Dollar Duration of Future Contracts

To increase the dollar duration => buy future contracts

To reduce the dollar duration => sell future contracts

Future contract price has opposition movement to the interest rate

*** Dollar duration of bond is negative!

Interest rate future has underlying an obligation whose value depends on interest rate.

Buy a contract (long) is to long the underlying and lock the investment rate (NOT borrowing cost)!!!

Therefore, buy a contract has –ve dollar duration!

Interest Rate Futures:

Price = face value/100 * futures price (e.g. 1million for face value in treasury bill, futures price depends on the yield)

Dollar Duration of Futures Contract:

= – effective duration * interest rate change * face value * contract price/100

=DD_CTD/conversion factor

Price Basis = spot price – futures delivery price

Cross Hedge: hedging portfolio with futures contract’s underlying securities not being the same

Hedge Ratio = Exposure of bond portfolio to risk factor/ Exposure of futures to risk factor

=DD_P/DD_CTD * conversion factor

Yield Beta = change of bond yield / change of futures yield

(change of bond yield = alpha + beta*change of futures yield + error_

Hedge Ratio = DD_P/DD_CTD * conversion factor * Yield Beta

Interest rate swap: fixed receiver increases duration, fixed rate paying reduces duration