defined in the European Market Infrastructure Regulation (EMIR),34 but does include ‘transactions that are commonly referred to as liquidity swaps and collateral swaps, which do not fall under the definition of derivative contracts in [EMIR]’. Article 3(18) defines ‘total return swap’ as ‘a derivative contract as defined in [EMIR] in which one counterparty transfers the total economic performance, including income from interest and fees, gains and losses from price movements, and credit losses, of a reference obligation to another counterparty’. Recital (7) is clear that this concerns liquidity swaps, that is, funded transactions rather than (net zero supply) derivative transactions, but the definition could be read to be a nominal value, that is, not a funded, total return swap.

  3. (c)  The financing party provides securities to the funded party by way of a securities loan agreement, whereby the financing party agrees to transfer securities in return for a fee, and the funded party agrees to provide initial margin (p. 53) collateral and a variation margin collateral in the form of cash or cash equivalents, and to return equivalent securities on expiration or termination of the loan.35

2.23  Repos, securities loans, and swaps are typically documented under market- developed standard agreements.36

2.24  Securities financing transactions can facilitate short selling. Short selling concerns the sale of a financial asset that the seller does not own at the time of the trade. The repo or securities loan can provide the securities needed for settlement, and the short seller/borrower can discharge the loan at a later date, presumably by buying the borrowed securities at a lower price than the price received on the original short sale. Short sales come in two categories: a covered short sale where the seller has made arrangements to borrow the securities before the sale, and a naked short sale where the seller has not (yet) borrowed the securities when the short sale occurs. Short selling brings economic benefits because it permits an investor to express a view and invest if there is an expectation that market prices will be reduced. The participating investor enhances price discovery and also improves market liquidity. That does not mean that short selling is always a force for good. Excessive short selling naturally can cause negative price spirals, potentially causing systemic risks. During the onset of the down turn of 2008 and 2009, many countries took action to suspend or ban short selling, and in 2012 the EU adopted the Short Selling Regulation.37 The Short Selling Regulation aims to increase market transparency by requiring investors to report net short positions,38 and to curtail potential excessive short-selling by prohibiting naked short selling.

(p. 54) B.  Investment Risk

1.  The value of a financial asset

2.25  Oscar Wilde’s description of a cynic as someone who ‘knows the price of everything and the value of nothing’,39 is often quoted in the context of valuation of financial assets. Damodaran observes that some analysts and investors today fit the description of Wilde’s cynic because they subscribe to the theory that the value of a financial asset is irrelevant if there is a ‘bigger fool’ around willing to buy the asset at a higher price.40 That perception of reality can be traced back in the ancient Latin maxim res tantum valet quantum vendi potest, meaning that a thing is worth only what someone else will pay for it.41 Indeed, the Dutch typically respond to a question about the potential value of a thing that ‘it is worth what a fool is willing to give in exchange’.

2.26  It may be true that meaningful investment returns can be obtained in the short run based merely on assessment of market sentiment. Investment in financial assets, however, at the core concerns expectations about future cash flows. Perceptions of value must be backed up by realistic expectations, that is, the price that is paid should reflect the cash flow reasonably expected on the financial asset.42 That approach to valuation is based on a notion of intrinsic value, which is determined by careful analysis of economic factors and prospects.43 Estimated cash flows vary, naturally, depending on the type of financial asset.

2.27  Damodaran summarizes three approaches to intrinsic valuation, which are all based on the present value of the estimated future cash flow:44

The first, discounted cash flow (DCF) valuation relates the value of an asset to the present value (PV) of expected future cash flow of an asset. The second, relative valuation, estimates the value of an asset by looking at the pricing of comparable assets relative to a common variable such as earnings, cash flow, book value, or sales. The third, contingent claim valuation, uses options pricing models to measure the value of assets that share option characteristics … While discounted cash flow valuation is only one of three ways of approaching valuation and most valuations done in the real world are relative valuations, it is the foundation on which all other valuations approaches are built. To do relative valuation correctly, we need to understand the (p. 55) fundamentals of discounted cash flow valuation. To apply option pricing models to value assets, we often have to begin with discounted cash flow valuation.

2.28  Future cash flows from equity securities depend on the risks to an issuer’s business, the expected annual growth rate of earnings and dividends, and interest rates. Growth rates of dividend and earnings can deliver a compounded return. Interest rates that are high enough can offer a stable alternative to stocks and may drive equity prices down due to capital flight.45 The characteristic return property of equity investments, therefore, is the alignment with macro-economic factors,46 permitting returns well above the risk-free rate—being the rate available from a financial asset whose expected return equals the actual return47—over longer periods of time.48 Conversely, in times of economic distress, equity investments can rapidly lose a substantial part of their value.

2.29  It is often said that equity securities, as an asset class, tend to have inflation-hedge properties on the assumption that business profits tend to correlate closely with inflation rates.49 In fact, the opposite appears true. Equities fare badly in periods of high inflation, which reduces future firm profitability because firms cannot pass inflation costs through immediately and completely. High inflation also tends to increase business risk so that investors demand higher risk premiums resulting in price cuts.50

2.30  Future cash flows from fixed income securities are more certain. Fixed income securities pay interest and principal, the ‘face value’, during a certain period. The nominal risk-free interest rate is a compound existing of a real rate of return to compensate the investor for providing capital, and a rate to compensate for expected inflation. For issuers that cannot borrow at the risk-free rate, the compound rate will include an additional risk premium to compensate for idiosyncratic risks (p. 56) such as default risk, liquidity risk, and other risks that are specific to the type of issue or the issuer.51

2.31  The interest rates for borrowers of the same quality but for different lending periods that prevail on a certain date can be plotted as a graph called the ‘yield curve’. It shows the cost of borrowing for a given credit-default risk in a given currency at different maturity dates. Yield curves corresponding to the fixed-income securities issued by governments in their own currency are called the ‘government bond’, or ‘risk-free’ yield curve.52 Zero-coupon bonds do not pay interest but are issued at a discount to reflect the interest due at maturity.

2.32  Intrinsic valuation of stocks and bonds based on discounted cash flow valuation takes the sum of the estimated future cash flows—that is, cash dividends for equities and coupons and par value for bonds—and the estimated capital appreciation or depreciation—that is, the change in price of the financial asset—measured over a certain time interval and applies a discount rate to determine the present value. The discount rate will be a function of the riskiness of the estimated cash flows, with higher rates for the riskier financial assets.53 Relative valuation derives the value of a financial asset from the pricing of comparable assets using a common standardized variable (eg earnings, cash flows, book value, or revenues) and, accordingly, is less a search for intrinsic value and more about referencing asset class pricing to determine whether the pricing of the individual asset might be off mark.54

2.33  Derivatives present a special valuation challenge because their payoffs are contingent on the occurrence or non-occurrence of an event in relation to another financial asset. Option pricing models have been developed since the 1970s that permit valuation of contingent claims.55 The value of an option for its buyer is determined by six variables that relate to the reference financial asset and market developments: current value of the reference asset, the volatility of the price of that asset, the dividends paid on the asset, the strike price of the option, the time to expiration, and the interest rate corresponding to the life of the option.56 Further valuation complexity is introduced by the fact that most of the actively (p. 57) traded options are ‘American’ style options, which permit exercise at any time during their lifespan. Options that have a fixed exercise point at expiration, called a ‘European’ style option, are less complex to value.57 The option pricing models rely on valuation by reference to the expected returns of a replica portfolio of the reference asset(s) financed with riskless lending or borrowing. The valuation is based on the notion that no arbitration opportunity should exist between the option and the replica portfolio.58 The option should then sell for the same price as the cost of the replica portfolio.59

2.  The concept of ‘risk’60

2.34  Peter Bernstein opens his ingenious book on the history of risk with an enlightening question: ‘What is it that distinguishes thousands of years of history from what we think of as modern times?’ The answer follows swiftly:

The revolutionary idea that defines the boundary between modern times and the past is the mastery of risk: the notion that the future is more than a whim of the gods and that men and women are not passive before nature … This book tells the story of a group of thinkers whose remarkable vision revealed how to put the future at the service of the present. By showing the world how to understand risk, measure it, and weigh its consequences, they converted risk-taking into one of the prime catalysts that drives modern Western society.61

2.35  The shift in the analysis of risk can be traced back to the Renaissance. In 1654 Pascal and Fermat, the French mathematicians, formulated the theory of probability, the mathematical heart of the scientific concept of risk. Over the years, this discovery was transformed into a tool for organizing, interpreting, and applying information.62 It culminated in the mathematically driven apparatus of modern risk analysis that seeks to underpin forward-looking decision making.

2.36  The quantitative techniques that were developed to analyse risk raise the question whether risk must be defined as a quantity susceptible of measurement. If so, measurable uncertainties (risk) would need to be treated separately from unmeasurable uncertainties (not risk). Knight writes in 1921:

Uncertainty must be taken in a sense radically distinct from the familiar notions of Risk, from which it has never been properly separated … It will appear that a (p. 58) measurable uncertainty, or ‘risk’ proper … is so far different from an unmeasurable one that it is not in fact an uncertainty at all.63

That equates risk with probability, that is, measurable uncertainty, which is, perhaps, not uncertainty at all. And, indeed, Knight insists that forecasts ‘must be radically distinguished from probability or chance … it is meaningless and fatally misleading to speak of the probability, in an objective sense, that a judgment is correct.’64

2.37  Keynes does not distinguish categorically between risk and (unmeasurable) uncertainty, but between what can be defined (or known, in some mathematical fashion) and what cannot. In 1937 he wrote:

By ‘uncertain’ knowledge … I do not mean merely to distinguish what is known for certain for what is only probable. The game of roulette is not subject, in this sense, to uncertainty … The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention … About these matters, there is no scientific basis on which to form an calculable probability whatsoever. We simply do not know!65

2.38  In that mould, Damodaran observes that in the concept of risk, all uncertainty matters, whether measurable or not.66 He offers the view of Holton, who notes that two ingredients are needed for risk to exist: uncertainty about potential outcomes from an experiment, and relevance of the potential outcomes in terms of providing utility.67 This permits a definition of risk that captures both potential positive and negative outcomes, specified relative to a certain desired or expected objective.

