Target Beta

An investment management firm wishes to decrease the beta of one of its portfolios under management from 1.15 to 0.65 for a five-month period. The portfolio has a market value of $200,000,000. The investment firm plans to use a futures contract priced at $102,500 in order to adjust the portfolio beta. The futures contract has a beta of 1.02.

A) Calculate the number of futures contracts that should be bought or sold to achieve a decrease in the portfolio beta.The number of the contracts should be a whole number.

B) At the end of 5 months, the overall equity market is down by 3.5%. The stock portfolio under management is down by 4.025%. The futures contract is priced at $98,840.75. Calculate the value of the overall position and the effective (realized or ex post) beta of the portfolio.

t = 0t = 5 mo

S =$200,000,000-4.025%

Beta(stock) = 1.15

Beta(tgt) = 0.65

f = $102,500$98,840.75

CHG(mkt) = 1%-3.50%