chapter 3 solution - Chapter 3 Risk and Return: Part II...

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Answers and Solutions: 3 - 1 Chapter 3 Risk and Return: Part II ANSWERS TO BEGINNING-OF-CHAPTER QUESTIONS 3-1 In finance theory, the value of an investment is found as the PV of the asset’s expected stream of cash flows. The CAPM is an ―asset pricing theory‖ that specifies how the discount rate in the valuation equation should be determined. Although the theory is quite complex and has many component parts, its ―bottom line‖ is the SML equation, often called the CAPM equation: r s = r rf + b(r m – r rf ) The CAPM is the product of a number of different researchers, but its principal developer was William Sharpe. Sharpe was a UCLA doctoral student employed by Rand Corporation in the early 1960s while he worked on his dissertation. Harry Markowitz, who in the early 1950s had developed the concept of efficient portfolios as illustrated in Figure 3-3 and Equation 3-5, also worked at Rand, and he helped Sharpe formulate his ideas. Sharpe expanded Markowitz’s portfolio theory to include the riskless rate of return and thus the CML as shown in Figure 3-7. Sharpe also recognized that the ―relevant risk‖ of any individual stock could be measured by its beta coefficient, and thus he developed the SML as shown back in Figure 2-10 and Equation 2-9. A number of simplifying assumptions, including the following, were made in order to derive the CAPM: 1. Investors focus on a single holding period. 2. Investors can borrow or lend unlimited amounts at the riskless rate. 3. Investors have homogeneous expectations regarding the returns of different assets. 4. There are no transactions costs. 5. There are no taxes. 6. The buy/sell decisions of any single investor do not influence market prices. Since these assumptions are not true in the real world, the SML equation may not be correct, i.e., investors may not establish discount rates in accordance with the CAPM. Sharpe and Markowitz received the Nobel Prize for their work, which has had a profound effect on the finance profession. 3-2 Covariance shows how two variables move in relation to one another. There are different ―states of nature,‖ each with a probability of occurrence, and a return on each asset under each state. This probability data can be used to determine the SD of returns for each asset, the variance of those returns, and the correlation between returns on the different assets. Equation 3-2 in the text can be used to calculate the covariance. We calculate the
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Answers and Solutions: 3 - 2 covariance of two stocks and the market, and their correlation coefficients and beta coefficients, in the Excel BOC model for this chapter. The model goes on to show how efficient portfolios are formed. Markowitz noted that the returns on a portfolio are simply a weighted average of the expected returns so the individual stocks in the portfolio, but the riskiness of the portfolio as measured by the portfolio’s SD is a function of the covariance of returns between the securities. See Equation 3-4 for the SD of a 2-asset portfolio, and note that terms can be added to that equation to deal with the n-asset case.
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This note was uploaded on 09/21/2011 for the course FINANCE 4320 taught by Professor Omaral-nasser during the Spring '11 term at University of Houston-Victoria.

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chapter 3 solution - Chapter 3 Risk and Return: Part II...

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