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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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Chapter 13 Solutions
Fundamentals of Corporate Finance with Connect Access Card
- Consider the following regression Pt * - Pt = .07(1.4) + .4*Pt (3.6) + et where Pt * is Shiller’s ex post price of a stock, Pt is the actual price and t-ratios are in brackets. Explain in words and analytically what the dependent variable Pt * - Pt should be equal to under the efficient markets theory. Hence interpret the regression. Does it support the efficient markets theory?arrow_forwardWhen working with the CAPM, which of the following factors can be determined with the most precision? a. The beta coefficient of "the market," which is the same as the beta of an average stock. b. The beta coefficient, bi, of a relatively safe stock. c. The market risk premium (RPM). d. The most appropriate risk-free rate, rRF. e. The expected rate of return on the market, rM.arrow_forwardThe slope of a regression line when the return on an individual stock's returns are regressed on the return on the market portfolio, would be: OAR BR-₁ B OC none of the answers listed here. ODO imarrow_forward
- When working with the CAPM, which of the following factors can be determined with the most precision? a. The most appropriate risk-free rate, rRF. b. The market risk premium (RPM). c. The beta coefficient, bi, of a relatively safe stock. d. The expected rate of return on the market, rM. e. The beta coefficient of "the market," which is the same as the beta of an average stock.arrow_forwardThe Beta coefficients of TSLA and JPM are 1.99 and 1.18 respectively. What does Beta measure and how is it interpreted? Explain the beta values of TSLA and JPM by providing a calculated example of how they relate to market returns.arrow_forwardThe correlation with Market index, Beta and CAPM Req. Return worked out manually.arrow_forward
- Assume that using the Security Market Line(SML) the required rate of return(RA)on stock A is found to be halfof the required return (RB) on stock B. The risk-free rate (Rf) is one-fourthof the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A(βA) to beta of B(βB).arrow_forwardAssume that using the Security Market Line (SML) the required rate of return (RA) on stock A is found to be half of the required return (RB) on stock B. The risk-free rate (Rf) is one-fourth of the required return on A. Return on market portfolio is denoted by RM. Find the ratio of beta of A (bA) to beta of B (bB). please show all workings and not merely : Ra = 1/2 rbRf = 1/4 Raarrow_forwardSuppose you have mean-variance utility function with a coefficient of risk Aversion-0, which stocks are preferred to P. E(r) III IP II IV Standard Deviationarrow_forward
- There are two assets 1 and 2, with returns X and Y correspondingly. Return X is a random variable with mean 1 and variance 1; return Y is a random variable with mean 1 and variance 3. We know that the expectation of X*Y is equal to 0. Find the share of asset 1 in the risk-minimizing portfolio.arrow_forwardSuppose the utility function is U = E(r) - 0.5Ao2. Draw the indifference curve corresponding to a utility level of 0.2 for an investor with a risk aversion coefficient of 3. Please note the vertical line indicates expected return, and plot standard deviation on the horizontal line.arrow_forwarda) Discuss the difference between a price-weighted index and a value-weighted index. Give one example for the price-weighted index and one example for the value-weighted index and discuss any problems/advantages associated with the specific indices. b) We assume that investors use mean-variance utility: U = E(r) – 0.5 × Ao², where E(r) is the expected return, A is the risk aversion coefficient and o? is the variance of returns. Given that the optimal proportion of the risky asset in the complete port- folio is given by the equation y* = E , where r; is the risk-free rate, E(rp) is the expected returm of the risky portfolio, o, is variance of returns, and A is the risk aversion coefficient. For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. Aoarrow_forward