2.39  Risk thus denotes potential outcomes assessed against a specific objective, such as investment risk, liquidity risk, or operational risk. This is the prevailing approach in the financial services industry, that is, the coupling of downside potential (cost or loss) and upside potential (revenue, profitability, or investment return), which recognizes that the concept of risk is strategic: no risk, no reward. Risk is about forward-looking choices to exploit or not to exploit opportunities for sometimes certain, sometimes uncertain reward that expose the decision-maker to sometimes certain, sometimes uncertain adverse outcomes.68

(p. 59) 3.  The concept of ‘investment risk’

2.40  Modern investment risk analysis is concerned with the selection of investments that have different risk and return properties. Return is defined as the sum of the estimated future cash flows—that is, cash dividends for equities and coupons and par value for bonds—and the estimated capital appreciation or depreciation—that is, the change in price of the financial asset—measured over a certain time interval. Investment risk is defined as the likelihood that the actual return on investment will differ from the return that is expected,69 or in statistical terms, investment risk is the variance, or standard deviation, of returns.70

2.41  Measuring investment risk thus concerns the determination of two different components: the expected return—which represents the opportunity—and the variance of potential returns—which represents the risk.71 In statistical terms, the expected return is the central point in a set of potential returns. The potential returns are estimations based on scenario forecasts of future macro-economic and other relevant developments. The further the investment horizon, the wider the distribution of potential returns. Each potential return in the set is assigned a probability, which is calculated and assigned by reference to statistical approximations derived from historical data and trends.72 The expected return, or ‘mean return’, on the investment is the probability-weighted arithmetic mean of potential returns, that is, the sum of the potential returns, each multiplied by its assigned probability.73

2.42  The distribution of potential returns of one investment may vary considerably from that of another investment, although both investments may have the same expected return. That variance is the investment risk. An investment whose returns are not likely to depart much, if at all, from its average or expected return is said to carry little or no risk. An investment whose returns over the intended investment period are likely to be quite volatile is said to be risky.74 Accordingly, a risk-free asset is an asset that has a single return outcome, with an assigned probability ratio of 1.0. A probability ratio of 1.0 necessarily assumes that the probability that the issuer will become insolvent before the instrument in question (p. 60) matures is negligible, so that the future return of the instrument over a given investment period can be calculated with certainty.75 The typical proxy for the risk-free rate is a short-term government bond of a developed economy, eg AAA-rated Euro area short-term government bonds for Euro denominated financial assets, or US Treasury Bills for USD denominated financial assets.76

2.43  Modern investment risk analysis assumes that investors are unwilling to invest in an asset that has a variable return unless the expected return is above the return on a risk-free asset, which is called the ‘expected excess return’, or the ‘risk premium’. In investment risk terms, investors are presumed to be risk-averse, not in the sense of being unwilling to accept risk, but in the sense that the level of risk must be proportionate to the expected excess return.77 The presumed seminal question for each investor is what the price of an investment must be so that it may be expected to yield a return that is commensurate to its risk. It is not sufficient to determine the expected return of an asset and the risk implied in that expected return. It is also necessary to determine what level of risk is appropriate given the expected return—that is, to understand and evaluate the relationship between that risk and that expected return and arrive at the best possible trade-off between that risk and that return—and so at the optimal allocation of capital between risk-free assets on the one hand and risky assets on the other, as well as among the risky assets.

4.  Measuring investment risk: volatility

2.44  The basic risk measure used in investment risk analysis is the variability as a function of the dispersion of the potential returns. The wider the spread of possible returns above and below the weighted mean return, the higher the risk. This is called the ‘volatility’ of the distribution of the potential returns, or ‘spread’. Another way of describing volatility is to say that a variability of zero around the mean return means that the investment is risk-free.

2.45  There are several statistical methods that may be used to measure variability. A good index, however, should be independent of the mean, so that a unit of (p. 61) measurement is created that permits the comparison of separate sets of data. Variability is measured by reference to the deviations around the mean. By focusing on how far a potential return lies from the mean return, and in which direction, the value of the mean return is eliminated from the resulting unit of measurement. Measurements of dispersion defined in terms of deviations around the mean will be independent of that mean. This also implies that the sum of the deviations will always be zero so that, as such, the sum of the deviations cannot be a measure of variability. Another way of arriving at a measure of variability around the mean could be to average the sum of the absolute deviations. However, this will not permit convenient mathematical manipulation. Therefore, the traditional statistical method of calculating the variability of a data set is to average the sum of the squared deviations around the mean. The resulting value is called the ‘variance’, denoted as sigma squared (σ2). The wider the spread, the higher the values of the squared deviations will be, and therefore, the higher the variance will be. Usually, statisticians take one extra step and use the square root of the variance, which is called the ‘standard deviation’ and is denoted as sigma (√σ2 = σ‎). The standard deviation is considered to be more convenient for interpreting the variability of a data set, since the variance is expressed in squared units while the standard deviation is expressed in the same units as the original data.78 A statistical rule of thumb for interpreting a standard deviation value is that in a symmetrical, bell-shaped, or normal, distribution, about 68 per cent of all values in a data set will fall within one standard deviation (σ‎) centred on the mean, about 95 per cent of all values will fall within two standard deviations (2σ‎) centred on the mean, and about 99 per cent of all values fall within three standard deviations (3σ‎) to either side of the mean. Accordingly, if the mean and the standard deviation of a certain data set are known and it may be assumed that the data set has a normal distribution, it is possible to give a good description of the variability of that data set as well as its central point.79

2.46  Investment risk analysis uses the variance and the standard deviation of a population of potential returns as an expression of how sensitive the expected return is to changes in certain relevant market data. Accordingly, ‘risk’, in portfolio theory, is a statistical concept, which includes both potential worse-than-expected as well as better-than-expected returns. It is calculated by taking the probability-weighted average of the squared deviations about the mean return. In its most basic form, it refers to the levels of dispersion of the potential returns on the investment in question relative to the average, or arithmetic mean, return. The greater the variability of the spread of potential returns relative to the mean return, that is the (p. 62) greater the ‘variance’ or ‘volatility’ of the potential returns, the greater the level of risk that is associated with that investment.80

2.47  The problem with the concept of standard deviation is that it only reliably describes the volatility of a normal distribution, that is, a symmetric distribution along a bell-curve that tops at the mean value. It does not accurately highlight an uneven distribution, where the probability of a negative return may be much higher than the probability of a positive return. One way of revealing whether negative values incorporated in the expected return are large relative to the positive values is to calculate the standard deviation for the negative deviations separately. Another way is to quantify the asymmetry by taking the sum of the cubed, rather than the squared, deviations, thus emphasizing the larger deviations relative to the normal deviations, which causes the ‘long tail’ of the distribution to dominate the measure of skewness.81 In other words, cubing the deviations before taking the sum will reveal which way the distribution curve is skewed, that is where the top of the curve lies relative to the mean. If the curve is skewed to the left of the mean, that is dominated by negative deviations from the expected return, the skewness will be a negative number because the cubed values of the negative deviations will exceed the cubed values of the positive deviations, and vice versa.

5.  Measuring investment risk: tail risk

2.48  Notwithstanding its usefulness, volatility alone may be insufficient to describe the risk properties of an investment. If the distribution is significantly skewed or unequal across the range of values (heteroskedastic), then informative value of the metrics is reduced. To deal with that gap, much work has been done to estimate the tail risk to create an estimate of maximum loss for a given probability. The leading tail risk measurement technique, which emerged during the 1990s, is called the ‘value at risk’ (VaR) method and is now widely used by investors, banks, investment firms, and regulators. VaR is an estimate of the loss that is expected to be exceeded with a given level of probability over a certain period. In other words, a given VaR value, expressed as a percentage of the reference value or as an absolute value, is an estimate of the maximum loss that might occur during a certain period. The actual loss could, of course, be much larger.

2.49  In statistical terms, the VaR highlights the probability that, relative to the mean return, a negative return occurs, that is, the VaR expresses a quantile of the distribution of possible outcomes. The methodology is based on dividing a data set into a specified number of groups, each containing the same number of values. For (p. 63) example, percentiles divide the data in 100 equal parts, each representing 1 per cent of all values, while 5 per cent quantiles divide the data into 20 equal parts, each representing 5 per cent of all values. The median of the distribution is the 50 per cent quantile, or 50th percentile. Thus, the 90th percentile would be the value that has 90 per cent of the values in the relevant data set below it, and 10 per cent of those values above it.82 Typically, the VaR value, as a measure that focuses on negative returns, is the value below which lie 5 per cent of the values; that is, typically, the VaR value is the 5 per cent quantile. In other words, a 5 per cent quantile VaR of -32 per cent indicates that the probability is 5 per cent that the value of the investment will fall by 32 per cent, or more, over the period in question. Of course, a VaR may relate to the 1 per cent quantile.83 Another way of expressing the probability is to refer to ‘confidence levels’. Thus, the 5 per cent quantile, or 0.05 probability, equates to a 95 per cent confidence level, and the 1 per cent quantile, or 0.01 probability, equates to a 99 per cent confidence level.

2.50  VaR, as a measurement tool, has become an industry standard. However, the methodology is subject to several assumptions and discretionary variables. The assumptions are, usually, that market movements are distributed normally, and consequently, that the losses will be distributed normally. The main variables are the quantile or probability level, the measurement interval or period over which to measure the VaR, and, most importantly, the loss distribution modelling. The chosen confidence levels are typically between 95 and 99 per cent, or probabilities of 0.05 to 0.01. The lower the probability, the more conservative the measurement, because a probability of 0.01 means that the chance that the loss will exceed the VaR amount at that level is less than 1 per cent. VaR is often measured over a one-day time interval but regulators may require a much longer period, for example two weeks, to accept the value as a meaningful risk-management tool.84

2.51  Loss distribution models divide, broadly, into three methodologies, the ‘analytical’ or ‘variance–covariance’ method, the ‘historical’ method, and the ‘Monte Carlo simulation’ method. The analytical method assumes that the returns of the investment in question are normally distributed and relies on certain statistical truths that apply in the case of standard normal distributions to calculate 5 per cent VaR values based on the investment’s expected return and standard deviation. Accordingly, the analytical method uses estimates of forward data and relies on the estimates of expected returns, albeit these, in turn, are mostly based on historical data and trends. The historical method uses historic data, applying historical price changes during a given period in the recent past to the current investment. The advantage is that this method does not involve probability-distribution (p. 64) assumptions. However, it does rely entirely on probability distributions of the past that might not hold true in the future. The Monte Carlo simulation method assumes a certain probability distribution and, subject to certain input parameters, generates random return outcomes that can then be used to determine VaR levels.85 As all VaR loss-distribution methods rely on assumptions and expected returns which themselves are the product of estimates, the realized risks may deviate substantially from the estimated risks, and it is therefore essential that the VaR methodology used is ‘back-tested’ regularly, that is, the user of the VaR model should compare the actual losses that have occurred over a certain period with the applicable VaR model. If the dispersion of back-testing results versus the expectations under the VaR model exceeds a certain threshold, then the efficacy of the model may be questioned and where the VaR model is used as a tool to comply with regulatory risk management and capital requirements, the competent regulator may direct the firm to adjust their VaR model.

