d The characteristic line for a particular stock is obtained by regressing the

D the characteristic line for a particular stock is

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return and risk. d. The characteristic line for a particular stock is obtained by regressing the historical returns on that stock against the historical returns on the general stock market. The slope of the characteristic line is the stock's beta, which measures the amount by which the stock's expected return increases for a given increase in the expected return on the market. Answers and Solutions: 3 - 6
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The beta coefficient (b) is a measure of a stock's market risk. It measures the stock's volatility relative to an average stock, which has a beta of 1.0. e. Arbitrage Pricing Theory (APT) is an approach to measuring the equilibrium risk/return relationship for a given stock as a function of multiple factors, rather than the single factor (the market return) used by the CAPM. The APT is based on complex mathematical and statistical theory, but can account for several factors (such as GNP and the level of inflation) in determining the required return for a particular stock. The Fama-French 3-factor model has one factor for the excess market return (the market return minus the risk free rate), a second factor for size (defined as the return on a portfolio of small firms minus the return on a portfolio of big firms), and a third factor for the book-to-market effect (defined as the return on a portfolio of firms with a high book-to-market ratio minus the return on a portfolio of firms with a low book-to-market ratio). Most people don’t behave rationally in all aspects of their personal lives, and behavioral finance assumes that investors have the same types of psychological behaviors in their financial lives as in their personal lives. 3-2 Security A is less risky if held in a diversified portfolio because of its lower beta and negative correlation with other stocks. In a single-asset portfolio, Security A would be more risky because σ A > σ B and CV A > CV B . Answers and Solutions: 3 - 7
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3-1. Beta: The standard deviation of stock returns for Stock A is 40%. The standard deviation of the market return is 20%. If the correlation between Stock A and the market is 0.70, what is Stock A’s beta? b i = iM ( i / M ) = 0.70(0.40/0.20) = 1.4. 3-2 r i = r RF + (r 1 r RF )b i1 + (r 2 r RF )b ij = 0.06 + (0.12 – 0.06)(0.7) + (0.08 – 0.06)(0.9) = 0.12 = 12%. 3-3 r i = r RF + a i + b i (r M r RF ) + c i (r SMB ) + d i (r HML ) = 5% + 0.0% + 1.2(10% - 5%) + (-0.4)(3.2%) + 1.3(4.8%) = 15.96% 3-4 r p = w A r A + (1 w A ) r B = 0.30(12%) + 0.70(18%) = 16.20% p = = = = = 0.459 = 45.9% 3-5 a. . ) r r ( r b ) r r ( r r M i iM RF M RF i RF M RF i b. CML: . r r r r p M RF M RF p SML: . r r r r r i iM M RF M RF i With some arranging, the similarities between the CML and SML are obvious. When in this form, both have the same market price of risk, or slope, (r M - r RF )/σ M .
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