# The Capital asset pricing model (CAPM)

‘The Capital asset pricing model (CAPM) is a very useful model and it is used widely in the industry even though it is based on very strong assumptions. Discuss in the light of recent developments in the area.’

“Sometimes your best investments are the ones you don't make."[1] This maxim shows the complexity of investing.

In 1963, the finance journal article “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk” introduced the foundations of the Capital Asset Pricing Model. The CAPM, initially proposed by Sharpe (1964) and Lintner (1965) has provided a simple and compelling theory of asset market pricing through the association of a portfolio investment to a single risk factor (the Beta factor)[2].This theory predicts that the expected return on an asset above the risk-free rate is proportional to the nondiversifiable risk. In this sense the higher the quantity of beta of a security, the higher is the expected return of that asset.

In the years following the publication of the CAPM, and after comparing actual returns with expected returns, several Economists have criticised its simplicity and the reality of its application. Although the CAPM has been the basis for more than one hundred academic papers and has had significant impact on the non-academic financial community, it is still subject to theoretical and empirical criticism. Despite its apparent invalidity, the model is still commonly used by firms as an effective model for calculating cost of capital by explaining higher return in securities with higher betas. This paper will then discuss these implications in light of recent development in the area. First, I will attempt in this paper to explain and discuss the different assumptions of the model. Second, I will discuss the main theories and furthermore, the whole debate surrounding this area especially through the critics of the assumptions.

The financial applications of the CAPM are numerous. Indeed, it is used to value a firm’s common stock, for capital budgeting, for merger and acquisition analysis and the valuation of warrants and convertible securities[3]. For the CAPM to be valid, William Sharpe made several assumptions for investors in creating market equilibrium. The proponents of the model argue that the capital market operates “as if” these assumptions were satisfied. The model derives what is the price that any asset must command in order for the investors to be happy to hold the current market portfolio (portfolio of all assets in the economy). In short, the model determines for X amount of market risk this is the expected return.

Under CAPM, everyone is bearing the same risk in different amounts. Investors hold diversified portfolios and they will require a return for the systematic risk of their portfolios since unsystematic risk has been removed and can be ignored. An investor will then rank a portfolio according to a utility function which depends on this portfolio’s expected rate of return. Since everybody holds the same portfolio of risky assets; it is ordinary that everybody is exactly happy to buy the “market” portfolio (the portfolio of all assets that are being offered on the market).

Moreover, it is possible to diversify part of the risk through the purchase of many different assets.[4] The riskiness of a stock is not essentially related to the variability of its return. The variability would be the appropriate measure if one investor is putting all his money in a single asset. In reality, it is possible to diversify part of the risk through the purchase of many different assets.[5]Indeed, through diversification, it is possible to eliminate the risk that is unique to individual stocks but not the risk that the market as a whole may decline. The nondiversifiable risk arises from macroeconomic factors which influence all assets at the same time. As an example, during the “credit-crunch” most companies tend to have low profits and negative cash flows.

While the assumptions held by the CAPM allow it to focus on the relationship between return and systematic risk, the idealised world proposed by the assumptions is clearly not the same as the real world in which investment decisions are mostly made by companies and individual. The extent to which these assumptions are not met with the real world will affect the validity of the CAPM[6].

These assumptions are a major part of classical economic doctrine. Indeed, they are the standard assumptions of a perfect market, and their merits have been discussed widely in the literature. William Sharpe emphasises this by saying “needless to say, these are highly restrictive and undoubtedly unrealistic assumptions”[7] Indeed, real-world capital markets are undoubtedly not perfect. Even though, well-developed stock markets do exhibit high efficiency; there is an extent for stock market securities to be mispriced.

The CAPM assumes no transaction costs, in the way that trading is costless and investments are priced to all fall on the capital market line. However, we know that many investments such as the acquisition of a small business for example, involve significant transaction costs. Furthermore, under CAPM, investment trading is tax-free and returns are unaffected by taxes. But most of the returns such as dividends and capital gains are taxed in a different way and thus, forces investors to consider taxes. Additionally, many investment transactions have capital gains taxes. In reality, the different investors are also taxed differently according to their status: individuals versus pension’s plans. Moreover, the assumption that investors hold diversified portfolios means that all investors want to hold a portfolio which reflects the stock market as a whole, the market portfolio. However, it is impossible to own the market portfolio itself.

Under CAPM, investors can borrow money at risk-free rates. Risk-free asset is an asset which has a certain future return, such as treasuries (T-bills). This is done to increase the number of risk assets in a portfolio. However, in reality it is impossible for investors to borrow at the risk-free rate because the risk associated with individual investors is much higher than that associated with the Government.

