Risk, Return, and the
Capital Asset Pricing Model
ANSWERS TO END-OF-CHAPTER QUESTIONS
7-1 a. Stand-alone risk is only a part of total risk and pertains to the risk an investor takes by holding only one asset. Risk is the chance that some unfavourable event will occur. For instance, the risk of an asset is essentially the chance that the asset’s cash flows will be unfavourable or less than expected. A probability distribution is a listing, chart, or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome. When in graph form, the tighter the probability distribution, the less uncertain the outcome.
b. The expected rate of return () is the expected value of a probability distribution of expected returns.
c. A continuous probability distribution contains an infinite number of outcomes and is graphed from - and +.
d. The standard deviation (σ) is a statistical measure of the variability of a set of observations. The variance (σ2) of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation. The coefficient of variation (CV) is equal to the standard deviation divided by the expected return; it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations.
e. A risk-averse investor dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their expected return.
f. A risk premium is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk. The market risk premium is the difference between the expected return on the market and the risk-free rate.
g. CAPM is a model based upon the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium reflecting only the risk remaining after diversification.
h. The expected return on a portfolio. p, is simply the weighted-average expected return of the individual stocks in the portfolio, with the weights being the fraction of total portfolio value invested in each stock. The market portfolio is a portfolio consisting of all stocks.
i. Correlation is the tendency of two variables to move together. A correlation coefficient (ρ) of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions. A correlation coefficient of zero suggests that the two variables are not related to one another; that is, they are independent.
j. Market risk is that part of a security’s total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. Diversifiable risk is also known as company specific risk, that part of a security’s total risk associated with random events not affecting the market as a whole. This risk can be eliminated by proper diversification. The relevant risk of a stock is its contribution to the riskiness of a well-diversified portfolio.
k. The beta coefficient is a measure of a stock’s market risk, or the extent to which the returns on a given stock move with the stock market. The average stock’s beta would move on average with the market so it would have a beta of 1.0.
l. The security market line (SML) represents in a graphical form, the relationship between the risk of an asset as measured by its beta and the required rates of return for individual securities. The SML equation is essentially the CAPM, ri = rRF + bi(rM - rRF).
m. The slope of the SML equation is (rM - rRF), the market risk premium. The slope of the SML reflects the degree of risk aversion in the economy. The greater the average investor’s aversion to risk, then the steeper the slope, the higher the risk premium