p1.t3.r12.c6.q4 Effects of Volatility on Duration.

[Pflik]

I'm looking at question 4 of reading 12 chapter 6.

if a bond portfolio with a duration of 9.0 years is hedged with futures contracts in which the underlying asset has a duration of only 3.0 years, but the volatility of the 3 year interest rate is greater than the volatility of the 9 year interest rate, what is the likely impact on a duration based hedge?

now my first impression was that volatility is not taken into account with the formula: n*=(PDp)/FcDf

but reading the limitations it made me realize that it doesn't apply in this question...

However i'm still trying to figure out why the portfolio would be overhedged? Is it because you use a future and the price of the future is higher, due to the increased volatility? (i.e. forward = future -1/2o^2 t1 t2)

Also what i understood from duration was that the lower duration has less sensitivity to volatility. So it would make me believe that the hedge would be less affected by the volatility

 

[David Harper CFA FRM]

Hi Pflik, see discussion thread here at http://forum.bionicturtle.com/threa...es-and-duration-based-hedges.4570/#post-15713 i.e.,

Say you have a $1 million portfolio (duration = 9.0 years) hedged with (generic!) futures contracts priced at $100,000 (duration = 3.0 years). So you hedge a long (short) position with short (long) 30 contracts = ($1 mm * 9)/(100K * 3) = 30 contracts. That's the typical duration hedge which is predicated on small, parallel yield curves, for example:
If rates increase by 1%, the portfolio LOSES by 1%*9 years*$ 1 million = $90,000 but the futures contract hedges with 1%*3 years*(30 contracts *$100,000 per) = +90,000. Hedge works!

But consider the non-parallel shift implied by a short rate that is more volatile:

Long rate goes up 1% but short rate goes up 2%: futures hedge gains $180,000 which is +$90,000 more than the loss,
Long rate goes down by 1% but short rate goes down by 2%: futures hedge loses $180,000 which is -$90,000. This is an "over-hedge," in my simple example, a more accurate hedge would use FEWER contracts and produce less offsetting gain but also less offsetting loss.