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).
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.
12 See Bluemke (n 10) 34–35.
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,  OJ L347/35 (Securitization Regulation):
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’.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.”
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.
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).
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.
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.
140 Grinold and Kahn (n 97) 559–62 (discussing the historical record for average active management).
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.
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).