# Yield to Maturity

On February 24 a company decides to issue \$5 million in new bonds on May 24.They desire to issue them at their current coupon rate of 13.76%. They will be priced at par value with a 20-year maturity and duration of 7.22 years.However, if rates rise while due diligence is occurring, the market will factor that into the bonds’ value, resulting in less funds being raised. To deal with this, they decide to hedge the issue.

a. June futures contracts are trading at 68-11.The CTD bond underlying the contract has a yield of 13.60% and a projected duration of 7.83 years.

b. The optimal number of contracts is given by:

N* = (Pb X Db) (1+YTMctd)where

(Pf X Df ) (1+YTMb)

Pb = dollar value of bond portfolio at par

Db = duration of bond portfolio

Pf = dollar value of one futures contract at current price

Df = duration of CTD bond for futures contract

YTMctd = Yield to Maturity of CTD bond

YTMb = Yield to Maturity of the portfolio

c. Should they take a short or long position and why?

d. On May 24 the bonds are issued and the futures position closed out.The yield on comparable bonds is now 15.25%, so the bonds are issued at a 13.76 coupon but at a price of 90.74638/100 face.Compute the new value of the portfolio and how much it lost in value because of the rate change.

e. The futures price at close is now 60-25.Compute the gain on the futures position based on this and N*.

f. Compute the performance of the hedge.Did the hedged portfolio gain or lose value?

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