Finance Homework

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Homework #3. (Due: Oct 5) Name: (ID: ) Note: Hand-write your answer in the blank, then upload your (scanned or photo-copied) work in Canvas. 1) You run a regression of a stock’s returns versus a market index and find the following: Please interpret the above results in the context of CAPM. 2) What is the expected return on the market? If a stock is 100% more risky than the market, what is the expected return of this stock? In this economy, what is the risk free rate?

 

 

 

 

 

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3) If the simple CAPM is valid and all portfolios are priced correctly, which of the situations below is possible? Consider each situation independently, and assume the risk-free rate is 5%. (Hint: compute expected return for the below four case, using CAPM)

 

 

 

 

 

 

4) The risk premium for exposure to aluminum commodity prices is 4%, and the firm has a beta relative to aluminum commodity prices of .6. The risk premium for exposure to GDP changes is 6%, and the firm has a beta relative to GDP of 1.2. If the risk-free rate is 4%, what is the expected return on this stock? (Hint: Use APT) 5) There are two independent economic factors, M1 and M2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 25%. Portfolios A and B are well diversified. Given the data below, write a proper pricing model?

 

 

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6) Consider the single factor APT. Portfolio A has a beta of 1.3 and an expected return of 21%. Portfolio B has a beta of 0.7 and an expected return of 17%. The risk-free rate of return is 8%. If you wanted to take advantage of an arbitrage opportunity, you should sell (take a short position in) portfolio __(A or B)__ and buy (take a long position in) portfolio __(A or B)_. Write your reasoning. 7) Florida Enterprise has bonds on the market making annual payments, with the eight-year maturity, a par value of $1,000, and selling for $948. At this price, the bonds yield 5.9%. What must the coupon rate be on the bond? (a coupon rate is coupon payments over the face value)

 

 

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8) A coupon bond that pays interest (coupon) semiannually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 6%. If the coupon rate is 8%, the intrinsic value of the bond today will be __________. 9) Suppose that you are converting a well-diversified portfolio (Portfolio P) into an arbitrage portfolio.

The excess returns of Portfolio P can be explained by two factor APT model (i.e., = + ( ) +

( )

+ , where < 0 ( ) = 0, represent the two factors and the excess returns of Benchmark 1 and Benchmark 2). In this economy, there is a risk-free asset, the rate of which

is zero. Suppose α = −3%, ( ) = 1.2, ( ) = 0.8. To construct the arbitrage portfolio by using Portfolio P, do you need to sell or buy the portfolio? Show your arbitrage portfolio (i.e., you need to provide the weights of required assets). For this question, assume that your amount of buying or selling Portfolio P is one unit. What is your arbitrage profits (in percentage)?

 

 

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10) Compute the covariance and correlation between asset 1 and asset 2 and the covariance and correlation between asset 2 and asset 3.

 

State Probability Asset 1 Asset 2 Asset 3

Bad 0.3 0.03 -0.02 0.02

Normal 0.5 0.07 0.04 0.01

Good 0.2 0.11 0.05 -0.01