How to compute the futures contract price?

[sridhar]

"For example, assume a porfolio value of $10 million. The manager hedges with Tbond
futures (each contract delivers $100,000) with a current price of 98. She
thinks the duration of the portfolio at hedge maturity will be 6.0 and the duration
of futures contract with be 5.0. How many futures contracts should be shorted?"

I see the above problem on page 28 of the Mkt Risk Study Notes. You compute the futures price of the contract as 98,000 -- I "sort of" understand how you compute this, but I don't quite understand the "physics" of this:

Does each contract assume a $100 par value?


In the above problem, if you replaced "T bond" with "Corp bond" -- would everything be the same? Or would we need additional information to compute the futures contract price?

--sridhar

 

[David Harper CFA FRM]

Hi sridhar,

Note the "each contract delivers $100,000." This is by definition of the futures contract. Please note here the $100,000 is built-in definition.. Recall the key difference between forward and futures is the futures are standardized contracts that trade on exchanges. So, every future has a set of features common to all traders, including contract size; e.g., a corn futures contract is 5,000 bushels, in this way the price of a single corn futures contract will equal (futures price/bushel)*(5,000).

In this way, the T-bond contract delivers $100,000 of face value (par value) by definition.

"If you replaced "T bond" with "Corp bond"—would everything be the same?" Yes, it would essentially be the same. Instead of $98,000 (T-bond duration) in the denominator, we would replace with (Price of forward bond contract)(duration of same). Hope that helps

David