# final_practice_4000_fall2008_answers - Name Practice Final...

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Name _________________ Practice Final Exam--Answers Fi 4000 Fall 2008 Problem 1 [25 points] Suppose the expected return of the market portfolio is μ m = 12%, the standard deviation of the market return is σ m = 18%, and the risk-free rate of interest is 5%. In addition, you have the following information on two risky assets in the marketplace: Asset Expected return Standard Deviation β A ? ? 1.2 B 10% 22% ? Assume the CAPM model assumptions hold. 1a. If the economy is in equilibrium, what is the expected return on asset A? 134 . 0 ) 05 . 0 12 . 0 ( 2 . 1 05 . 0 ) ] [ ( ] [ = - + = - + = f m A f A r r E r r E β 1b. If the economy is in equilibrium, what is the beta for asset B? From the CAPM, ) ] [ ( ] [ f m B f B r r E r r E - = - So 7143 . 0 05 . 0 12 . 0 05 . 0 10 . 0 ] [ ] [ = - - = - - = f m f B B r r E r r E 1

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Name _________________ 1c. Suppose you observe that there is a third risky asset C with expected return of 15% and beta of 1.4. Such an asset would be underpriced relative to A, B. (True/False) TRUE. Let’s calculate the expected return that would be consistent with the CAPM: 148 . 0 ) 05 . 0 12 . 0 ( 4 . 1 05 . 0 ) ] [ ( ] [ = - + = - + = f m C f C r r E r r E β In other words, the expected return is higher than it should be, so the price is lower than it should be. 1d. If there were an asset C as in part 1c. above, traders could make arbitrage profits by selling C and buying A (True/False) FALSE. You’d want to buy C and sell A. But in any event, such a trade would not be riskless. 1e. Is it possible for asset A to have a standard deviation of 16% in equilibrium? Explain. NO. To see this, use part 1a and compute the Sharpe ratios for asset A and for the market: 389 . 0 18 . 0 05 . 0 12 . 0 ] [ 525 . 0 16 . 0 05 . 0 134 . 0 ] [ = - = - = - = - m f m A f A r r E r r E σ That is, asset A would be more efficient than the market, which is not possible. 2
Name _________________ Problem 2 [25 points] BCD stock currently trades for \$80 per share. Each year, there are two possible outcomes. The stock price can either increase by 10% or decrease by 10%. The risk-free interest rate is 5% per annum. You work for an investment bank that has to write a European call option on BCD stock which expires in 12 months and has an exercise (strike) price of \$85. Assume that BCD is not expected to pay dividends in the next 12 months. 2a. Use binomial trees to describe the price processes of the stock and of \$1 invested in a risk-free bond. 3 S d = 72 S u = 88 S 0 = 80 B d = 1.05 B u = 1.05 B 0 = 1

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Name _________________ 2b. Calculate the no-arbitrage price of the European call option. Let’s first solve for the state prices d u q q , . Because these prices must be consistent with the stock and bond tree, we have two equations: d u d u q q q q 05 . 1 1.05 1 72 88 80 + = + = From the second equation, we have that d u q q + = 0.9524 Rearranging this to get an expression for u q and then plugging into the first equation, we have
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