6.  Measuring investment risk: stress testing

2.52  VaR and volatility-risk models are often supplemented with other risk-measurement techniques. An important technique is ‘stress testing’. Whereas the main purpose of VaR and volatility measures is a forward-looking quantification of potential maximum losses or ‘tail risk’, based on the returns for the type of asset over the last 12, 36 or 60 months, stress testing seeks to review the potential losses of a portfolio of assets in several specific scenarios, typically severe market conditions, that are relevant for the type of asset and relies on data further back in history than the data that is used to estimate VaR. Stress testing seeks to identify unusual circumstances that could lead to losses that exceed those typically expected, that is, those at the extreme ends of the return distribution curve, to the left of the expected return. It involves, inter alia, ‘scenario analysis’, in which the potential price movement of an investment is calculated by simulating changes in essential economic factors, such as interest rates, stock prices, exchange rates, real property prices, and commodity prices, or ‘stressing models’.

C.  Investment Risk in a Portfolio Context: The Effect of Covariance

1.  Investment risk reduction through diversification

2.53  It was not until 1952, when Harry Markowitz published ‘Portfolio Construction’,86 that it was recognized in academia that the riskiness of a single financial asset (p. 65) needs to be measured not only by reference to its own risk, but also by reference to the riskiness of the portfolio of assets of which it forms part. Portfolio Construction showed that the riskiness of a portfolio depends on the covariance of its holdings, not on the average riskiness of the independent investments. Whereas previously portfolio theory focused on predicting returns and treated risk as a secondary matter, Markowitz put risk at the heart of investment analysis and emphasized the notion of the portfolio of financial assets as the primary tool for maximizing the trade-off between risk and return.87 Markowitz demonstrated that risk is ultimately a function of the composition of the investment portfolio based on the volatilities of the individual portfolio assets and their correlation with each other, and not just a function of the riskiness of the individual investments. Thanks to Markowitz’s work, almost all investors understand or know these days that a properly diversified portfolio of financial assets reduces overall investment risk.

2.54  The covariance of investment A and investment B is a measure of the correlation of the returns forecast for those two investments. If the returns move in tandem, the covariance will be a positive number. If the returns move out of phase, the covariance will be a negative number.88 Covariance values are calculated by taking the probability-weighted average of the products of the deviations about the mean returns.89 A covariance matrix represents all covariances of all investments in a portfolio. The key point that Markowitz proved was that portfolios of risky investments, based on their covariances, might be put together in such a way that the portfolio would actually be less risky than any one of the individual investments in it.90 In other words, certain risks, though not all, can be eliminated through diversification as part of a properly selected portfolio. Based on that notion, Markowitz’s proposition is that, out of the entire universe of possible portfolios, a certain portfolio will optimally balance risk and reward. That portfolio lies on what Markowitz called an ‘efficient frontier’. It is referred to as the ‘tangent’ portfolio and is the portfolio that has the highest return per unit of risk. The principal concept is that, for any risk level, the investor will only be interested in the asset that gives the highest expected return, in return for the lowest possible level of risk. Inversely, the tangent portfolio on the efficient frontier is the portfolio that (p. 66) minimizes the variance for any target expected return.91 Thus, investors can and will avoid certain risks that can be diversified away if that investment is part of a properly selected portfolio, because they will not be, and ought not to be, compensated for diversifiable risks, only for non-diversifiable risks. Empirical studies have shown that Markowitz’s proposition is correct.

2.55  From Markowitz’s proposition follows that the optimized portfolio of risky assets, for any investor, is always the correct asset mix. Nobel laureate James Tobin showed that, in such a world, all investors should hold the same portfolio of risky assets, regardless of each investor’s risk aversion and investment objective.92 The riskiness of the portfolio should be adjusted to the investor’s investment objective, that is, the investor’s individual risk–return trade-off, by leveraging or de-leveraging the risk-optimized portfolio of risky assets with positions in risk-free assets so as to achieve a desired level of overall risk. In other words, once the risk-optimized portfolio has been identified, the only way to decrease or increase non-diversifiable risk efficiently, that is without decreasing or increasing diversifiable risk, is to leverage the portfolio by borrowing at the risk-free rate to increase the size of the portfolio without changing its composition. This concept came to be known as ‘Tobin’s theory of separation’. In practice, it means that once an asset manager who specializes in an asset class has determined what the optimized portfolio is for that class of assets, that portfolio ought to be offered to all clients, regardless of risk aversion, so that the investment manager can serve a number of clients with relatively low incremental costs. The individual client’s risk appetite can be reflected in the mix of that portfolio with risk-free assets, or in the leverage ratio.93

2.  Short selling increases investment opportunities

2.56  Investors have the possibility, subject to applicable legal and regulatory limitations, to sell securities short, that is, to sell a security that they do not own, but that they borrow from an investor who does, so that the sales transaction is settled by transferring borrowed securities. In practice, the securities loan will typically be documented under a standard market master agreement such as the Global Master Repurchase Agreement or the Global Master Securities Lending Agreement. In both cases, the investor will have to provide collateral to the value of the securities loan, on a mark-to-market basis, plus a margin. What remains after completion of the transaction is a cash position, the proceeds from the sale, a securities loan, and a collateral requirement. Usually, the cash proceeds are used to satisfy the collateral requirement, but if the portfolio consists of cash-equivalent assets, these might be used as well. In some circumstances the provider of the securities loan may accept other collateral which is not as liquid and therefore riskier.

(p. 67) 2.57  Regardless of the modus operandi, the possibility of short selling creates a new set of investment opportunities. In theory, the number of possible investments doubles as each security can be held long or short. It offers the potential for more efficient use of information, in particular downside information. A short position realizes a positive return if the price of the security in question decreases enough for the difference between the price for which it was sold and the price for which it can bought (to discharge the securities loan) exceeds the cost of covering the short position, that is, the borrowing cost, which includes the fee for the securities loan as well as the cost of maintaining collateral. Short positions can operate as a hedge to long positions and reduce market risk considerably. Obviously, the risk of a short position can also increase market risk, theoretically to infinite levels, as the short seller is exposed if the price of a stock rises. Therefore, the effect of the ability to sell short is that Markowitz’s efficient frontier, that is, the line along which a risk-optimized portfolio can be constructed, moves up in the risk–return plane.94

2.58  The rationale offered to explain the benefits of long/short investment relative to long-only investment, is the enhanced efficiency that results, at least in theory, from loosening the long-only constraint. The direct effect of the long-only constraint is to prevent the exploitation of negative ‘alphas’.95 The indirect effect of the constraint is to prevent full investment. Short investing permits extension of underweighting relative to the benchmark. A particular aspect of long/short investment strategies is that the possibility exists to create a ‘market-neutral’ portfolio by cancelling out non-diversifiable risks, or ‘betas’,96 in long positions through the short selling of securities with an equal beta. A market-neutral portfolio has a beta of zero and equal long and short positions. Long/short market-neutral strategies, thus, are ‘pure’ active strategies. In theory, there is only exposure to idiosyncratic, that is, active, risks.97

D.  Optimizing Risk and Return Relationships

1.  Returns that relate to systematic risk factors (beta)

2.59  Markowitz’s notion of portfolio construction has been developed into theories that allow for the modelling of the risk–return ratios of an individual investment (p. 68) in the context of a certain market. These models are commonly referred to as ‘asset pricing models’, after the original model, the ‘Capital Asset Pricing Model’ (CAPM), which was developed by Nobel laureate William Sharpe, based on Markowitz’s theory.98 Sharpe sought to identify the factors that cause the variability of a particular security’s return and reasoned that, although a security’s return variability has many causes, it is mostly dependent on one factor in particular, the movement in the market itself. Sharpe called the security’s variability due to the general market movement ‘systematic risk’, and the balance due to idiosyncratic factors, ‘unsystematic risk’.99 CAPM takes Markowitz’s notion that certain risks of an asset can be diversified through portfolio construction a step further by identifying the non-diversifiable risk as risk due to a single exogenous factor, that is the market. Thus, the appropriate risk premium on an asset ought to be determined by that risk, the systematic risk, but not other risks. Systematic risk can only be avoided by holding risk-free assets.

2.60  Armed with these theoretical notions, CAPM seeks to describe how market prices, and therefore risk premiums relative to a security’s systematic risk, are formed. As a model, it necessarily needs to make certain assumptions to create a proxy for reality that may be mathematically manipulated. Accordingly, the model assumes that the investment universe consists of publicly traded risky financial assets and risk-free borrowing and lending arrangements only,100 that there is no market friction or price manipulation,101 that all investors hold for an identical period, that all investors are mean-variance optimizers as described by Markowitz’s model, and that all investors hold similar economic views so that all return forecasts and risk quantifications, that is the ‘input lists’ for the Markowitz model, are identical.102

2.61  Given the assumptions under CAPM, all investors will arrive at an identical portfolio of risky assets, because that is the risk-optimized portfolio, that is, the tangent portfolio on Markowitz’s efficient frontier. If all investors use the Markowitz model, applied to the same universe of financial assets, and use the same economic assumptions to arrive at return forecasts and risk quantifications, they must all (p. 69) arrive at the same determination of the optimally risky portfolio.103 The only difference between individual portfolios is the size. CAPM implies that, as the composition of each of the investors’ risk-optimized portfolios will be identical, the composition of the portfolio that results if all investor portfolios are aggregated, which under CAPM necessarily cancels out all lending and borrowing, must be identical to the composition of each individual portfolio. In CAPM terms, the aggregate of all investor portfolios is referred to as the ‘market portfolio’.

2.62  If the market portfolio represents the risk-optimized portfolio, then the risk–return ratio of the market portfolio represents the equilibrium risk–return ratio because it must be assumed that the operating principle of equilibrium in relation to the risk premium is that all assets should offer the same reward-to-risk ratio. If the ratio were better for one investment than for another, investors would rearrange their portfolio to increase the proportion of the alternative investment with the better trade-off. That activity would result in pressure on the prices of the securities involved, until the risk–return ratios are equalized.104 Accordingly, on the assumptions of CAPM, that is, that all investors hold for an identical period, are mean-variance optimizers as described by Markowitz’s model, and hold similar economic views so that all return forecasts and risk quantifications are identical, the risk–return ratio of individual investments and the risk–return ratio of the market portfolio should be equal.