We also know that the CAPM assumes that there are zero–risk securities of various maturities and enough quantities to allow for portfolio risk adjustments. But for example, Treasury bills have various risks (reinvestment risk, inflation risk or currency risk).

Theoretically, homogenous investors in market equilibrium have access to and use identical information and behave identically with regards to risk in portfolios. Everybody have the same information, and then will buy more good stocks and less bad stocks. For example, if investor A buys more of X than Y, then everyone will do the same and focus of X. Investors are assumed to valuate information the same way through the same articles and newspapers, and consequently they reach the same conclusions. According to William Sharpe, all investors have the same beliefs about expected returns, investment strategies and risks of available investments as long as they stay risk-averters. However, in real life, investors may have different opinions, risk preferences, investment horizons and expectations. The CAPM does not take into account the diversity. The homogeneous expectation assumption leads to a highly inefficient market with periodic and predictable booms and crashes.[8]

According to George Soros (Manager of Quantum Group Fund in 1995) “Classical economic theory assumes that market participants act on the basis of perfect knowledge. That assumption is false. The participants cannot obtain perfect knowledge of the market because their thinking is always affecting the market and the market is affecting their thinking” [9] In real life, some investors may attribute a great importance to numerical data (accounting data, price earnings ratio) others may have time-series prediction formulas. In this case, investors will have different expectations and different optimal diversification strategies.

The CAPM has several advantages over other methods for calculating required return. This is mainly why it has remained popular for more than 40 years. Indeed, the CAPM focuses only on systematic risk, reflecting a reality in which most investors have diversified portfolios where unsystematic risk has been removed. The relationship between required return and systematic risk has been the result of numerous empirical researches and testing. The CAPM is seen to be much useful to calculate the cost of equity than the Dividend Growth Model for example, because it takes into account a company’s level of systematic risk relative to the stock market as a whole.[10] It is also superior to the Weighted Average Cost of Capital (WACC) in providing discount rates for use in investment appraisal.

In the years following the creation of the CAPM, several researchers in the field developed models to counter it. The CAPM assumes that risk is measured by the standard deviation of an asset’s systematic risk, relative to the standard deviation of the market as a whole.[11]The standard deviation on the rate of return on an investment is a measure of the volatility of the investment. However, in 1973, Fama and McBeth stressed that “Beta” does not matter and that the standard deviation on the return of any asset is also irrelevant for explaining its excess return since it does not measure risk when returns are not evenly distributed around the mean[12].

Furthermore, in 1977, Richard Roll in an important analysis of the model stated that the CAPM is “not testable”[13] due to factors such as the impossibility of testing the true market portfolio and benchmark error by using an inefficient market proxy. He pointed out that using a proxy for a market portfolio is subject to difficulties[14]. While Roll’s work dismisses the CAPM as mathematically not testable, other economists consider other variables of risk that leads to the misspecification of the CAPM model, such as Rolf Banz, in his 1981 article “The Relationship Between Return and Market Value of Common Stocks”. He empirically found that “smaller firms have had higher risk adjusted returns, on average, than larger firms.”[15] The ‘size effect’[16] leads to the CAPM being “misspecified”[17] and concluding that, “there is no theoretical foundation for such an effect”[18] Following the publication of Banz’s article, Berk in his 1995 article “A Critique of Size related Anomalies” stressed that riskier firms will have lower market values and higher expected returns. Berk concluded that “the empirically size effect is not, by itself, evidence of a relation between firm size and risk”[19].

Additionally, Fama and French’s multi factor model consider book-to-market ratio and market index. In addition to the ‘size effect’, Fama and French both argue that these variables “produce undiversifiable risks in returns that are not capture by the market return and are prices separately from market betas”[20]In short, these ‘nondiversifiable risks’ are not linked to the beta factor and thus, are not shown in the CAPM. Fama and French believe that their ‘Three Factor Model’ is a more complete and empirically correct version of the CAPM. Also, the CAPM suggests difficulties in quantifying investor behaviour. F&F have studied whether the behaviour of stock prices, in relation to the size and book-to-market-equity (Three Factor Model) is consistent with the behaviour of earnings.[21] Consequently, they concluded that this could be true for rational pricing only.

