Dollar Loss

A bond fund currently holds a bond portfolio with a face value of $10 million.The current market value of the portfolio is only 92.2% of face, however.The fund’s managers anticipate a rise in bond yields (interest rates) in the near future, so they desire a T-bond hedging strategy to protect themselves.

• Given their rate expectations, should they short or go long in T-bond futures? Explain.
• The risk managers use $100,000 face value T-bond contracts.If they use a 1-1(naïve) hedge ratio between cash and futures positions, how many contracts should they use if they hedge the market value of the portfolio??
• The deliverable bonds are 10 ¾% with a conversion factor of 1.2922.If accrued interest is zero, what cash amount would be transacted per contract if the quoted futures price is 76-31?

d.At close, the market value of the bond portfolio is now 90.2% of face.The cash amount transacted per contract is .97458 times the face value of the futures contract.Calculate the loss in the bond portfolio’s market value versus the change in value of the hedge.

e.Did the hedge work?Explain.

2.A portfolio manager has an equity portfolio that is valued at $75 million.The

portfolio has a current beta of .9 and a dividend yield of 1%.It is currently August 15 and the manager is concerned that markets are volatile and the portfolio could lose value, so they decide to hedge.

a.The manager will use the S&P 500 index contracts to hedge.The contract is settled in cash at $250 times the contract price.The current S&P index value is 1484.43 and a December S&P 500 index contract has a price of 1517.20

b.Based on these expectations, should they take a short or long futures position and why?

c.An optimal number of contracts is N* = (Dollar value of the portfolio/dollar value of one futures contract) X portfolio beta.

d.Based on (c) above, compute N* and set up the appropriate hedge.

e.On December 15 the position will be closed. The current S&P 500 index is 1410.20 and the current contract matures, so convergence takes place. Compute the percentage loss in the S&P index and the percentage loss in the portfolio, which will be (% loss in market X portfolio beta).

f.Compute the dollar loss on the portfolio, the dollar change in the futures position, and any dividends earned on the portfolio (3 months).Add these up to get the total hedged portfolio value.

g.How good was the hedge? Answer this by comparing the change in the market value of the portfolio to the change in the futures position.