Market Efficiency: a Theoretical Distinction and So What? Harry M
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Market Efficiency: A Theoretical Distinction and So What? Harry M. Markowitz The capital asset pricing model (CAPM) is an elegant theory. With the aid of some simplifying assumptions, it comes to dramatic conclu- sions about practical matters, such as how to choose an investment portfolio, how to forecast the expected return of a security or asset class, how to price a new security, or how to price risky assets in a merger or acquisition. The CAPM starts with some assumptions about investors and markets and deduces its dramatic conclusions from these assump- tions. First, it assumes that investors seek mean–variance efficient portfolios; in other words, it assumes that investors seek low volatil- ity and high return on average. Different investors may have different trade-offs between these two, depending on their aversion to risk. Second, the CAPM assumes that taxes, transaction costs, and other illiquidities can be ignored for the purposes of this analysis. In effect, When one it assumes that such illiquidities may impede the market’s approach to the CAPM solution but do not change the general tendency of the clearly unrealistic market. A third CAPM assumption is that all investors have the same predictions for the expected returns, volatilities, and correlations of assumption of the securities. This assumption is usually not critical.1 Finally, the CAPM makes assumptions about what portfolios the investor can select. The capital asset pricing original Sharpe (1964)–Lintner (1965) CAPM considered long posi- tions only and assumed that the investor could borrow without limit at the risk-free rate. From this assumption, and the three preceding model is replaced assumptions, one can deduce conclusions of the sort outlined in the first paragraph. by a real-world The assumption that the investor can borrow without limit is crucial to the Sharpe–Lintner model’s conclusions. As illustrated later version, some of the in this article, if we accept the other three CAPM assumptions but assume limited (or no) borrowing, the Sharpe–Lintner conclusions no longer follow. For example, if the four premises of the Sharpe– dramatic CAPM Lintner original CAPM were true, then the “market portfolio”—a portfolio whose amounts invested are proportional to each security’s conclusions no market capitalization—would be an efficient portfolio. We could not find a portfolio with greater return (on average) without greater longer follow. volatility. In fact, if the four premises of the Sharpe–Lintner original CAPM were true, the market portfolio, plus perhaps borrowing and lending, would be the only efficient portfolio. If, however, we assume the first three premises of the Sharpe–Lintner CAPM but take into account the fact that investors have limited borrowing capacity, then it no longer follows that the market portfolio is efficient. As this article will illustrate, this inefficiency of the market portfolio could be sub- stantial and it would not be arbitraged away even if some investors could borrow without limit. Harry M. Markowitz is president of Harry Markowitz Company, San Diego, California. ©2005, CFA Institute www.cfapubs.org 17 Copyright, 2005 CFA Institute. Reproduced and republished from Financial Analysts Journal with permission from CFA Institute. All rights reserved. Before the CAPM, conventional wisdom was trated in the simple examples generalize to more that some investments were suitable for widows complex cases. Finally, I will discuss the implica- and orphans whereas others were suitable only for tions of the analysis for financial theory, practice, those prepared to take on “a businessman’s risk.” and pedagogy. The CAPM convinced many that this conventional wisdom was wrong; the market portfolio is the A Distinction proper mix among risky securities for everyone. The portfolios of the widow and businessman We should distinguish between the statement that should differ only in the amount of cash or leverage “the market is efficient,” in the sense that market used. As we will see, however, an analysis that participants have accurate information and use it takes into account limited borrowing capacity correctly to their benefit, and the statement that “the implies that the pre-CAPM conventional wisdom market portfolio is an efficient portfolio.” Under is probably correct. some conditions, the former implies the latter. In An alternate version of the CAPM speaks of particular, if one makes the following assumptions, investors holding short as well as long positions. A1. transaction costs and other illiquidities can be But the portfolios this alternate CAPM permits are ignored (as I will do throughout this article), as unrealistic as those of the Sharpe–Lintner CAPM A2. all investors hold mean–variance efficient with unlimited borrowing. The