A bond fund currently holds a bond portfolio with a face value of $$10$ million. The

current market value of the portfolio is only $92\mathrm{.}2\%$ 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.

a$.$ Given their rate expectations, should they short or go long in T$-$bond futures?

Explain.

b$.$ The risk managers use $$100,000$ face value T$-$bond contracts. If they use a $1-1($na$$ve$)$

hedge ratio between cash and futures positions, how many contracts should they use

if they hedge the market value of the portfolio??

c$.$ The deliverable bonds are $\frac{103}{4}\%$ with a conversion factor of $1\mathrm{.}2922.$ 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 $90\mathrm{.}2\%$ of face. The cash

amount transacted per contract is $\mathrm{.}97458$ 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.