2.63  Once it is known what the equilibrium risk–return ratio is, the risk premium for individual securities in the market portfolio can be discovered. It must be a function of the excess return on the market portfolio, that is, the expected return minus the risk-free rate, and the proportion of systematic risk that is contributed by the security in question to the market portfolio, because the systematic risk is the non-diversifiable part of the risk contributed to the overall portfolio, that is the part for which the investor is compensated by way of the risk premium.105 If the compensation for the variance of the market portfolio is known, the compensation for a proportionate part of the variance can be derived. A security’s risk–contribution ratio, that is its contribution to the variance of the market portfolio as a fraction of the total variance of the market portfolio, is referred to as the ‘beta coefficient’, or simply ‘beta’ (β‎). It is a function of the covariance between the single security and the market portfolio, divided by the variance of the market portfolio. The beta value of a security denotes both the contribution of the variance of that security to the market portfolio, as well as the sensitivity of the return of that security to movements in the market. It also permits the comparison of that security’s indigenous systematic risk with the indigenous systematic risk of another security in the market portfolio.

(p. 70) 2.64  Once a security’s beta has been established, the ‘fair’ risk premium can be calculated by multiplying the difference between the market portfolio’s expected return minus the risk-free rate by the security’s beta.106 If the beta is less than 1.0, which means that the security is less sensitive to systematic risk in the market portfolio, the risk premium is lower than the equilibrium premium and vice versa.107 CAPM thus produces a formula: E(Rp) = Rf + β‎[E(Rm)–Rf], in which E(Rp) is the mean return of the portfolio or single security, Rf is the risk-free rate, E(Rm) is the mean return of the market, and β‎ is the estimated beta of the portfolio or single security. In other words, CAPM proposes that the equilibrium expected return of an asset should be equal to the risk-free rate plus a risk premium that is proportionate to the covariance of the asset return with the return on the market portfolio.

2.65  A practical hurdle that hinders the full implementation of CAPM is that the market portfolio cannot be identified with any precision. A correctly identified market portfolio, in the real world, must include the full complement of risky assets, including private equity.108 In practice, therefore, broad financial indices such as the FTSE All Share Index serve as a proxy for the market portfolio. A financial market index is an index of a nominal portfolio of securities that is representative of a certain market or a portion of it. If the index is broad enough, a security’s beta can be determined by reference to that index as a proxy for the market portfolio, because a well-diversified portfolio will be so highly correlated with the market portfolio that a security’s beta relative to the market proxy will still be a useful measure.109 Equity market indices are typically composed of constituents that are selected by reference to the issuer’s geographic locations and market capitalization on a weighted basis. Betas, therefore, are estimated based on historical data relative to a certain index or other identified proxy of the market portfolio. Different methodologies are used. There are a number of professional data vendors that calculate security betas and other risk metrics relative to a particular index or composition of indices.110

2.66  CAPM cannot be proven to hold true. One obvious reason is that the model is based on theoretical assumptions that cannot be tested in practice. In particular, it can be argued that the market proxy is imperfect and therefore, that the measurement of beta is necessarily imperfect. Further, empirically, it appears that the actual risk–return relationship is flatter than predicted by CAPM, implying that low beta securities earn a higher return than predicted and high beta securities a lower return, while the discrepancy increases if measured over short investment (p. 71) periods.111 In addition, betas are estimated from historical data, which makes the values mere estimates. Past betas naturally are not necessarily useful predictors for future betas.112 Overall, however, CAPM has proven to provide a powerful insight in how to manage and optimize the risk–return relationship for a portfolio of investments. Ang writes:113

I state upfront that the CAPM is well known to be a spectacular failure. It predicts that asset premiums depend only on the assets beta and that there is only one factor that matters, the market portfolio. Both of these predictions have been demolished in thousands of empirical studies. But, the failure has been glorious, opening new vistas of understanding for asset owners who must hunt for risk premiums and manage risk. The basis intuition of CAPM still holds true: that the factors underlying the assets determine asset risk premiums and that these risk premiums are compensation for investors’ losses during bad times. Risk is a property not of an asset in isolation but how the assets move in relation to each other.

In particular, CAPM has been proved useful as a consensus procedure for calculating expected returns, resulting in a standard of comparison.114

2.67  Following Markowitz’s revelations, standard CAPM has been further developed and modified by relaxing one or more of the assumptions that underlie standard CAPM, while still subscribing to its basic notion that investors are mean-variance optimizers. CAPM now has a place among several factor models used in the investment management industry. One line of development took CAPM, which expresses the return on a security or portfolio as a linear function of a single common factor, the market portfolio, and expanded it into a multi-factor model, which measures the betas of factors in addition to the correlation to the market factor.115 Another line development has moved away from CAPM altogether. One particularly influential model is the ‘arbitrage pricing theory’ (APT).116 APT postulates a multiple-factor model of excess returns. It is also based on the Markowitz notion that uncertainty in expected return, which is ‘risk’, has two sources: common macro-economic factors (systematic risks), and firm- specific events (non-systematic risks), and that idiosyncratic risk can be eliminated through diversification, so that investors will ‘arbitrage away’ any expected return (p. 72) difference in relation to assets that have the same risk profile. Unlike CAPM, the APT does not identify the precise factors or describe the relationship between the systematic and idiosyncratic risk factors. That is left to the judgement of the user of the model.117 Further, CAPM assumes that in the event of price differentiation between securities with the same risk properties, that is, if the equilibrium price is violated, many investors will make small amendments to their market portfolio. In aggregate, the small variations will create trading volumes that will lead to price adjustment. APT, on the other hand, assumes that if an arbitrage opportunity exists, rational investors will want to take as large a position as possible to maximize profit, so that a small number of investors can move the market. Therefore, APT and CAPM have different implications for price forming.118

2.  Informational efficiency of the markets

2.68  Pricing models return forecasts, covariance calculations, etc, are all consistent only if the markets produce fair prices, that is, prices that incorporate all information available at the time the price is formed. The price forming must respond only to new information, which, by definition, is unpredictable information. If it could be predicted, then the prediction is part of today’s information. Accordingly, price forming in response to incorporation of unpredictable information must also be unpredictable, that is, random. Portfolio theory is founded on the notion that well-functioning, informationally ‘efficient’ markets produce random returns, that is, prices follow a ‘random walk’. Randomly evolving prices are the necessary consequence of intelligent investors competing to discover relevant information on which to buy or sell securities. This is called the ‘efficient market hypothesis’ (EMH).119

2.69  The EMH was developed between 1965 and 1970, during which many empirical studies were performed on stock price behaviour and investment manager performance, resulting in a landmark paper by Eugene Fama.120 EMH recognizes three different aspects to informational efficiency, depending on the information set that is the reference point. At the basic level, called ‘weak-form’ efficiency, the information set is historic data about prices and trading volumes of the security in question. Empirical evidence suggests that, in markets in respect of which historical data is freely available, the next move in a price is largely unpredictable based on past performance, with one exception. There is a long-run uptrend in most averages of stock prices in line with the long-run growth of earnings and dividends. In other words, the financial markets are largely weak-form efficient. This (p. 73) implies that ‘technical analysis’, that is, the study of historical data with a view to predicting future performance of a security, is mostly a futile exercise.121 Therefore, studying past prices to identify profitable trading strategies will be futile.

2.70  At the next level, called ‘semi-strong’ efficiency, the information set, in addition to historic data, contains all publicly available information. Studies of semi-strong efficiency observe price movements following the publication of new information, such as stock splits or earnings announcements. If a market is semi-strong efficient, ‘fundamental analysis’, which uses both historic and forward data in an attempt to determine the present discounted value of the expected returns of a security, like technical analysis, is futile, unless the investment manager has a unique insight.122 Empirical evidence suggests that the markets mostly incorporate new information so rapidly, that, on average, it is not possible to devise trading strategies that permit capitalization on insights gained through fundamental analysis.123 On occasion, however, analysts will uncover violations of semi-strong efficiency principles.124 Such violations are not permanent, since the markets will incorporate the technique at some point. That raises the question whether these trading opportunities concern a violation of the semi-strong efficiency principle, or whether it is information based on a unique insight that is not publicly available.

2.71  In the strongest form of EMH, the information set, in addition to historic data and all publicly available information, contains non-public information available only to issuer-insiders. Empirical evidence supports the notion that insiders can earn excess returns based on non-public information, which in many cases will constitute market abuse. Fama, therefore, concluded that the question is not whether the markets are strong-form efficient. Clearly, they are not. The question is whether there was any evidence of some strong-form efficiency:125

Since we already have enough evidence to determine that the model is not strictly valid, we can now turn to other interesting questions. Specifically, how far down through the investment community do deviations from the model permeate? Does it pay for the average investor (or the average economist) to expend resources (p. 74) searching out little known information? Are such activities even generally profitable for various groups of market ‘professionals’? More generally, who are the people in the investment community that have access to ‘special information’?

2.72  Although the evidence on insider trading demonstrates that the very strongest form of EMH does not hold true, there is considerable evidence that the markets come reasonably close to strong-form efficiency.126 Ang describes the work on the efficient market hypothesis published by Nobel prize winner Joseph Stiglitz and Sanford Grossman in 1980:127

Grossman and Stiglitz developed a model in which markets are near-efficient. Active managers seek for pockets of inefficiency, and in doing so cause the markets to be efficient. In these pockets of inefficiency, active managers earn excess returns as a reward for gathering and acting on costly information.

3.  Returns that are not related to market factors (alpha)

2.73  EMH implies that competition among investors ensures that all publicly available information, including any insights derived from security analysis, is already reflected in the market price. Markowitz’s portfolio theory implies that in an efficient market there will be no reward for residual risk, that is, risk that can be diversified away. The ultimate consequence of these propositions is that it should not be possible to construct a portfolio that delivers a return that exceeds the return associated with systematic risk, except where the investor would act based on material price-sensitive information that is not publicly available. Thus, each investor should select a market portfolio and leverage or de-leverage that portfolio in accordance with Tobin’s theory of separation to reflect risk appetite.128 In practice, however, the market efficiency and equilibrium propositions cannot be proved to hold true in all circumstances.129 That means that active management should be able to add excess return that is not correlated to the market, that is, which is not derived from systematic risk-taking but from manager skill, without increasing the risk in the portfolio disproportionally. The notions of market efficiency, equilibrium risk–return ratios, and the separation of systematic and idiosyncratic risks can assist the active manager in developing investment strategies that include effective risk-and-return modelling and that avoid unproductive investment philosophies that cannot pass scrutiny in a market with a modicum of efficiency.

