Like much else in modern financial theory, critics of the CAPM maintain that its assumptions are so restrictive as to invalidate its conclusions, notably investor rationality, perfect markets and linearity. Moreover, the CAPM is only a single-period model, based on estimates for the risk-free rate, market return and beta factor, which are all said to be difficult to determine in practice. Finally, the CAPM also assumes that investors will hold a well diversified portfolio. It therefore ignores unsystematic risk, which may be of vital importance to investors who do not. However, as we have emphasized elsewhere in our studies, the relevant question is whether a model works, despite its limitations?

Although there is evidence by Black (1993) to suggest that the CAPM does not work accurately for investments with very high or low betas, overstating the required return for the former and understating the required return for the latter (suggesting compensation for unsystematic risk) most tests validate the CAPM for a broad spectrum of beta values.

The beta-return characteristics of individual securities also hold for portfolios. In fact, the beta of a portfolio seems more stable because fluctuations among its constituents tend to cancel each other out.

Way back in 1972, Black, Jensen and Scholes analyzed the New York Stock Exchange over a 35 year period by dividing the listing into 10 portfolios, the first comprising constituents with the lowest beta factors and so on. Based on time series tests and cross-sectional analyses they found that the intercept term was not equal to the risk-free rate of interest, rf , (which they approximated by 30 day Treasury bills). However, their study revealed an almost straight-line relationship between a portfolio's beta and its average return.

Critics still maintained that beta will only be stable if a company's systematic risk remains the same because it continues in the same line of business. However, subsequent studies using historical data to establish the stability of beta over time confirmed that if beta factors are calculated from past observable returns this problem can be resolved.

- The longer the period analyzed, the better.

- The more data, the better, which suggests the use of a sector beta, rather than a company beta.

As an alternative to the basic CAPM, Black (1972) also tested a two-factor model, which assumed that investors couldn't borrow at a risk free rate but at a rate, rz, defined as the return on a portfolio with a beta value of zero. This is equivalent to a portfolio whose covariance with the market portfolio's rate of return is zero.

The Black two-factor model confirmed the study by Black, Jensen and Scholes (op.cit.) and that a zero beta portfolio with an expected return, rz exceeds the risk free rate of interests, rf .

Despite further modifications to the original model, which need not detain us here, (multi-factors, multi-periods) the CAPM in its traditional guise continues to attract criticism, particularly in relation to its fundamental assumptions.

For example, even if we accept that all investors can borrow or lend at the risk-free rate, it does not follow that rf describes a risk-free investment in real terms. Future inflation rates are neither pre-determined, nor affect individuals equally.

Marginal adjustments to a portfolio's constituents may also be prohibited by substantial transaction costs that outweigh their future benefits.

The fiscal system can also be biased with differential tax rates on income and capital gains. So much so, that different investors will construct or subscribe to portfolios that minimise their personal tax liability (a clientele effect).

And what if the stock market is inefficient? As we have discussed at great length in this study and elsewhere in our SFM companion texts, investors can not only profit from legitimate data by paying for the privilege. With access to insider information, which may even anticipate global events (such as the 1987 crash, millennium dot. com. fiasco and 2007 meltdown) perhaps they can also destabilize markets.

Conversely, even if we assume that the market is efficient, it has not always responded to significant changes in information, ranging from patterns of dividend distribution, takeover activity and government policies through to global geo-political events. Why else do even professional active managed portfolio funds periodically under-perform relative to the market index? The only way to "beat" the market, or so the argument goes, is either through pure speculation or insider information. Otherwise, adopt a passive policy of "buy and hold" to track the market portfolio and hope for the best

Other forces are also at work to invalidate the CAPM. You will recall that the model implies that the optimum portfolio is the market portfolio, which lies on the Security Market Line (SML) with a beta factor of one. Individual securities and portfolios with different levels of risk (betas) can be priced because their expected rate of return and beta can be compared with the SML. In equilibrium, all securities will lie on the line, because those above or below are either under or over priced in relation to their expected return. Thus, market demand, or the lack of it, will elicit either a rise or fall on price, until the return matches that of the market.

However, we have a problem, namely how to define the market. It is frequently forgotten that the CAPM is a linear model based on partial equilibrium analysis that subscribes to the Modigliani-Miller (MM) law of one price. Based on their arbitrage process, (1958 and 1961) explained in our SFM companion texts, you will recall that two similar assets must be valued equally. In other words, two portfolio constituents that contribute the same amount of risk to the overall portfolio are close substitutes. So, they should exhibit the same return. But what if an asset has no close substitute, such as the market itself? How do we establish whether the market is under or overvalued?

As Roll (1977) first noted, most CAPM tests may be invalid because all stock exchange indices are only a partial measure of the true global market portfolio. Explained simply, by definition the market portfolio should include every security world-wide.

To prove the point, Roll demonstrated that a change in the surrogate for the American stock market from the Standard and Poor 500 to the Wilshire 5000 could radically alter a security's expected return as predicted by the CAPM. Furthermore, if betas and returns derived from a stock market listing were unrelated, the securities might still be priced correctly relative to the global market portfolio. Conversely, even if the listing was efficient (shares with high betas did exhibit high returns) there is no obvious reason for assuming that each constituent's return is only affected by global systematic risk.

A further criticism of the CAPM is that however one defines the capital market, movements up and down are dominated by price changes in the securities of larger companies, Yet as Fama and French (1992) first observed, it is to these companies that institutional portfolio fund managers (active or passive) are attracted, though they may under-perform relative to smaller companies. Explained simply, fund managers with perhaps billions to spend are hostages to fortune, even in a "bull" scenario. They have neither the time, nor research budgets to scrutinize innumerable companies "neglected" by the market with small capitalizations based on little information.

