However, the straight line connecting r RF with m, the point of tangency between the line and the portfolio's efficient set curve, is the one that all investors would choose. Since all portfolios on the line r RF mz are preferred to the other risky portfolio opportunities on the efficient frontier AB, the points on the line r RF mz now represent the best attainable combinations of risk and return. Any combination under the r RF mz line offers less return for the same amount of risk, or offers more risk for the same amount of return. Thus, everybody wants to hold portfolios which are located on the r RF mz line. h. Write out the equation for the capital market line (CML) and draw it on the Mini Case: 5 - 13
graph. Interpret the CML. Now add a set of indifference curves, and illustrate how an investor's optimal portfolio is some combination of the risky portfolio and the risk-free asset. What is the composition of the risky portfolio ? Answer: The line r RF mz in the figure above is called the capital market line (CML) . It has an intercept of r RF and a slope of M RF M / ) r r ( . Therefore the equation for the capital market line may be expressed as follows: CML: . r r r r p M RF M ^ RF p The CML tells us that the expected rate of return on any efficient portfolio (that is, any Mini Case: 5 - 14 Expected Portfolio Return, ^ r p r RF risk, P
portfolio on the CML) is equal to the risk-free rate plus a risk premium, and the risk premium is equal to M RF M / ) r r ( multiplied by the portfolio's standard deviation, p . Thus, the CML specifies a linear relationship between expected return and risk, with the slope of the CML being equal to the expected return on the market portfolio of risky stocks, M r , minus the risk-free rate, r RF , which is called the market risk premium, all divided by the standard deviation of returns on the market portfolio, σ m . The figure above shows a set of indifference curves (i 1 , i 2 , and i 3 ), with i 1 touching the CML. This point of tangency defines the optimal portfolio for this investor, and he or she will buy a combination of the market portfolio and the risk-free asset. The risky portfolio, m, must contain every asset in exact proportion to that asset's fraction of the total market value of all assets; that is, if security g is x percent of the total market value of all securities, x percent of the market portfolio must consist of security g. Mini Case: 5 - 15 Expected Rate of Return, ^ r p r RF
i. What is a characteristic line? How is this line used to estimate a stock’s beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk. Answer: Betas are calculated as the slope of the characteristic line , which is the regression line formed by plotting returns on a given stock on the y axis against returns on the general stock market on the x axis. In practice, 5 years of monthly data, with 60 observations, would be used, and a computer would be used to obtain a least squares regression line.