2.74  There is economic logic and some empirical evidence that exceptional portfolio managers can beat the average forecasts incorporated in market prices, although (p. 75) there appears to be no evidence that they can do so consistently. Economic logic dictates that, without active management, prices will no longer be formed based on information competition, which should result in informational inefficiencies that can be exploited, arbitraged in APT terms, luring active managers back to the market. Empirical evidence shows that some anomalies exist that are statistically relevant, although perhaps as of yet unexplained.130 There is an argument that there may be at least three statistically relevant residual risk factors common to certain categories of excess return. These are the extra risk of equity securities versus fixed-income securities (the market factor), the extra risk of small-cap stocks over large-cap stocks (the size factor), and the extra risk of value stocks over growth stocks (the value factor).131 These arguments suggest that active management is about the constant search for above-market return through the exploitation of market inefficiencies, which, paradoxically, is the very reason for market efficiency.132

2.75  To determine whether there is a possibility for exceptional returns in excess of the return correlated to systematic risk, it is necessary to determine whether total expected return forecast by the active manager exceeds the fair return expected for taking systematic risk, so as to extract a return that can be attributed to the portfolio’s beta and a return that can be attributed to other factors. Here, CAPM can assist the active manager, as it provides a model to determine the fair, or consensus, return that might be expected for taking systematic risk. If a security’s beta allows for the calculation of a consensus expected return, a security that is underpriced or a good buy should provide an expected return in excess of the fair return, or vice versa. The ideas behind CAPM help the active manager to focus research on returns from residual risks that have a consensus expectation return under CAPM of zero.133 The difference between the fair, or equilibrium, expected return and the actual expected return is called a security’s alpha (α‎). Looking forward, (p. 76) alpha is a forecast of residual returns. Looking backward, alpha is the average of the realized residual returns over a certain period.134 A positive backward-looking alpha, therefore, is the extra return awarded to the investor for taking active risk, instead of accepting the market return.135 Forward-looking alpha is also referred to as ex ante alpha; backward-looking alpha as ex post alpha.

2.76  Alpha was first defined and measured by Michael Jensen in 1968. He was investigating the principles of the emerging EMH and sought to determine whether historical returns indicated that certain investment managers were able to deliver returns in excess of the market return. CAPM permitted Jensen to separate beta-related returns from extra, or excess, returns. Jensen was interested in whether active managers could consistently add value over a longer period through skill, privileged information, or intuition. Jensen adjusted the CAPM formula to reflect the possibility of alpha. Recall that CAPM describes the risk–return relationship as follows: E(Rp) = Rf + β‎[E(Rm)–Rf].136 Jensen sought to define alpha as the difference between the fair expected return based on the beta relationship and the real return, thus describing the relationship as follows: E(Rp) = α‎ + Rf + β‎[E(Rm)–Rf]. Jensen’s alpha component in the return, therefore, is the difference between the fair return that may be expected based on the portfolio’s beta,137 and the forecast expected return. Jensen then looked for alpha on an ex post basis. Based on empirical evidence, he observed:138

An examination [of the data] … reveals only 3 funds which have performance measures which are significantly positive at the 5% level. But before concluding that these funds are superior we should remember that even if all 115 of these funds had a true α‎ equal to zero, we would expect (merely because of random chance) to find 5% of them or about 5 or 6 funds … at the 5% level.

2.77  Jensen thus found that no investment manager was able, on balance, consistently to produce statistically relevant positive alpha. Thus, although CAPM and EMH cannot be proved to hold true absolutely,139 it is a fact that the average investment managers will not be able to outperform a passive strategy consistently, if performance is measured on a risk-adjusted basis.140 Ang points out that alpha, as a the (p. 77) average return in excess of a benchmark, ‘tells us more about the set of factors used to construct the benchmark than about the skill involved in beating it’,141 and therefore, that measuring true alpha is perhaps impossible, because it presents a joint hypothesis problem similar to testing for market efficiency.142 Notwithstanding, since Grossman and Stiglitz,143 the market recognizes that perfectly efficient markets cannot exist and so the quest for alpha endures. There is a perception that if a manager uses superior information skilfully, it is possible to identify positive alphas that can be exploited by market-timing strategies or security-selection strategies based on a fundamental analysis. Market timing, in its purest form, is an asset allocation strategy. It relies on shifting allocation levels between a proxy market portfolio, that is, an index portfolio, and a risk-free asset. Security-selection strategies rely on selecting securities that will deliver superior or inferior returns, that is determining whether a security has a positive or negative alpha.

4.  Measuring alpha

2.78  As demonstrated by Markowitz, absolute returns can be increased simply by increasing the systematic risk of the portfolio. That has little to do with an investment manager’s ability to predict the market or select securities based on a fundamental analysis. The question, therefore, is how to measure that risk-adjusted excess return, that is, how to separate alpha from beta. To aid that quest, portfolio theory has developed risk-adjusted portfolio performance measures. A commonly used measure is the Sharpe ratio, devised by Nobel laureate William Sharpe. Sharpe’s measure divides the average risk premium over the sample period (ie the portfolio return in excess of the risk-free rate) by the standard deviation of returns over that period, thus measuring the reward-to-volatility trade-off. It measures the excess return per unit of volatility. A Sharpe ratio of 0.80 implies that an increase of 1 per cent volatility correlates to a return reward of 0.80 per cent. Treynor’s measure, like Sharpe’s, gives excess return per unit of risk, but it uses beta, that is, the systematic risk component, rather than total risk. Sharpe’s measure compares alpha and volatility. Treynor’s measure compares alpha and beta.144

2.79  The dominant measure that is used to assess active returns, however, is the ‘information ratio’.145 This seeks to capture and quantify a manager’s success in (p. 78) identifying and realizing alpha. Ex ante, the information ratio quantifies opportunity, ex post it quantifies achievement.146 The information ratio is the ratio of the annualized residual return to the annualized residual risk, that is, is calculated by dividing the alpha of the portfolio by the non-systematic risk of the portfolio. It measures abnormal return per unit of diversifiable risk,147 which, on the propositions of Markowitz, could be diversified away by holding the market index portfolio and therefore, in theory, should not be rewarded with any returns at all. Higher return metrics relative to the risk metrics give a higher information ratio. The higher the information ratio, the more value the active manager is perceived to be adding. In other words, the information ratio measures the manager’s opportunities. If the manager exploits those opportunities in a way that is mean/variance-efficient, then the value added by the manager will be proportional to the information ratio squared. As a rule of thumb, the information ratio can be approximated as a function of the breadth of the manager’s investment strategy, that is, the number of independent investment decisions aimed at exploiting identified opportunities made during a certain investment period, and the skill applied. The skill is represented by the manager’s information coefficient, that is, the correlation of the forecast underlying each investment decision with the realized outcome. This rule is called the ‘fundamental law of active management’. It implies that more breadth is better if one can maintain the skill level, which is consistent with the rule that breadth, at the same skill level, lets the manager diversify the residual risk.148

2.80  Measuring risk-adjusted excess return, that is, separating alpha from beta, relies on identifying beta first, and then calculating alpha as a function of the excess return over that which is attributed to the portfolio’s beta coefficient. Accordingly, alpha as a concept only has meaning relative to a beta: alpha represents the return from uncorrelated, idiosyncratic risk factors, but it can only be calculated by separating it from the beta-related return of the investment universe of the portfolio for which the return is being measured. The alpha value extracted from a return stream, therefore, is a useful metric only if the chosen beta factor is meaningful in relation to the portfolio that produces the return. Beta, as an exogenous risk factor of a portfolio, is less useful if the portfolio moves away from broad-index portfolios, for example because it holds mixed, uncorrelated exposures, or because (p. 79) it includes options that alter the risk outlook of that portfolio.149 Beta can be estimated using a factor model. Factor models are relative. The value is derived by reference to the values of exogenous assets, the factor, in casu the market portfolio.150 If the benchmark portfolio is not a good proxy for the systemic-risk characteristics of the investment universe, the risk metrics are of little value. In summary, in order to separate it, alpha must be calculated relative to an appropriate benchmark portfolio. It follows that the concept of alpha does not make much sense in the context of an absolute-return strategy, which implies that a certain risk-free rate of return is taken as the performance benchmark. For instance, the performance of hedge fund strategies is often measured relative to a benchmark market cash rate as a proxy for a risk-free rate.151 There are practical reasons for doing this, as it will often be challenging to identify an appropriate benchmark where the investment universe is broad and diversified, and leverage is applied. However, that also means that it will be very difficult to assess what systematic risks are embedded in the hedge fund strategy and therefore, to what extent the manager is adding excess returns.152

2.81  Institutional investors, in particular defined benefit pension schemes, seek to distinguish between alpha and beta performance in an attempt to improve the management of the risk–return relationships in the overall portfolio, using alpha and beta as the building blocks. As a result, these investors select investment managers based on their ability either to generate alpha consistently or to provide cheap sources of beta. The investment management industry has responded by offering increasingly complex strategies, seeking to deliver alpha from a multiple of conceivably uncorrelated asset classes, including real assets, such as commodities and real property. For investment managers, that dynamic not only has product-development implications, but also pricing ramifications, as investors are likely to pay less for returns that are considered to be attributable to a portfolio’s beta. Given the fact that analysis of performance data over longer time intervals will improve the attribution ratio,153 the distinction between alpha and beta performance will continue to become more transparent with the passage of time.

