Concept explainers
Beta is often estimated by linear regression. A model commonly used is called the market model, which is:
In this regression, Rt is the return on the stock and Rft is the risk-free rate for the same period. RMt is the return on a stock market index such as the S&P 500 index. αi is the regression intercept, and βi is the slope (and the stock’s estimated beta). εt represents the residuals for the regression. What do you think is the motivation for this particular regression? The intercept, αi, is often called Jensen’s alpha. What does it measure? If an asset has a positive Jensen’s alpha, where would it plot with respect to the SML? What is the financial interpretation of the residuals in the regression?
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EBK FUNDAMENTALS OF CORPORATE FINANCE A
- Security A has an expected rate of return of 6%, a standard deviation of returns of 30%, a correlation coefficient with the market of −0.25, and a beta coefficient of −0.5. Security B has an expected return of 11%, a standard deviation of returns of 10%, a correlation with the market of 0.75, and a beta coefficient of 0.5. Which security is more risky? Why?arrow_forwardYou have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?arrow_forwardWhat is a characteristic line? How is this line used to estimate a stocks beta coefficient? Write out and explain the formula that relates total risk, market risk, and diversifiable risk.arrow_forward
- Which of the following statements is CORRECT? (Assume that the risk-free rate is a constant.) a. The effect of a change in the market risk premium depends on the slope of the yield curve. b. If the market risk premium increases by 1%, then the required return on all stocks will rise by 1%. c. If the market risk premium increases by 1%, then the required return will increase by 1% for a stock that has a beta of 1.0. d. The effect of a change in the market risk premium depends on the level of the risk-free rate. e. If the market risk premium increases by 1%, then the required return will increase for stocks that have a beta greater than 1.0, but it will decrease for stocks that have a beta less than 1.0.arrow_forwardSuppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?arrow_forwardThe market and Stock J have the following probability distributions: Probability rM rJ 0.3 15% 20% 0.4 9 5 0.3 18 12 Calculate the expected rates of return for the market and Stock J. Calculate the standard deviations for the market and Stock J. Calculate the coefficients of variation for the market and Stock J.arrow_forward
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