NAU FIN 331 - The Capital Asset Pricing Model

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Finance 331 CAPM Handout (Chapter 7)The Capital Asset Pricing Model, or CAPM, is a theory of the relationship betweenrisk and return and explains how financial assets are priced under certain conditions. The standard deviation, or , of a security’s returns is a measure of the total risk of that security. According to CAPM, however,  is not the relevant measure of a security’s risk, because part of the total risk is eliminated by diversification. Only that part of risk that remains after diversifying is important to diversified investors.= total risk = systematic risk + unsystematic riskThe unsystematic, or company-specific risk is the part that can be eliminated through diversification. The remaining systematic, or market risk, is measured by beta. The required rate of return on a stock is determined by individual investors after considering other investment opportunities (market conditions) and the stock’s risk. According to CAPM, this is expressed in the following equation, which is theformula for the Security Market Line (SML):ri = rf + i(ErM - rf)where: ri = required rate of return (RRR) on stock i rf = risk-free interest rate i = beta of stock i ErM = expected return on the marketNote: ri represents the required rate of return on stock i, not the predicted (or expected) return. The required return will equal the predicted return only if the stock price equals its intrinsic value, as discussed below.Together, the risk-free rate and the expected return on the market define marketconditions, and beta measures the relevant portion of the stock’s risk.The beta for a stock can be calculated as follows:i = (covariance between i and M) / (variance of M) = corri,M (i / M)As shown in the equation above, a stock’s beta depends on the stock’s total risk (s) and the correlation between the stock’s returns and the returns on the market. Beta provides a measure of the sensitivity of a stock’s returns to changes in the stock market. The beta of the stock market is equal to one, and therefore the average beta for all stocks is equal to one. If a stock has a beta greater than one, it has above-average market risk, and if its beta is less than one, it has below-average market risk.The graph of the SML is shown below.1The graph of the SML is determined entirely by market conditions, that is, by rf and ErM. To obtain the RRR for a given stock, the only additional information we need is the stock’s beta. Because the RRR on stock i depends on only one characteristic of the stock, CAPM is a single-factor model. CAPM by itself cannot be used to identify undervalued securities. In addition to the RRR, investors estimate the predicted return on a stock. This estimate is the result of a fundamental analysis of the company’s future prospects and the market price of the stock. If the stock price is less than its intrinsic value, the stock is said to be undervalued, and the predicted return on that stock will be greater than the required rate of return. (The less you pay for an asset, the higher your rate of return will be.) An undervalued stock will plot above the SML.For example: rf = 5%ErM = 10%Bi = 1.20Based on this information, ri = 5 + 1.20 (10 - 5) = 11% Assume the dividend the firm is expected to pay in the coming year is $1.00, and dividends are expected to increase at a constant annual rate of 6%. The intrinsic value, V0 is:V0 = D1 / (ri - g) = 1 / (.11 - .06) = $20If the market price of the stock is $15 (and the expected growth rate is constant)then the predicted return is:predicted ret = D1 / price + g = 1/15 + .06 = .127 = 12.7%The market for this stock is not in equilibrium: predicted return > RRRmarket price < intrinsic valueWe can calculate the alpha for this stock by subtracting the required return from the predicted return:i = predicted return – required return = 12.7 – 11 = 1.7%2If a stock has a positive alpha, it is undervalued. If the predicted return is plottedon the SML graph, it plots above the SML.If you bought the stock at a price of $15, and if the stock price increases at the same rate as g, you will earn 12.7%. However, if other investors recognize that itis undervalued, and the price is bid up to $20, you will earn far more than 12.7%. As the price of the stock increases to its intrinsic value, the expected return will be reduced until it equals the required rate of return, and the market will then be in equilibrium. The required return on the stock does not change as equilibrium is restored.For stocks that are in equilibrium, the return indicated by CAPM represents both the required rate of return and the expected return. If the stock market is efficient, stock prices tend to be in equilibrium, and move to the new equilibriumlevel very quickly when investors receive new information that causes them to revise their view of the stock’s intrinsic value. In any case, while some stocks might be undervalued and others might be overvalued at a particular time, on average, market prices are probably close to intrinsic values.More about beta:1. The portfolio beta is a weighted average of individual stock betas. 2. The beta of a stock (or portfolio) indicates how responsive it is to a change in the market. For example, the expected change in the value of a stock (or portfolio):expected change in value = beta x change in marketIf the market drops 10 percent and beta is 1.5:expected change in value = 1.5 x -10% = -15%If the market goes up 10%: expected change in value = 1.5 x 10% = 15%So, if you are very bullish on the stock market, hold a high beta portfolio. If you are less bullish (or bearish) hold a low beta portfolio. One way to lower your portfolio beta is to combine a position in M with the risk-free asset. If you invest half your wealth in M, with a beta of 1, and half in the risk-free asset, with a betaof 0, your portfolio beta is: p = .5(1) + .5(0) = .5Suppose an investor has only two investment alternatives, stock X and the market: investment ER  market 10% 1 20%stock X 10% 1 40%If you must put all of your money in one or the other, which should it be? Why?3“Beta is the relevant measure of a security’s risk for a diversified investor, but  is the relevant measure for an undiversified investor.” Why?4Fin 331 Problems on CAPM and Portfolio 1. rf = 4% ERM = 12% M = 20%a. Draw and correctly label the SML & CMLb. X = 1.21. Calculate rX.2. Plot the required return and beta for X on the


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NAU FIN 331 - The Capital Asset Pricing Model

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