Question

Maria VanHusen, CFA, suggests that forward contracts on fixed-income securities can beused to protect the value of the Star Hospital Pension Plan’s bond portfolio against thepossibility of rising interest rates. VanHusen prepares the following example to illustratehow such protection would work:

• A 10-year bond with a face value of \(1,000 is issued today at par value. The bond pays an annual coupon.
• An investor intends to buy this bond today and sell it in six months.
• The six-month risk-free interest rate today is 5% (annualized).
• A six-month forward contract on this bond is available, with a forward price of \)1,024.70.
• In six months, the price of the bond, including accrued interest, is forecast to fall to$978.40 as a result of a rise in interest rates

a. Should the investor buy or sell the forward contract to protect the value of the bondagainst rising interest rates during the holding period?

b. Calculate the value of the forward contract for the investor at the maturity of theforward contract if VanHusen’s bond price forecast turns out to be accurate.

c. Calculate the change in value of the combined portfolio (the underlying bond and theappropriate forward contract position) six months after contract initiation.

Short answer

a. Selling futures contract

b. On the 4.98% YTM increase, the contact price in 6 months = $976.72

c. Increase in value of combined portfolio = 1.38

Step-by-step solution

Explanation on buy or sell of forward contract ‘a’

With the increase in rates, prices will fall. This will benefit the selling of futures contracts.

Calculation of the value of forward contracts ‘b’

$25 interest on bond will be accrued in 6 months. This will be subtracted from the price $978.40 to give the bond value of $953.40.

This implies the YTM of 5.3%

Let’s assume that the bond of the contract has 5% coupon and 10 year maturity. Hence the YTM on contract = 4.68%

This drop implies an increase in YTM of 30%.

Hence, on the 4.98% YTM increase, the contact price in 6 months = $976.72

Calculation of change in value of the combined portfolio ‘c’

The drop in contract price = 47.98 and (excluding accrued interest)

the drop in bond price = 46.60 (excluding accrued interest)

Thus increase in value of combined portfolio = 1.38 (because of short position in contract)