(p. 80) 5.  Relative risk: tracking error

2.82  Volatility measures risk as a function of the variability of returns.154 VaR measures downside risk as a function of a probability that a certain loss, or worse, will occur.155 Both volatility and VaR, however, measure total risk, that is, the aggregate of systematic risks and non-systematic risks. To measure active (non-systematic) risk separately, it must be measured as a function of a portfolio’s alpha relative to its market beta estimates. This value is referred to as the ‘tracking error’ of a portfolio. The concept of tracking error connotes a quantification of the degree to which the performance of a portfolio differs, ex ante or ex post, from that of a certain benchmark portfolio, that is, the proxy for the diversified market portfolio. The benchmark portfolio is typically a published financial index. A low tracking error implies a high correlation between the risk and return characteristics of the portfolio, and the risk and return characteristics of the benchmark, or market, portfolio. Several definitions of tracking error are used in practice. In the most straightforward approach, it simply is the difference between the return of the portfolio and the return of the benchmark portfolio, in which case the tracking error is synonymous with the outperformance or underperformance of the portfolio as measured against the benchmark over a certain time interval. The more common definition of tracking error, however, is volatility-oriented and defines ‘tracking error’ as the standard deviation of the excess return of the portfolio relative to the benchmark return, that is, it expresses the variability of the excess portfolio return.156 This is also referred to as the ‘active risk’ of a portfolio.157 In other words, tracking-error calculations seek to measure the dispersion, or volatility, of the alpha component of a return stream.158 It connotes the variability of the excess returns over the beta returns. A high tracking error, whether measured ex ante or ex post, implies a material deviation from the benchmark return. Conversely, a low tracking error indicates a return close to that of the chosen beta benchmark. Index tracking, also known as ‘passive investment’, is based on constructing a portfolio that produces a tracking error versus the chosen benchmark portfolio that is as close to nil as possible.159

(p. 81) 2.83  Ex ante tracking-error metrics are used as risk-budgeting tools. A mandate may prescribe that a manager must use all reasonable efforts to manage a portfolio in such a manner that the ex ante tracking error of the portfolio does not exceed a certain value. In that case, the investor and the manager must ensure that they agree on the methodology that will be used to calculate that ex ante tracking error, for example by using the model offered by a professional services provider such as BARRA. As tracking-error calculations are based on separating alpha and beta, tracking-error parameters can only be an effective ex post measure or ex ante control of risk if a benchmark portfolio is used that reflects the primary risk characteristics of the investment strategy that is the subject of the risk measurement. If the manager’s investment universe is not limited to either the securities in the benchmark or securities with similar risk characteristics to those in the benchmark, the potential exists for a significant risk variation.160 Just as an appropriate benchmark is needed to calculate the alpha of a portfolio,161 tracking-error calculations cannot be meaningful if the systematic-risk characteristics of the measured portfolio do not correlate with those of the benchmark portfolio. Accordingly, to represent a good proxy for measuring the active risk implied in a portfolio as well as for measuring the information ratio, that is, the active skill of the manager, the benchmark portfolio should be representative of the manager’s opportunity set and should also exhibit systematic-risk characteristics that are similar to the risk characteristics of the measured portfolio. If the mandate permits investment in mixed or alternative asset classes,162 it might be difficult to identify a proper benchmark portfolio. If the manager experiences style drift, it might be impossible to measure the risk characteristics properly because that would require a revolving benchmark portfolio.(p. 82)


1  Zvie Bodie, Alex Kane, and Alan Marcus, Investments and Portfolio Management (9th edn, McGraw-Hill Higher Education 2011) 30.

2  cf, Iain G MacNeil, An Introduction to the Law on Financial Investment (Hart Publishing 2012) 3–25 (observing that three approaches can be taken in giving meaning to the term ‘investment’: an economic approach, defining ‘investment’ by distinguishing between real assets and financial assets; a legal approach, defining ‘investment’ by reference to the various sources of proprietary rights, interests, and powers that may be acquired by way of investment; and a process approach, defining ‘investment’ as a process of capital allocation through the market infrastructure).

3  MacNeil (n 2) 33–34.

4  See Isabel Schnabel and Hyun Song Shin, ‘Money and Trust: Lessons from the 1620s for Money in the Digital Age’ (2018) BIS Working Papers 698 <https://ssrn.com/abstract=3119402>, accessed 3 October 2018.

5  Charles Proctor, Mann on the Legal Aspects of Money (6th edn, OUP 2005) paras 1.35–1.36.

6  See on the economic distinction between investing, speculating, and gambling in the Glossary in Chapter 1, para 1.66.

7  In its report ‘Communication from the Commission to the European Parliament, the Council, the European Central Bank, the European Economic and Social Committee and the Committee of the Regions—FinTech Action Plan: For a more competitive and innovative European financial sector’ (Communication) COM (2018) 109 final, 13, the European Commission observes that

[s]peculative investments in crypto-assets and ICO-tokens expose investors to significant market risk, fraud and to cybersecurity risks arising from exchanges and service providers that allow investors to purchase crypto assets and tokens, hold them or trade them. In November 2017, the European Supervisory Markets Authority (ESMA) issued two statements to inform investors of potential risks posed by certain ICOs and to remind firms involved in ICOs that these activities may fall under existing EU legislation, depending on their precise structure and characteristics. Authorities in the EU and across the world are evaluating ICOs and regulation that may be applicable to them, while China and South Korea have banned them.

8  See Colin Bamford, Principles of International Financial Law (2nd edn, OUP 2015) 2.21–2.22. Bamford raises several questions: is it property under English law, noting that it is neither a chose in action nor a chose in possession; if not, is it capable of being stolen; is it capable of being held on trust; and is it a negotiable unit of exchange?

9  Balance-sheet funding through a structured note programme can be advantageous compared to a traditional programme, see Richard Bateson, Financial Derivative Investments—An Introduction to Structured Products (Imperial College Press 2011) 16–17.

10  See Andreas Bluemke, How to Invest in Structured Products—A Guide for Investors and Asset Managers (Wiley 2009) 7. A similar investment possibility may be offered by different legal constructions such as structured collective investment schemes, structured bank deposits, or a specialized insurance contract, see Bateson (n 9) 16.

11  See Bateson (n 9) 6.

12  See Bluemke (n 10) 34–35.

13  Bluemke (n 10) 43–45.

14  Bluemke (n 10) 53–54.

15  The prevailing benchmark cash rates have been the London Interbank Rates (LIBOR). LIBOR comprises an average of interest rates in relation to a certain currency and borrowing period (a ‘tenor’) that each of the leading banks in London estimates that it would be charged were it to borrow that currency from other banks. LIBOR was administered and published by the British Bankers Association (BBA). Following revelations in 2012 of significant fraud and collusion by member banks in connection with their LIBOR submissions to the BBA, the administration and publication of benchmark rates has been designated as a regulated activity, subject to authorization by the Financial Conduct Authority (FCA). Knowingly or deliberately making false or misleading statements in relation to benchmark-setting was made a criminal offence under the Financial Services Act 2012. The European Commission has published a ‘Proposal for Regulation on indices used as benchmarks in financial instruments and financial contracts’, COM (2013) 641 final, 2013/0314 (COD). Other jurisdictions have also made new rules. As a result, the services market for benchmark setting has been changing. The administration of LIBOR was reformed in 2014 and it is now published by ICE Benchmark Administration.

16  See Bateson (n 9) 28–29.

17  The intermediating vehicle’s portfolio may of course include secondary financial assets offered by third party intermediating vehicles.

18  cf s 235 of the Financial Services and Markets Act 2000.

19  See Recital (1) of Regulation (EU) 2017/2402 of the European Parliament and of the Council of 12 December 2017 laying down a general framework for securitization and creating a specific framework for simple, transparent and standardized securitization, and amending Directives 2009/65/EC, 2009/138/EC and 2011/61/EU and Regulations (EC) 1060/2009 and (EU) 648/2012, [2017] OJ L347/35 (Securitization Regulation):

Securitization involves transactions that enable a lender or a creditor – typically a credit institution or a corporation – to refinance a set of loans, exposures or receivables, such as residential loans, auto loans or leases, consumer loans, credit cards or trade receivables, by transforming them into tradable securities. The lender pools and repackages a portfolio of its loans and organizes them into different risk categories for different investors, thus giving investors access to investments in loans and other exposures to which they normally would not have direct access. Returns to investors are generated from the cash flows of the underlying loans.

20  Securitization schemes structure the securitized portfolios in different ways. Under the most common structure, which achieves the removal of the assets from the originator’s balance sheet, the assets are transferred to a vehicle that has been specially created for securitizing a portfolio of assets. See on the common elements of asset-backed schemes, Joanna Benjamin, Financial Law (OUP 2007) paras 18.10–18.23. The Securitization Regulation sets out certain expectations around ‘true sales’ of the assets to the securitization vehicle in the context of ‘simple, transparent and standardised’ securitizations: see arts 18ff of the Securitization Regulation.

21  See Recital (8) and art 8 of the Securitization Regulation.

22  See Patricia Jackson, ‘Introduction: Understanding Risk Culture and What To Do About It’ in Patricia Jackson (ed), Risk Culture and Effective Risk Governance (Risk Books 2014) 6 (noting that HSBC provided US$35 billion in funding to bail out its SIVs).

23  See generally, on the way the collapse of the housing market undermined financial stability, notwithstanding the protection offered by financial engineering, market norms, and financial regulation, Steven L Schwarcz, ‘Protecting Financial Markets: Lessons from the Subprime Mortgage Meltdown’ (2008) 93 Minnesota Law Review 2.

24  See for an unusually crisp and to-the-point analysis of the function of derivative contracts: Christopher Culp and James Overdahl, ‘An Overview of Derivatives—Their Mechanics, Participants, Scope of Activity, and Benefits’ in Clifford Krisch (ed), The Financial Services Revolution—Understanding the Changing Roles of Banks, Mutual Funds, and Insurance Companies (McGraw-Hill 1997) 120–37.

25  Culp and Overdahl (n 24) 120.

26  See European Commission, ‘Shadow Banking—Addressing New Sources of Risk in the Financial Sector’ (Communication from the Commission to the Council and the European Parliament) COM (2013) 614 final, 9–10.

27  Regulation (EU) 2015/2365 of the European Parliament and of the Council of 25 November 2015 on transparency of securities financing transactions and of reuse and amending Regulation (EU) 648/2012, the ‘Securities Financing Regulation’.

28  See the definition of ‘margin lending transaction’ in art 3(10) of the Securities Financing Regulation: ‘a transaction in which a counterparty extends credit in connection with the purchase, sale, carrying or trading of securities, but not including other loans that are secured by collateral in the form of securities’.

29  See the definition of ‘repurchase transaction’ in art 3(9) of the Securities Financing Regulation: ‘a transaction governed by an agreement by which a counterparty transfers securities, commodities, or guaranteed rights relating to title to securities or commodities where that guarantee is issued by a recognised exchange which holds the rights to the securities or commodities and the agreement does not allow a counterparty to transfer or pledge a particular security or commodity to more than one counterparty at a time, subject to a commitment to repurchase them, or substituted securities or commodities of the same description at a specified price on a future date specified, or to be specified, by the transferor, being a repurchase agreement for the counterparty selling the securities or commodities and a reverse repurchase agreement for the counterparty buying them’.

30  See the definition of ‘buy-sell back transaction’ or ‘sell-buy back transaction’ in art 3(8) of the Securities Financing Regulation: ‘a transaction by which a counterparty buys or sells securities, commodities, or guaranteed rights relating to title to securities or commodities, agreeing, respectively, to sell or to buy back securities, commodities or such guaranteed rights of the same description at a specified price on a future date, that transaction being a buy-sell back transaction for the counterparty buying the securities, commodities or guaranteed rights, and a sell-buy back transaction for the counterparty selling them, such buy-sell back transaction or sell-buy back transaction not being governed by a repurchase agreement or by a reverse-repurchase agreement within the meaning of [art 3](9)’.