Turning to "bear" markets characterised by rising systematic risk, multi-national portfolio fund managers still have little room for maneuver. According to Hill and Meredith (1994):

The first option is to liquidate all or part of a portfolio. However, if the whole portfolio were sold it could be difficult to dispose of a large fund quickly and efficiently without affecting the market. Unlike a private investor, total disposal may also be against the fund's trust deed. If only part of the portfolio was liquidated there is the further question of which securities to sell.

The second option is to reduce all holdings, to be followed by subsequent reinvestment when the market bottoms out. However, the fall in prices may have to be in excess of 2 per cent to cover transaction and commission costs,).

Clearly, both alternatives may be untenable and impose significant constraints upon the opportunities to control risk. Indeed, those skeptical of portfolio management generally and the CAPM in particular, regard successful investment as a matter of luck rather than judgment, insider information, or unlikely economic circumstances where all prices move in unison.

Review Activity

Assuming the risk-free rate and expected return on the market portfolio for Muse plc are 10 per cent and 18 per cent respectively:

(1) Use the CAPM to calculate the expected returns on stocks with the following beta values:

b = 0, 0.5, 1.0, 1.5

(2) How would each stock fit into the investment plans for an actively managed portfolio?

(1) Using the data and Equation (34) to derive the expected returns, the CAPM reveals that if:

(2) The investment plans for an actively portfolio can be explained as follows.

With a beta value greater than one, a stock's expected return should "beat" the market and vice versa. A beta of one produces a return equal to the market return and a beta value of zero produces an expected return equal to the risk-free rate.

Thus, we can classify investment into three broad categories of risk for the purpose of "active" portfolio management:

A portfolio manager's interest in each category of beta factor concerns the likely impact of changes in a market index on the share's expected return. Aggressive shares can be expected to outperform the market in either direction. If the return on the index is expected to rise, the returns on high beta shares will rise faster. Conversely, if the market is expected to fall, then their returns will fall faster. Defensive shares with beta values lower than one will obviously under-perform relative to the market in each direction. Neutral shares will tend to shadow it.

b > 1.0 = Aggressive b < 1.0 = Defensive b = 1.0 = Neutral

Hence, rather than adopt a passive policy of "buy and hold" by constructing a tracker fund representative of a stock market index, "active" portfolio managers will wish to pursue:

An aggressive investment strategy by moving into high beta shares when stock market returns are expected to rise (a bull market).

A defensive strategy based on low beta shares and even risk-free assets with zero betas, when the market is about to fall (a bear market).

6.5. Summary and Conclusions

If the capital market is so unpredictable that it is impossible for investors to beat it using the CAPM, it is important to remember that the operational usefulness of alternative mean-variance analyses and expected utility models explained at the very beginning of this text are also severely limited in their application. This is why the investment community turned to Markowitz portfolio theory and the Sharpe CAPM for inspiration. And why others refined these models into a coherent body of work now termed Modern Portfolio Theory (MPT) to facilitate the efficient diversification of investment.

Since the new millennium, despite the volatility of financial markets and their tendency to crash (or perhaps because of it) the portfolio objectives of investors remain the same:

To eliminate unsystematic risk and to establish the optimum relationship between the systematic risk of a financial security, project, or portfolio, and their respective returns; a trade-off with which investors feels comfortable.

So to conclude our studies, what does the single-period model CAPM based on Markowitz efficiency contribute to Strategic Financial Management within the context of their multi-period investment, dividend and financing decisions, which previous models considered throughout this text and SFM have failed to deliver?

6.6. Selected References

1. Sharpe, W., "A Simplified Model for Portfolio Analysis", Management Science, Vol. 9, No. 2, January 1963.

2. Lintner, J., "The Valuation of Risk Assets and the Selection of Risk Investments in Stock Portfolios and Capital Budgets", Review of Economic Statistics, Vol. 47, No. 1, December 1965.

3. Treynor, J.L., "How to Rate Management of Investment Funds", Harvard Business Review, January-February 1965.

4. Mossin, J., "Equilibrium in a Capital Asset Market", Econometrica, Vol. 34, 1966.

5. Gordon, M. J., The Investment, Financing and Valuation of a Corporation, Irwin, 1962.

6. Miller, M.H. and Modigliani, F., "Dividend policy, growth and the valuation of shares", The Journal of Business of the University of Chicago, Vol. XXXIV, No. 4 October 1961.

7. Black, F., "Beta and Return", Journal of Portfolio Management Vol. 20, Fall 1993.

8. Black, F., Jensen, M.L. and Scholes, M., "The Capital Asset Pricing Model: Some Empirical Tests", reprinted in Jensen, M.L. ed, Studies in the Theory of Capital Markets, Praeger (New York), 1972.

9. Black, F., "Capital Market Equilibrium with Restricted Borrowing", Journal of Business, Vol. 45, July 1972.

10. Modigliani, F. and Miller, M.H., "The Cost of Capital, Corporation Finance and the Theory of Investment", American Economic Review, Vol. XLVIII, No.4, September 1958.

11. Roll, R., "A Critique of the Asset Pricing Theory's Tests", Journal of Financial Economics, Vol. 4, March 1977.

12. Fama, E.F. and French, KR., "The Cross-Section of Expected Stock Returns", Journal of Finance, Vol. 47, No. 3, June 1992.

13. Hill, R.A., and Meredith, S., "Insurance Institutions and Fund Management: A UK Perspective", Journal of Applied Accounting Research, Vol. 1, No. 1994.

14. Fisher, I., The Theory of Interest, Macmillan (London), 1930.

15. Markowitz, H.M., "Portfolio Selection", The Journal of Finance, Vol. 13, No. 1, March 1952.