Duration Hedging!

[itsyourz]

hi David,

here is an example question from FRM Handbook

a corporate treasurer wants to hedge a July 17 issue of $5 million of
commercial paper with a maturity of 180 days, leading to anticipated proceeds of
$4.52 million. The September Eurodollar futures trades at 92, and has a notional
amount of $1 million.

Compute
a. The current dollar value of the futures contract
b. The number of contracts to buy/sell for optimal protection

Answer
a. The current dollar price is given by $10,000[100 − 0.25(100 − 92)] =$980,000. -> why 10,000 notional amount?
Note that the duration of the futures is always three months
(90 days), since the contract refers to three-month LIBOR.
b. If rates increase, the cost of borrowing will be higher. We need to offset this by
a gain, or a short position in the futures. The optimal number is from Equation

N = - (180*4,520,000) / (90*980,000) = -9.2 -> why 4,520,000 is used instead of 5million?

thanks!!

suk

 

[dennis_cmpe]

I think $10,000 is the price of one Eurodollar futures contract

 

[skcd]

The 0.25 is a basis point change and hence 0.01 * 1mn = 10,000 So, 10K*[100 -0.25(100-EDFquote)]
4.52 because that is the proceeds for optimal hedge. Normal hedge would take into account 5mn which will lead to more negative position hence loss.
Delta N = Delta S * Ns - Delta F * Nf * Optimal hedge ratio.
If we set this to 0 we get optimal hedge ratio as per David's note and if we rather use hedge based on original contract value (here 5mn) we get a delta N as non zero (i might be screwing up some of the terms but the method is fine i guess)