The capital asset pricing model and arbitrage pricing theory: Theory

Abstract

For a long time, academic theorists were grappling with explaining the variation in cross section of expected stock returns. That is, we need a model to link the risk and return of investing in stocks and other assets. The breakthrough came when Markowitz, and later Sharpe, laid the foundations of modern portfolio theory. The capital asset pricing model (CAPM) hypothesizes that a stock's return is a function of its systematic risk. The model is simple and intuitive to use. But, it has come under attack from other academics because of its inability to adequately explain ex-post variation in cross section of stock returns and several anomalies in the US capital markets. The arbitrage pricing theory has emerged as one of the competitors to CAPM. This chapter describes these two theories of asset pricing. This chapter has the following objectives: • Describe how to measure returns of individual and portfolios of stocks • Explain what constitutes risk in a single stock as well as a portfolio context • Review the performance of major markets around the world • Introduce CAPM and APT Suppose an investor purchased 100 shares of a company at $ 120, received dividends amounting to $ 60 during the year, and sold the shares at $ 140 at the end of the year. The rate of return an investor receives from buying shares and holding them for a given period of time is equal to the cash dividends received plus the capital gain (or minus the capital loss) during the holding period divided by the purchase price of the security. Expressed as a formula, realized return R = [D1 +(P1P0)] P0 , (4.1) where D1 = dividend received; P1 = selling price; P0 = purchase price The rate of return on the investment = ($60+$20)/120= 66.66%. Now consider a multi-period situation. The investor has a 3-year investment horizon. Purchase price = $ 200 Dividend receipts = $ 5, $ 6, and $ 10, respectively. Selling price = $ 225 Formula presented One measure of return is the arithmetic average of returns in these 3 years. R = [R1+R2+R3] 3 , where R is the average return and R1, R2, and R3 are periodic returns. Another measure is the geometric mean of returns. Rg = [(1+R1) (1+R2)(1+R3)]1/31. In general, the geometric mean can be expressed as follows: Rg = [(1+R1)(1+R 2)(1+R3) . . . (1+RN]1/N1. (4.2) In the above equation, N is the number of periods. In the above example, the investor had a 3-year horizon. The holding period could be in months as well, say, January, February, and March. The principle remains the same, except that the rate of return will have to be converted to an annual rate. Exhibit 4.1 presents the summary of returns on common stocks in the US [proxied by SandP (Standard and Poor) index] between 1871 and 2001. The returns are calculated using monthly data and assume that dividends are reinvested at each month-end. The geometric mean of returns for the entire period is 9.0641%. Investors receive returns in two forms: dividends and capital gains. The dividend return on the SandP 500 index has declined to about 1.5% in 2000s from 3.5% to 4.0% in the 1960s. Academic studies in the United States have attempted to forecast future stock returns using dividend yields and expected rates of growth in stock price appreciation (Jones et al. 2002). An important study by Fama and French (2001) suggests that the propensity of firms to pay dividends is lower now, suggesting that dividend returns are unlikely to grow. Academic studies take several proxies for the stock price appreciation (e.g., GDP growth rate). These studies suggest that stock returns are likely to be in the range of 7-9%. © 2009 Springer-Verlag Berlin Heidelberg.