Question

It is March and Bank A is concerned about what an increase in interest rates will do to the value of its bond portfolio. The portfolio currently has a market value of $101.1 million and Bank A management intends to liquidate $1.1 million in bonds in June to fund additional corporate loans. If interest rates rise to 6% the bond will sell for $1 million with a loss of $100000.Bank A's management sells 10 June Treasury bond contracts at 109-050 in March. Interest rates do go up, and in June Bank A's management offsets its position by buying 10 June treasury bond contracts at 100-030.

a) What is the dollar gain/loss to Bank A from the combined cash and futures market operations described above?

b) What is the basis at the initiation of the hedge?

Answer 1

The treasuries are quoted with increments of 1/32 of a dollar. Hence, the price of the futures contract is as follows-

109-050	=109+ (5/32)	109.15625
100-030	=100+ (3/32)	100.09375

Initial value of bond position to be hedged is $1.1 Mn, Hence, the bank must sell contracts worth $1.1 Mn. The multiplication factor for the 10-year treasuries contracts is $1000
No of contracts=
1,100,000/(109.15625*1000)
=10.0773

Since partial contracts are not available, the bank will purchase number of contract equal to nearest integer that is 10 contracts. Each contract has a face value of $100,000
Actual value of treasuries sold=
10*109.15625*1000
=$1,091,562.5

Basis risk = Base position value - hedged position value
=1,100,000-1,091,562.5
= $8,437.50

This difference in the underlying asset value and the hedging contract value is the basis risk.

Gain/loss from hedged positions

Loss on cash (bond) position=
1,000,000-1,100,000
= $(100,000)

Gains from futures hedge position=
10*(109.15625-100.09375)*1000
= $90,625

Overall gain/ loss on the combined position=
90,625-100,000
= $(9,375)