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Finance Chapter 3 Hw

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Foundations of Finance Homework 3
Prof. Johannes Stroebel Due at the start of class 9

Topic 5: The Capital Asset Pricing Model
1. Assume the risk free rate equals Rf = 4%, and the return on the market portfolio has expectation E [RM ] = 12% and standard deviation σM = 15%. (a) What is the equilibrium risk premium (that is, the excess return on the market portfolio)? (b) If a certain stock has a realized return of 14%, what can we say about the beta of this stock? (c) If a certain stock has an expected return of 14%, what can we say about the beta of this stock? 2. You are given the following two equations: E(Ri ) = Rf + (E(RM ) − Rf )βi E(RM ) − Rf σp E(Rp ) = Rf + σM (1) (2)

You also have the following information: E(RM ) = .15, Rf = .06, σM = .15. Answer the following questions, assuming that the capital asset pricing model is correct: (a) Which equation would you use to determine the expected return on an individual security with a standard deviation of returns =.5 and a β = 2? Given the parameters above, what is the expected return for that security? (b) Which equation would you use to determine the expected return on a portfolio knowing that it is an efficient portfolio (consisting of the market portfolio M combined with the 1

risk-free rate)? If you were told that the standard deviation of returns on that portfolio is equal to σM and you were given the above parameters, what is the expected return on that portfolio? (c) Can you determine the β of the portfolio in (b)? (d) Given your answers above, expand on what type of risky assets equation (1) can be used for, and what type of risky assets equation (2) can be used for.

Topic 6: Arbitrage
The stock PolarBear.com trades on both the South Pole Stock Exchange and the North Pole Stock Exchange. 1. Suppose the price on the North Pole is $18. What does the No-Arbitrage Condition say about the price on

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