Based on the price sensitivity hedge ratio approach,what is the optimal number of futures contracts to deploy,given the following information.The yield beta is 0.65,the present value of a basis point change for the underlying bond portfolio is $33,000,and the present value of a basis point change for the bond futures contract is $325.(Select the closest answer. )
A)long 100 futures contracts
B)long 55 futures contracts
C)short 66 futures contracts
D)short 22 futures contracts
E)short 11 futures contracts

Question

Quizplus · Accepted Answer

The optimal number of futures contracts can be determined using the following formula:

Number of contracts = (Yield beta x Portfolio value) / (Futures beta x Futures value)

where:
- Yield beta = 0.65
- Portfolio value = unknown
- Futures beta = 1 (all futures contracts have a beta of 1)
- Futures value = $325

To solve for Portfolio value:
Portfolio value = (Number of contracts x Futures beta x Futures value) / Yield beta

Portfolio value = (Number of contracts x $325) / 0.65

Portfolio value = 500 x Number of contracts

Now we need to calculate the value of a basis point change in the portfolio:

Value of a basis point change = Portfolio value x 0.0001 x $33,000

Value of a basis point change = (500 x Number of contracts) x 0.0001 x $33,000

Value of a basis point change = $165 x Number of contracts

Since we want to long or short the futures contracts, we need to compare the values of a basis point change in the portfolio and in the futures contract.

Value of a basis point change in the futures contract = $325 x 0.0001 = $0.0325

If the value of a basis point change in the portfolio is greater than the value of a basis point change in the futures contract, we need to short the futures contracts. If the value of a basis point change in the portfolio is lower than the value of a basis point change in the futures contract, we need to long the futures contracts.

In this case:

Value of a basis point change in the portfolio = $165 x Number of contracts = 0.165 x Portfolio value

Value of a basis point change in the futures contract = $0.0325 x Number of contracts

0.165 x Portfolio value > $0.0325 x Number of contracts

500 x Number of contracts x 0.165 > 500 x Number of contracts x $0.0325

Number of contracts < 66.15

Therefore, we should short 66 futures contracts, which is the closest answer.

Based on the Price Sensitivity Hedge Ratio Approach,what Is the Optimal