Homework+2+Solution

# Homework+2+Solution - Hong Kong University of Science and...

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1 Hong Kong University of Science and Technology FINA 3104: Investment Analysis and Portfolio Management Fall 2011 Instructor: Prof. Darwin Choi Homework Assignment 2 – Testing the CAPM/ Single-Index Model Suggested Solution Problem 1 – Betas a) (You do not have to answer this part in the write-up) Calculate the excess return for all the stocks and the S&P 500. The excess return on index/stock i at the end of month t is given by R i,t = r i,t – r f,t , where r i,t is the raw return on index/stock i in month t , and r f,t is the one-month U.S. Treasury bill rate in month t . b) Calculate the arithmetic average excess return for each of the stocks and the S&P 500. Also find the CAPM beta for each of the stocks, assuming that the S&P 500 is the market portfolio. (You can report these numbers in a table.) Solution: The average excess return for the S&P 500 is 0.07%. See the table in Problem 4 a) for the average excess returns and betas of the stocks. c) What is the beta of an equally-weighted portfolio of the 30 Dow stocks? (You can find the beta without constructing the equally-weighted portfolio.) Using the CAPM, what is the expected monthly return of this equally-weighted portfolio? Solution: The beta of the equally-weighted portfolio is 0.996 (which is the average beta of the 30 Dow stocks). Using the CAPM, the expected monthly return of this equally-weighted portfolio is 0.18% + 0.996*0.07% = 0.25%, where 0.18% is the average riskfree rate and 0.07% is the average excess market return. (Note: you could also use the most current riskfree rate, 0.01%, instead of 0.18%. This is because the current riskfree rate is the guaranteed rate you get if you invest now. If you use the current riskfree rate the expected monthly return of the equally-weighted portfolio will be 0.01% + 0.996*0.07% = 0.08%.)

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2 Problem 2 – Alphas a) Assume that the S&P 500 is the market portfolio. Calculate the alpha (i.e., the intercept) for each of the Dow stocks (again you can report these numbers in a table.) What is the alpha of an equally-weighted portfolio of the 30 Dow stocks? (Similar to Problem 1 c), you can find the alpha without constructing the equally-weighted portfolio.)
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## This note was uploaded on 11/27/2011 for the course FINA 3104 taught by Professor Darwin during the Spring '11 term at HKUST.

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Homework+2+Solution - Hong Kong University of Science and...

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