Despite the apparent invalidity of the CAPM, it remains used by firms as a famous model for calculating the cost of capital. Indeed, according to Harvey and Graham (2000), “the CAPM is by far the most popular method of estimating the cost of equity capital in firms, with 73.5% of respondents almost or always using the CAPM”[22]. Furthermore, the fact that the model compares two essential variables concerning capital budgeting in its equation such as risk (through the beta) and return, allows it to be considered a relatively simple, but mathematically sound model. In addition, the actual results agree with the expected results in a way that the riskier the project is the higher its return strengthens the justification of its extensive use in corporate finance. However, the CAPM is based on very strong assumptions concerning investor’s actions and while unrealistic in its perfect application, the model logically assesses ideas such as investors diversifying in order to reduce risk. The presence of alphas (deviations from the market security line) implies that it cannot fully be relied upon. This could be due to the presence of variables in risk that cannot be quantified mathematically such as investor behaviour. As CAPM calculated expected returns and not actual ones, and for the fact that future cannot be exactly predicted, it can be relied on as an accurate way to calculate a firm’s cost of capital by modelling risk and return.

### o References:

Banz, R. F., 1981, “The Relation between Return and Market Value of Common Stocks,” Journal of Financial Economics, 9, 3-18.

Black,F., Jensen, M., and Scholes, M.The Capital Asset Pricing Model: Some Empirical Tests, in M. Jensen ed., Studies in the Theory of Capital Markets. (1972).

Fama, Eugene F., French, Kenneth R. 1995. “Size and Book-To-Market Factors in Earnings and Returns”, The Journal of Finance, Vol. 50, No.1 (1995).

Fama, Eugene F., French, Kenneth R. 2004. “The Capital Asset Pricing Model: Theory and Evidence.” Journal of Economic Perspectives, Vol. 18, No. 3, (2004), pp. 25-46.

Fama, E.and French, K. (1992). The Cross-Section of Expected Stock Returns, Journal of Finance, June 1992, 427-466.

Graham, John R., Harvey, Campbell R., 2000, “The Theory and Practice of Corporate Finance: Evidence from the Field”, Duke University.

Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets, Review of Economics and Statistics, 47

Markowitz, Harry M. (1999). The early history of portfolio theory: 1600-1960, Financial Analysts Journal, 55 (4)

Roll, Richard. 1976. “A Critique of The Asset Pricing Theory’s Tests.”Journal of Financial Economics 4, 1977.

Ross, Stephen A. (1977). The Capital Asset Pricing Model (CAPM), Short-sale Restrictions and Related Issues, Journal of Finance, 32 (177)

Sharpe, William F., 1961, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.”The Journal of Financial Economics, Vol.19, No.3. (Sept. 1964) pp. 425-442

Haim Levy. "The Capital Asset Pricing Model with Diverse Holding Periods."The Capital Asset Pricing Model with Diverse Holding PeriodsVol. 70.2 (1988): 359-65. Print.

J. Fred Weston. "Investment Decisions Using the Capital Asset Pricing Model."Investment Decisions Using the Capital Asset Pricing ModelVol. 2.1 (1973): 25-33. Print.

Robert C. Merton. "An Intertemporal Capital Asset Pricing Model."An Intertemporal Capital Asset Pricing ModelVol. 41.5 (Sep 1973): 867-87. Print

Thomas H. Naylor and Francis Tapon. "The Capital Asset Pricing Model: An Evaluation of Its Potential As a Strategic Planning Tool."The Capital Asset Pricing Model: An Evaluation of Its Potential As a Strategic Planning ToolVol.28.No.10 (Oct.1982): 1166-173. Print.

Tim Bollerslev, Robert F. Engle, Jeffrey M. Wooldridge. "A Capital Asset Pricing Model with Time-Varying Covariances."A Capital Asset Pricing Model with Time-Varying CovariancesVol.96.No.1 (Feb.1988): 116-31. Print.

Shannon P.Pratt Roger, J.Grabowski. "Cost of Capital: Applications and examples."Cost of Capital: Applications and examplesEdition 2008 (1988): 778-83. Print.

[1] Donald Trump, 1946,

[2] William Sharpe, 1964, pp.425

[3] Thomas H. Naylor and Francis Tapon, Oct 1982, Pp.1166

[4] Marco Bassetto, 2002, pp.1

[5] Marco Bassetto, 2002, pp.1

[6] Shannon P. Pratt, Roger J. Grabowski, 2008, Pp. 122

[7] William F Sharpe, 1964, pp. 425-442

[8] M.Levy, H.Levy, 1996, p66

[9] G.Soros, Sept 4 1995, pp.90

[10] Watson D and Head A, 2007, pp.222-3

[11] Roll R, 1977, pp.134

[12] Fama, E & Mcbeth, J, 1973, pp.617

[13] Roll, 1976 Pp.54

[14] Bodie, Kane, Marcus, 2008

[15] Banz, 1981, pp.17

[16] Banz, 1981, p16

[17] Banz, 1981, p.16

[18] Banz 1981, p.17

[19] Berk, 1995, p.278

[20] Fama, French, 2004

[21] Fama, French, 1973

[22] Graham, Harvey, 2000, pp.240