31  See Moorad Choudry, The Global Repo Markets—Instruments and Applications (Wiley 2004) 93 (observing that the buy/sell back variant does not require the more complex IT systems necessary to administer the classic repo and is often found in emerging markets).

32  ‘Liquidity swaps’ are transactions which effect a liquidity transformation between two parties, one ‘long liquidity’ and the other ‘short liquidity’, typically by exchanging cash or high-credit quality, liquid assets such as gilts held by the former with illiquid or less liquid assets, such as asset-backed securities (ABS) held by the latter.

33  See Choudry (n 31) 104–08 (observing that this type of synthetic repo trade has the same goals and produces the same economic result, ie funding of the asset-owning party, as a classic repo transaction).

34  Regulation (EU) 648/2012 of the European Parliament and of the Council of 4 July 2012 on OTC derivatives, central counterparties and trade repositories, known as the ‘European Market Infrastructure Regulation’ (EMIR), see Chapter 3, paras 3.80ff (on EMIR’s role in shaping the EU markets’ infrastructure).

35  See the definition of ‘securities or commodities lending’ or ‘securities or commodities borrowing’ in art 3(7) of the Securities Financing Regulation: ‘a transaction by which a counterparty transfers securities or commodities subject to a commitment that the borrower will return equivalent securities or commodities on a future date or when requested to do so by the transferor, that transaction being considered as securities or commodities lending for the counterparty transferring the securities or commodities and being considered as securities or commodities borrowing for the counterparty to which they are transferred’.

36  The International Securities Lending Association (ISLA) published the Global Master Securities Lending Agreement (GMSLA), which is a document that may be used as a standard master agreement for securities lending transactions in the cross-border market. The International Capital Market Association (ICMA) has developed a standard master agreement for repo transactions in the cross-border market in conjunction with the Securities Industry and Financial Markets Association (SIFMA). The first version of the GMRA was published in 1992 and followed by substantially revised versions in 1995, 2000, and 2011. The International Swap Dealer Association (ISDA) has developed the standard ISDA Master Agreement to document swap transactions.

37  Regulation (EU) 236/2012 of the European Parliament and of the Council of 14 March 2012 on short selling and certain aspects of credit default swaps, the ‘Short Selling Regulation’.

38  See art 5.

39  Lady Windermere’s Fan (1892).

40  Aswath Damodaran, Investment Valuation—Tools and Techniques for Determining the Value of any Asset (3rd edn, Wiley Finance Series 2012) 1.

41  See Burton G Malkiel, A Random Walk Down Wall Street (12th edn, WW Norton and Co 2015) 35. (Burton mentions Oskar Morgenstern (1902–77), who, with mathematician John von Neumann, worked on game theory and its application to economics. Morgenstern believed that investors should post the Latin maxim above their desks.)

42  Damodaran, Investment Valuation (n 40) 1.

43  Malkiel (n 41) 31.

44  Damodaran, Investment Valuation (n 40) 11.

45  Malkiel (n 41) 118–26.

46  Andrew Ang, Asset Management—A Systematic Approach to Factor Investing (OUP 2014) 215–22, identifies as the three most important macro-economic factors: growth (‘[r]isky assets generally perform poorly and are much more volatile during periods of low economic growth’, ibid 215), inflation (‘[d]uring periods of high inflation, all assets tend to do poorly’, ibid 217), and volatility (‘[t]he negative relation between volatility and returns is called the leverage effect. When stock returns drop, the financial leverage of firms increases since debt is approximately constant while the market value of equity has fallen. This makes equities riskier and increases their volatilities’, ibid, 218). Increased volatility means a greater dispersion of returns for a financial asset or a portfolio of financial assets, see paras 2.44 ff (on variance of returns as a measure of risk).

47  See para 2.42 below (on the concept of a risk free financial asset).

48  Don Suskind, ‘The Equity Markets by Don Suskind’ in Sabrina C Callin, Portable Alpha Theory and Practice (Wiley 2008) 142, 141 (observing that the case for equity investment is built on the premise that long-term expected returns are greater from equities than from more conservative investments such as bonds, due to the higher embedded risk premium relative to the risk-free investment).

49  Gary L Gastineau, Andrew R Olma, and Robert G Zielinski, ‘Equity Portfolio Management’ in John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto (eds), Managing Investment Portfolios (3rd edn, Wiley 2007) 409.

50  See Ang (n 46) 256.

51  Bodie et al (n 1) 474.

52  See in general on interest rates, Frank J Fabozzi, ‘The Structure of Interest Rates’ in Frank J Fabozzi (ed), The Handbook of Fixed Income Securities (6th edn, McGraw-Hill Professional 2001) 131–38, and Moorad Choudry, An Introduction to Bond Markets (2nd edn, Wiley 2001) 15–34.

53  Damodaran, Investment Valuation (n 40) 12. See paras 2.59ff below (on systematic risk factors and risk premiums of financial assets).

54  Damodaran, Investment Valuation (n 40) 19.

55  Damodaran, Investment Valuation (n 40) 23–24. The models build on the original work of Fischer Black and Myron Scholes, ‘The Pricing of Options and Corporate Liabilities’ (1973) 81 Journal of Political Economy 637–54.

56  Bodie et al (n 1) 621; Damodaran, Investment Valuation (n 40) 89.

57  Bodie et al (n 1) 626; Damodaran, Investment Valuation (n 40) 100–01.

58  Damodaran, Investment Valuation (n 40) 94 (arbitration requires no investment, involves no risk, and delivers positive returns).

59  Bodie et al (n 1) 627.

60  This section is based in part on Lodewijk van Setten, ‘Risk, Risk Management, and Internal Controls’ in Danny Busch, Guido Ferrarini, and Gerard van Solinge (eds) Governance of Financial Institutions (OUP 2019) paras 9.01ff.

61  Peter L Bernstein, Against the Gods—The Remarkable Story of Risk (Wiley & Sons 1996) 1.

62  Bernstein (n 61) 5–6.

63  Frank H Knight, Risk, Uncertainty and Profit (Hart, Schaffner & Marx 1921) 205, as cited by Bernstein (n 61) 219 and Aswath Damodaran, Strategic Risk Taking—A Framework for Risk Management (Pearson 2008) 5.

64  Knight (n 63) 227, as cited by Bernstein (n 61) 221.

65  John M Keynes, ‘The General Theory’ (1937) LI Quarterly Journal of Economics 209–33, as cited by Bernstein (n 61) 229.

66  Damodaran, Strategic Risk Taking (n 63) 5.

67  Damodaran, Strategic Risk Taking (n 63) citing Glyn A Holton, ‘Defining Risk’ (2004) 60 Financial Analysts Journal 19–25.

68  Damodaran, Strategic Risk Taking (n 63) 10.

69  Damodaran, Investment Valuation (n 40) 58.

70  Malkiel (n 41).

71  Damodaran, Investment Valuation (n 40) 62.

72  Together, the probability numbers add up to 1.0, because that is the complete universe of possible outcomes. For example, if the expected return of the FTSE 100 Index is calculated based on a variety of economic forecasts, and the probability of a ‘boom’ or a ‘recession’ are each assessed as 0.25, the probability of ‘normal growth’ would be 0.5. The expected return would then be calculated by aggregating the forecast return of the FTSE 100 Index in a ‘boom’ multiplied by 0.25, the forecast return in a ‘recession’ multiplies by 0.25, and the forecast return in ‘normal’ circumstances multiplied by 0.5. See also the example provided by Malkiel (n 41) 192.

73  Bodie et al (n 1) 156.

74  Malkiel (n 41) 19.

75  Bodie et al (n 1) 197–98 (observing that ‘the only risk-free asset in real terms would be a perfectly price-indexed bond’ that offers a guaranteed real rate with a ‘maturity that is identical to the investor’s holding period’ but nevertheless that it is ‘common practice to view Treasury bills as “the” risk free asset’), and Damodaran, Investment Valuation (n 40) 154–55 (noting that two basic conditions are the absence of default risk and of reinvestment risk over the intended investment period).

76  Nonetheless, there is no such thing as a risk-free return that is absolute. Of the G20 countries, presumably the twenty wealthiest nations, only two have not defaulted and some have repeatedly.

77  Bodie et al (n 1) 190 (observing that the history of rates of return on various asset classes ‘leave no doubt that risky assets command a risk premium in the market place. This implies that most investors are risk averse’); Jeffrey F Bailey, Thomas M Richards, and David E Tierney, ‘Evaluating Portfolio Performance’ in John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto (eds), Managing Investment Portfolios—A Dynamic Process (3rd edn, Wiley 2007) 767.

78  See Donald L Harnett, Statistical Methods (3rd edn, Addison-Wesley Educational Publishers Inc 1982) 24–26.

79  Harnett (n 78) 28.

80  Bodie et al (n 1) 160–61. John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto, ‘The Portfolio Management Process and the Investment Policy Statement’ in John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto (eds), Managing Investment Portfolios (3rd edn, Wiley 2007) 11.

81  Bodie et al (n 1) 164–65.

82  Harnett (n 78) 35–36.

83  Bodie et al (n 1) 166.

84  See for a helpful exhibition on the use of VaR as a methodology to measure market risk, John-Peter Castagnino, Derivatives—The Key Principles (3rd edn, OUP 2009) paras 12.07–12.17.

85  See, on the concept of VaR in general, Don M Chance, Kenneth Grant, and John Marshland, ‘Risk Management’ in John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto (eds), Managing Investment Portfolios (3rd edn, Wiley 2007) 599–613.

86  Harry M Markowitz, ‘Portfolio Construction’ (1952) 7 Journal of Finance 77–91.

87  PeterP Bernstein, ‘Foreword: Nice Portfolios and the Unknown Future’ in John L Maginn, Donald L Tuttle, Dennis W McLeavey, and Jerald E Pinto (eds), Managing Investment Portfolios (3rd edn, Wiley 2007) xiii–xiv. Bodie et al (n 1) 239–42.

88  Malkiel (n 41) 198–99.

89  For example, if the expected return of the FTSE 100 Index is based on a variety of economic forecasts, and the probability of a ‘boom’, a ‘recession’, or ‘normal growth’ are estimated at 0.25, 0.25, and 0.5, respectively, the covariance between securities A and B would then be calculated by aggregating the products of the deviations of A’s and B’s forecast returns in a ‘boom’ multiplied by 0.25, the product of the deviations of A’s and B’s forecast returns in a ‘recession’ multiplied by 0.25, and the product of the deviations of A’s and B’s forecast returns in ‘normal’ circumstances multiplied by 0.5.

