Capital Asset Pricing Model 

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Capital Asset Pricing Model


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The 1990 Nobel Prize laureates for economics, Harry Markowitz and William Sharpe, developed theories about the financial markets that have had a profound effect on investors. Harry Markowitz’s work pioneered what is now known as the modern portfolio theory. Concerned with the composition of investments that investors would select for their portfolios, Markowitz determined that the major properties of an investment that should be of concern to investors are risk and return. By choosing a range of different investments for a portfolio, investors can determine and control the total risk in that portfolio through variance analysis of each investment. In other words, in plain English, investors can assemble portfolios of risky stocks in which the risk of the whole portfolio would be less than any of the individual stocks in the portfolio. By determining the given amount of risk, investors select the portfolio that offers the highest expected return.

A simple example illustrates this concept. Suppose that you have a portfolio with equal amounts invested in two stocks: a computer-related technology stock and a food stock. In good economic times, when computer sales are growing, the price of technology stocks is expected to increase by more than 50 percent, and food stocks have an expected return of 6 percent (including the dividends). During a recession, when computer sales are in the doldrums, the price of the technology stock is expected to decline by 20 percent. The food stock, however, because it is in a defensive industry, is expected to increase by 40 percent. Thus, in a good economy, the investors will earn an average return of 28 percent [(50% + 6%)/2]. In a recession, the portfolio will earn an average return of 10% [(40% - 20%)/2].

Although the technology stock is more risky than the food stock, by diversifying into the two different industries, the average returns are greater than if all the funds were invested in one stock. In addition to reducing your risk by increasing the number of stocks, you can reduce your risk by choosing stocks that react to economic conditions differently.

William Sharpe and John Lintner further developed Markowitz’s approach into the capital asset pricing model (CAPM). The capital asset pricing model links the relationship between risk and the expected return of a stock. The stock’s expected rate of return is the risk-free rate plus a risk premium based on the systematic risk of the stock. In this model, the risk of a stock or portfolio is broken down into two parts: systematic and unsystematic risk. The risk pertaining to the security itself (such as business and financial risks) can be reduced and eliminated through diversification. What remains is systematic risk, which becomes important in the relationship between risk and return. In other words, by combining several different stocks in a portfolio, the unsystematic or diversifiable risk is reduced, and all that is left is systematic risk. Systematic risk, also known as market risk, is the relationship of a security’s price to changes in security prices in the general market. Some stocks go up and down more than the market, and other stocks fluctuate less than the market as a whole. Systematic risk is measured by the Greek letter beta. The beta coefficient, a measure of the systematic risk of a stock, links the sensitivity of the stock’s rate of return to the rate of return of the market and is determined as follows:

β = (standard deviation of the return of a stock/ standard deviation of the return of the market) * correlation coefficient between return of the stock and the market

The larger the standard deviation of the return of a stock relative to the return of the market, the greater is the risk associated with that stock. The correlation coefficient indicates the relative importance of variability. The range of the correlation coefficient is from +1 to -1. If the correlation coefficient is +1, the stock return and the market return move together in a strong correlation. Thus, if the standard deviation of the stock is 15 percent and the standard deviation of the market is 10 percent with a correlation coefficient of 1, the beta coefficient is 1.5

β = (standard deviation of the return of a stock/ standard deviation of the return of the market) * correlation coefficient between return of the stock and the market
= (0.15/0.10) * 1
= 1.5

A correlation coefficient of -1 with a standard deviation of a stock equal to 8 percent and a standard deviation of 10 percent for the market results in a beta of -0.8:

β = (0.08/0.10)* -1
= -0.8

A negative correlation coefficient results in the stock and the market moving in opposite directions. If no relationship exists between the return on the stock and the return on the market, then the correlation coefficient is zero, which results in a beta coefficient of 0, or no market risk.

For a stock with a beta coefficient of 1, if the market rises by 20 percent, the stock price will increase by 20 percent. If the market falls by 20 percent, the stock price also will see a 20 percent decline. The market is assumed to have a beta coefficient of 1, which means that this stock is perfectly correlated with the market.

Figure 12–3 illustrates the relationship between a stock with a beta coefficient of 1.5 and the market with a beta of 1. The stock has a return of 15 percent when the market increases by 10 percent. A stock with a return that is less than the market is drawn below the market line in the positive quadrant and it is drawn above the market line in the negative quadrant. Thus a stock with a beta coefficient greater than 1 should produce above-average returns in a bull market and below-average returns in a bear market. Astock with a beta coefficient of less than 1 is less responsive to market changes. Investors who seek higher returns are willing to assume more risk.

Increased diversification into many different stocks in a portfolio does not eliminate the systematic risk. In other words, these stocks are not immune to a downturn in the market. However, diversification into at least 20 different stocks can eliminate the unsystematic risk, which is the risk that pertains to the company. This includes financial, business, and purchasing-power risks, which affect a company’s stock price.

Figure 12-3
Stock with a Beta Coefficient of 1.5

Stock with a Beta Coefficient of 1.5

Table 12-3
Comparison of Beta Coefficients (October 18, 2006)

Comparison of Beta Coefficients (October 18, 2006) Calculating the beta coefficient is tedious. You can obtain beta coefficients for individual stocks from several sources, such as Value Line and Standard & Poor’s, which are subscription services, and financial Web sites such as www.yahoo.com. You should not be alarmed if you find different beta coefficients for the same stock because beta coefficients can be derived using different market measures, such as the S&P 500 Index versus the Value Line Index. Similarly, discrepancies occur when the periods for the calculations differ, using, for example, three years versus five years of price data. Thus no correct beta coefficient exists. Table 12–3 compares different beta coefficients.




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