alternate CAPM portfolios, assumes that the proceeds of a short sale can be A3. all investors hold the same (correct) beliefs used, without limit, to buy securities long. For about means, variances, and covariances of example, the alternate CAPM assumes that an securities, and—in addition— investor could deposit $1,000 with a broker, short A4. every investor can lend all she or he has or can $1,000,000 worth of Stock A, then use the proceeds borrow all she or he wants at the risk-free rate, and the original deposit to buy $1,001,000 of Stock B. The world does not work this way. then Conclusion 1 follows: Like the original CAPM, the alternate CAPM C1. The market portfolio is a mean–variance effi- implies that the market portfolio is an efficient port- cient portfolio. folio, although not the only one (as in the original C1 also follows if A4 is replaced by A4c: CAPM). If one takes into account real-world con- straints on the holding of short and long positions, A4c. investors can sell short without limit and use however, the efficiency of the market portfolio no the proceeds of the sale to buy long positions. longer follows, as will be illustrated. In particular, A4c says that any investor can Both the original CAPM, with unlimited bor- deposit $1,000 with a broker, short $1,000,000 rowing, and the alternate CAPM, with unrealistic worth of one security, and buy long $1,001,000 short rules, imply that the expected return of a stock worth of another security. depends in a simple (linear) way on its beta, and Neither A4 nor A4c is realistic. Regarding A4, only on its beta. This conclusion has been used for when an investor borrows, not only does the inves- estimating expected returns, but it has lost favor for tor pay more than when the U.S. government bor- this use because of poor predictive results. It is still rows, but (a point of equal or greater importance used routinely in “risk adjustment,” however, for here) the amount of credit extended is limited to valuing assets and analyzing investment strategies what the lender believes the borrower has a reason- on a “risk-adjusted basis.” I will show here that the able probability of repaying. Regarding A4c, if the conclusion that expected returns are linear func- investor deposits $1,000 with a broker, Federal tions of beta does not hold when real-world limits Reserve Regulation T permits the investor to buy a on permitted portfolio holdings are introduced into $2,000 long position or take on a $2,000 short posi- the CAPM. This discussion will call into question tion or take on a $1,000 long and a $1,000 short the frequent use of beta in risk adjustment. position, but it does not allow an unlimited amount I will discuss the assumptions and conclusions short plus the same unlimited amount long, as of the CAPM formally and then illustrate the effect assumed in A4c. on CAPM conclusions of varying the CAPM If one replaces A4 or A4c with a more realistic assumptions concerning the investor’s constraint description of the investor’s investment constraints, set. Afterward, I will sketch how the points illus- then C1 usually no longer follows; even though all 18 www.cfapubs.org ©2005, CFA Institute investors share the same beliefs and each holds a This example consists of long positions in mean–variance efficient portfolio, the market port- three risky securities with the expected returns and folio need not be an efficient portfolio. This depar- standard deviations shown in Table 1. To keep ture from efficiency can be quite substantial. In fact, things simple, we will assume that returns are the market portfolio can have almost maximum vari- uncorrelated. However, the results also hold for ance among feasible portfolios with the same correlated returns. expected value rather than minimum such variance; that is, the market portfolio can be about as ineffi- cient as a feasible portfolio can get (see Chapter 11 Table 1. Expected Returns and Standard of Markowitz 1987 or Markowitz and Todd 2000). Deviations of Three Risky Securities In addition to C1, A1 through A4 (or A1 Expected Standard through A4c) imply Security Return Deviation 1 0.15% 0.18% C2. In equilibrium, the expected return for each 20.100.12 security depends only on its beta (the regres- 30.200.30 sion of its returns against the return on the market). This relationship between the secu- Let X1, X2, and X3 represent the fraction of her rity’s expected return and its beta is a simple, wealth that some investor invests in, respectively, linear relationship. Securities 1, 2, and 3. Assume that the investor can C2 is the basis for the CAPM’s prescriptions for choose any portfolio that meets the following con- risk adjustment and asset valuation. Like the first straints: conclusion, C2 does not follow from assumptions X1 + X2 + X3 = 1.0 (1) A1 through A3 if A4 (or A4c) is replaced by a more realistic description of the investor’s investment and constraints.