90  Malkiel (n 41) 197.

91  Bodie et al (n 1) 239.

92  James Tobin, ‘Liquidity Preference as Behavior towards Risk’ (1958) 67 The Review of Economic Studies 65–86.

93  Ben Warwick, Searching for Alpha (Wiley 2000) 9–10. Bodie et al (n 1) 242–43.

94  See Edwin Elton and Martin Gruber, ‘The Lessons of Modern Portfolio Theory’ in B Longstreth (ed), Modern Investment Management and the Prudent Man Rule (OUP 1986) 165–66. Bodie et al (n 1) 242.

95  See on the concept of ‘alpha’, paras 2.73ff (discussing uncorrelated risk factors).

96  See on the concept of ‘beta’, paras 2.59ff (discussing systematic risk factors).

97  RC Grinold and RN Kahn, Active Portfolio Management (2nd edn, McGraw-Hill 1999) 419–26, 438–39 (observing that market-neutral ‘long/short strategies offer no way to hide behind a benchmark’).

98  William F Sharpe, ‘Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk’ (1964) 19 Journal of Finance 425–42.

99  Warwick (n 93) 10–13.

100  It further assumes that all borrowing and lending can be done in unlimited amounts at the risk-free rate, and free of credit risk. In other words, CAPM assumes an investor is able to leverage the portfolio of risky assets at the risk-free rate. For a description of the variance of a leveraged portfolio, see Bodie et al (n 1) 200–01 (demonstrating that a leveraged portfolio has a higher standard deviation or variance than an unleveraged portfolio with the same composition of holdings in the same risky assets).

101  That means that there are no transaction costs, that investments can be bought or sold in infinitely small fractions or large quantities, that there is perfect competition, ie no market impact from a trade, and there are no income, capital gain, or transfer tax considerations.

102  See Bodie et al (n 1) 308–11. See Elton and Gruber (n 94) 169–70.

103  Bodie et al (n 1) 310.

104  Malkiel (n 41) 215. Bodie et al (n 1) 315.

105  See paras 2.53ff (on risk in the context of a diversified portfolio).

106  See generally on the concept of ‘beta’ (β‎), Bodie et al (n 1) 315–17.

107  The beta of the market portfolio is 1.0, see Bodie et al (n 1) 316.

108  See Elton and Gruber (n 94) 173–74.

109  Bodie et al (n 1) 315.

110  One of the most widely used vendors is BARRA, a trade name that is based on the founder’s name: Bar Rosenberg and Associates. BARRA was established in 1975.

111  Malkiel (n 41) 219–21.

112  Grinold and Kahn (n 97) 14, observe that historical betas are a reasonable forecast of the betas that will be realized in the future, although it is possible to do better. But also see Kenneth L Fisher, Markets Never Forget (But People Do) (Wiley 2012) 132–133, who notes that “[i]f the past predicted the future, stocks would be unidirectional. They are not. … [L]ong term, actual equity risk premiums by decade have been hugely variable.”

113  Ang (n 46) 197.

114  Grinold and Kahn (n 97) 11.

115  Suskind (n 48) 142 (observing two additional factors as being the difference in return between small-cap and large-cap stocks, and the difference between value and growth stocks).

116  Stephen Ross developed the arbitrage pricing theory in an article published in 1976; see Stephen A Ross, ‘Return, Risk and Arbitrage’ in I Friend and J Bicksler (eds), Risk and Return in Finance (Ballinger 1976).

117  Grinold and Kahn (n 97) 172–73. Bodie et al (n 1) 347–51.

118  Bodie et al (n 1) 351.

119  Bodie et al (n 1) 372.

120  Eugene F Fama, ‘Efficient Capital Markets: A Review of Theory and Empirical Work’ (1970) 25 Journal of Finance 383–417.

121  See on weak-form market efficiency and the implication for technical analysis, in general, Malkiel (n 41) 134–58, and Bodie et al (n 1) 375–76.

122  See Bodie et al (n 1) 375 (forward data includes forecasts of earnings, interest rates, and issuer-specific events).

123  See on semi-strong-form market efficiency and the implication for fundamental analysis, in general, Malkiel (n 41) 159–88.

124  See eg P Charles and RH Litzenberger, ‘Quarterly Earnings Reports and Intermediate Stock Price Trends’ (1970) 25 Journal of Finance 143–48 (demonstrating that the markets respond slowly to unexpectedly good earnings announcements, which permitted the construction of portfolios of securities of issuers that had recently announced unexpectedly good earnings, which portfolios outperformed the overall market in subsequent months). Other violations have been exploited over the years, see, in general, Malkiel (in the earlier 6th edition, 1996, of the work referenced in n 41) 194–209, and Bodie (n 1), 384–401.

125  Fama (n 120) 410.

126  Malkiel (n 41) Chapters 8 and 9.

127  Ang (n 46) 209, citing Sanford J. Grossman and Joseph E. Stiglitz, ‘On the impossibility of efficient markets’ (1980) 70 American Economic Review 393–498.

128  See para 2.55 (on Tobin’s theory of separation).

129  See paras 2.59ff (on CAPM) and paras 2.68ff (on EMH).

130  Bodie et al (n 1) 384–401, noting at 401 that there ,,are enough anomalies in the empirical evidence to justify the search for underpriced securities that clearly goes on. The bulk of the evidence, however, suggests that any supposedly superior investment strategy should be taken with a grain of salt. The market is competitive enough that only differentially superior information or insight will earn money; the easy pickings have been picked.

131  Warwick (n 93) 10–13. Value stocks are equity securities with a relatively low price-to-book value ratio for the sector. Growth stocks are issued by companies whose sales, earnings, and market share are perceived to be expanding at a faster rate than is average for the sector.

132  Bob Litterman provides four reasons for the existence of positive uncorrelated returns. First, there is a perception that most investors do not understand the distinction between market risk and uncorrelated risk, as a result of which there is investor aversion to uncorrelated risk which is not justified in equilibrium, creating arbitrage opportunities, eg in value stocks. Second, there is a perception that not all information is public and fully digested by the investors, so that market timing presents opportunities. Third, there are non-economic investors in the market, such as governmental organizations. Fourth, there are structural inefficiencies in the markets, such as barriers to foreign investors, that prevent investors from driving risk premiums to equilibrium levels. See Robert B Litterman, ‘The Value of Uncorrelated Sources of Return’ in RB Litterman (ed), Modern Investment Management—An Equilibrium Approach (Wiley 2003) 155.

133  Grinold and Kahn (n 97) 22–23.

134  Sabrina C Callin, (ed), Portable Alpha Theory and Practice (Wiley 2008) 96–97. Grinold and Kahn (n 97) 111.

135  For example, an ex post alpha of 0.4 means the portfolio outperformed the market-based return estimate by 0.4 per cent. An ex post alpha of -0.6 means the portfolio’s monthly return was 0.6 per cent less than would have been predicted from the change in the market alone.

136  See para 2.64.

137  A portfolio’s beta, in general, is the weighted average of the betas of its component parts: see Malkiel (n 41) 215.

138  Michael Jensen, ‘The Performance of Mutual Funds in the Period 1945–1964’ (1968) 23 Journal of Finance 389–416.

139  See paras 2.59ff (on CAPM) and paras 2.68ff (on EMH).

140  Grinold and Kahn (n 97) 559–62 (discussing the historical record for average active management).

141  Ang (n 46) 305.

142  Ang (n 46) 331.

143  See para 2.72 above.

144  François-Serge Lhabitant, Hedge Funds—Quantitative Insights (Wiley 2004) 65–66 and 75 (noting that the Sharpe ratio can be expressed as: return = risk-free rate + [Sharpe ratio × volatility]). There are a number of other risk-adjusted performance measures, such as the M2 and Graham-Harvey measures, as well as performance measures based on downside risk, such as the Sortino ratio, the upside potential ratio, the Sterling and Burke ratios, and the return-on-VaR ratios, ibid 78–85.

145  It was proposed by William Sharpe as a revision to the Sharpe ratio: see William F Sharpe, ‘The Sharpe Ratio’ (1994) 49 The Journal of Portfolio Management 49–58. See Lhabitant (n 144) 66–67 (noting that when the benchmark equals the risk-free rate, the information ratio equals the traditional Sharpe ratio).

146  Grinold and Kahn (n 97) 109–13.

147  Bodie et al (n 1) 847–48 (providing the following linear function: IR = α‎p/σ‎(ep), ie the information ratio is equal to the alpha of the portfolio divided by the standard deviation of the portfolio return that is attributable to idiosyncratic risk factors).

148  Grinold and Kahn (n 97) 147–50, 160.

149  Callin (n 134) 95–101.

150  Lhabitant (n 144) 177–78.

151  The prevailing benchmark cash rates have been LIBOR, but this is subject to change following the revelations in 2012 of LIBOR manipulation by the submitting banks, see n 15 above.

152  Callin (n 134) 109–10, noting an article published by M Barton Waring and Laurence Siegel, ‘The Myth of the Absolute Return Investor’ (2006) 62 Financial Analysts Journal 14–21, which concludes that there is no such thing as an absolute return investment strategy because all investment strategies are, by definition, relative-return strategies, based on the original observation by William Sharpe that all portfolios are part beta and part alpha and thus, that all investing is relative-return investing in which active returns are earned relative to an appropriate benchmark or mix of benchmarks.

153  See Grinold and Kahn (n 97) 477–507.

154  See paras 2.44ff (on variance of returns, or ‘volatility’, as a measure of risk).

155  See paras 2.48ff (on VaR as a measure of tail risk).

156  Grinold and Kahn (n 97) 49. Lhabitant (n 144) 59. Jacob Rosengarten and Peter Zangari, ‘Risk Monitoring and Performance Measurement’ in Litterman (ed), Modern Investment Management—An Equilibrium Approach (Wiley 2003) 249–50, observing, in accordance with the statistical rule-of-thumb for normal distributions (see para 2.45) that, if the excess returns are normally distributed, 67 per cent of all outcomes lie within the benchmark’s return plus or minus one standard deviation.

157  Grinold and Kahn (n 97) 49.

158  See para 2.44ff (on volatility as a measure of risk).

159  See Chapter 7, paras 7.23ff (discussing the difference between active and passive investment styles).

160  Callin (n 134) 102–03.

161  See para 2.73ff (on measuring alpha).

162  An asset class is a set of homogeneous investments that have similar risk–return characteristics, see Chapter 7, para 7.23ff (on asset classes).