Question

12. Stock Hedges You manage a well diversified portfolio of $21 million. The stock portion of your portfolio is 60% and it has a beta of 1.20. The other 40% of the portfolio is in riskless investments held for liquidity purposes. You want to change the complete portfolio beta to 0.90 using stock index futures. The futures contract has a multiplier of 250 and is priced at 1240. Should you buy or sell the contracts and how many contracts should you use?

a. buy 68 contracts b. buy 12 contract c. sell 12 contracts d. sell 68 contracts

Answer 1

Beta of protfolio = ?(beta of individual security* weight of security)

• ? of stock portfolio = 1.20
• ? of riskless invetsment = 0.00

? portfolio =(1.2*0.6)+(0*0.4) = 0.72

Since, we need to increase our portfolio ? from 0.72 to 0.90, we need to buy index futures contracts.

Number of contracts:, where:

• ?_P = Your portfolio’s current beta =0.72
• ?_T = Target beta, or where you would like your portfolio's beta to be =0.90
• Vp = The current market value of your portfolio =21 million
• ?_f = The beta of the equity futures contract that you will be buying or selling in order to adjust your portfolio's beta =1.00 (stock market index has a ? of 1.00)
• P_f = The unit price of the futures contract that you will be buying or selling =1240

Numbe of contracts = ((0.9-0.72)/1)*(21000000/(1240*250)) = 12.19 (approx)

Therefore: Ans. b. BUY 12 contracts

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