Hey guys,
I’m really struggling with a MM quiz solution. If credit spreads widen on corporate bonds while interest rates increase, the bonds empirical duration will be “greater than its effective duration”. Can anyone explain?
if credit spreads widen do empirical durations exceed effective durations and if they narrow the opposite is true?
Thanks
Pretty sure this is referring to the fact that effective duration ignores credit risk, focusing only on interest rate risk. With corporate bonds, especially as you go down the credit quality ladder, it is not only interest rate risk that impacts price movements, but also credit risk. So effective duration is not the best gauge for change in price when credit risk exists.
Empirical duration, since it observes actual historical price changes, better captures the interplay between interest rate risk and credit risk. If credit spreads widen, this has a negative pricing impact from a credit risk perspective. If at the same time benchmark interest rates increase, this also has negative price impact. Empirical duration would capture BOTH the negative price impact from interest rate risk AND credit risk, while effective duration would only incorporate the price impact of interest rate risk. Hence, if credit spreads widen, empirical duration > effective duration.
Can you xplain a bit more ?
By your version Emp. dur. Captures both Int. rate risk and Spread Risk as it observes Historical price movement , while ED only captures int. Rate risk. Is that so ?
Which quiz is this?
I don’t thing empirical duration can be wider than effective duration. Straight out of curriculum: “For all credit ratings, empirical duration is smaller than the theoretically based effective duration.” (Volume 4, reading 24, section 2.3)
If interest rates increase, credit spreads should decrease. And if interest rates decrease, credit spreads increase.
Yes. That is keeping one constant while the other changes. Further Emp. Dur. tracks the actual Historical Price Movement POORLY …which is why they are
In fact effective duration captures bond’s price sensitivity to interest rates change through a formula. It doesn’t measure the bond’s price sensitivity to credit spread change.
So, if interest rate rises, the bond price decreases but if in the same time credit spread widens the corporate bond price will decrease also.
Hence since the empirical duration takes into account only historical data, it will capture without distinction the negative and cumulative effect of both spread widening and interest rate increase on bond’s price.
As a conclusion, in that specific case empirical duration will be greater than effective duration.
can anyone write the FROMULA of empirical duration and analytical duration please?
Emeprical is done from observation of historical moves
Analystical - There are multiple version most seen at level 1
But
Approx mod.D = (change in price given yield shirt ip or down) / initiatl price x 2 x chnage yield