Hi David,

i did not get this formula for the question:

Suppose a 20-year annual coupon bond has a DV01 of 0.14865. Also suppose a 12-year annual coupon
bond, which will be used as the hedging instrument, has a DV01 of 0.09764. If the yield beta is 1.10,
which of the following statements accurately describes the situation?
a. The hedging instrument is significantly more volatile than the position in the 20-year bond, and the
hedge ratio is 1.67467.
b. The position in the 20-year bond is significantly more volatile than the hedging instrument, and the
hedge ratio is 0.72253.
c. In order to have a perfectly hedged position, for every USD 1 of the 20-year bond, USD 1.67467 of
the 12-year bond should be shorted.
d. In order to have a perfectly hedged position, for every USD 1 of the 20-year bond, USD 0.72253 of
the 12-year bond should be shorted.

Answer: c- Hedge Ratio = (0.14865 x 1.10) / 0.09764 = 1.674672. Interpretation in answer ‘C’ is
accurate for hedge ratio.

Ravi

Hi Ravi,

I don’t think “yield beta” is found in our assignments.

It refers to spread change between the two instruments, so if the one yield changes by 1%, the other changes by 1% multiplied by the yield beta. So the multiplier is adjusting the DV01 because without the adjustment, to hedge with DV01 is to assume both bonds are impacted by the same 1% yield change. Also, I think the question is imprecise for not saying “the yield beta of the one bond with respect to another”

But if the yield curve shifts by +1% for one bond, and the other has a yield beta of 1.1, then it means we expect a spread (between the two yields) to widen such that the other bond yield changes by 1% *1.1 = 1.1%. So we have to multiply this adjustment to ensure the dollar hedge (DV01) is accurate.

David