FBE459_Homework2_solutions

FBE459_Homework2_solutions - UNIVERSITY OF SOUTHERN...

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UNIVERSITY OF SOUTHERN CALIFORNIA MARSHALL SCHOOL OF BUSINESS FBE 459 Financial Derivatives (P. Matos – Spring 2011) Homework 2 (Solutions): 1. Consider an investor who in June holds 20,000 IBM shares, each worth $100. The investor decides to use the August futures contract on the S&P500 to hedge (imperfectly) her exposure during the next month period. The current level of the index is 900 and the futures price is 908. To figure out her hedging strategy, she has collected a series of monthly returns on IBM and S&P500 index futures for the last 5 years and runs a regression. The Excel results are: SUMMARY OUTPUT: Dependent Variable: CHANGES IN IBM PRICE Regression Statistics: R Square = 0.88 Observations = 60 Coefficients Standard Error Intercept -0.001 0.0023 S&P INDX FUT CHANGES 1.10 0.106 1.a. What is the optimal hedge ratio? Can the investor hedge the market risk and still profit if IBM outperforms the market? SOLUTION: Hedge ratio = 1.1 , the slope of the regression (the beta of IBM). This is the hedge ratio that minimizes the risk (variance) of the hedged position. This hedge ratio does not cancel all the variation of IBM prices (the R-square is not 1). So IBM can go up more than the market (or drop less than the market) and the investor can benefit even if hedged the market variation. Naturally, the opposite can also happen and investor looses if IBM underperforms the market. 1.b. If each S&P500 futures is for the delivery of $250 times the index level, how many futures contracts should the investor trade? Should she go long or short on the futures? SOLUTION: Since the investor is long on IBM it needs to short S&P futures contracts. The number of contracts that should be shorted is: 69 . 9 250 908 100 $ 000 , 20 1 . 1 Rounding to the nearest integer the hedger shorts 10 contracts.
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1.c. Suppose IBM stock price drops to $90 during the month, and the S&P500 futures drops to 800. What has been the result of the hedge? Was it a good or bad decision to hedge? SOLUTION: If the firm had not hedged: - Loss on value of portfolio = 20,000 * ($90 - $100) = - $200,000 The result of the hedge strategy is: - Loss on value of portfolio = 20,000 * ($90 - $100) = - $200,000 - Profit from short SP futures trading = - 10 * $250 * (800 – 908) = $270,000 So net profit is a total of +$70,000
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This note was uploaded on 04/20/2011 for the course FBE 459 taught by Professor Matos during the Spring '08 term at USC.

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FBE459_Homework2_solutions - UNIVERSITY OF SOUTHERN...

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