Question

An FI has a $100 million portfolio of six-year Eurodollar bonds that have an 8 percent coupon. The bonds are trading at par and have a duration of five years. The FI wishes to hedge the portfolio with T-bond options that have a delta of −0.625. The underlying long-term Treasury bonds for the option have a duration of 10.1 years and trade at a market value of $96,157 per $100,000 of par value. Each put option has a premium of $3.25 per $100 of face value. a. How many bond put options are necessary to hedge the bond portfolio? b. If interest rates increase\

Answer 1

A. 823.74

B.$4,614,028.00 gain

C.-$4,629,629.63

D.$2,678,000

Step-by-step explanation:

a.

Np= Bond Portfolio Value/δ*B*D

=$100,000,000/-0.625*-10.1*$96,157

=823.74

Approximately 824 Contract

b.

A $100,000 20-year, eight percent bond selling at $96,157 implies a yield of 8.4 percent.

∆P = ∆p * Np= 824 * -0.625 * -10.1/1.084 * $96,157 * 0.01 = $4,614,028.00 gain

c.

∆PVBond= -5 * .01/1.08 * $100,000,000 = -$4,629,629.63

d.

The price quote of $3.25 is per $100 of face value. Hence the cost of one put contract will be $3,250 while the cost of the hedge

= 824 contracts * $3,250 per contract

= $2,678,000.