Yield Volatility (bonds) reading, current, course, former, higher

mfleming1983

I'm reading the last Reading in Fixed Income (hallelujah!) and of course, FI did not fail me in confusing the heck out of me on the last page of this section.

From page 549-550 of the textbook,

"..the higher the coupon, the lower the duration; the higher the yield level, the lower the duration. Given these two properties, a 10-year non-investment grade bond has a lower duration than a current coupon 10-year Treasury note since the former has a higher coupon rate and trade at a higher yield level. Does this mean that a 10-year non-investment grade bond has less interest rate risk than a current coupon 10-year Treasury note?...The missing link is the relative volatility of rates,... [aka] yield volatility or interest rate volatility.... The greater the expected yield volatility, the greater the interest rate risk for a given duration and current value of a position."

The book doesn't provide sufficient information as to what the relationship between duration and interest rate risk is, because what makes sense is that, the higher the yield volatility, the greater the interest rate risk, then the higher the duration. But the above example states otherwise - specifically, the higher the yield volatility, the greater the interest rate risk, then the lower the duration. How can we explain this?

Your explanation will prove your superiority in this facet of knowledge above all other Level 1'ers.

pogo

Most of the elements are negatively correlated with duration of a bond. So higher coupon rate lower duration or interest rate risk. Now also keep in mind that we are only talking about interest rate risk here or duration here though tere are other types of risk like credit risk; downgrade risk, default risk, creadit spread risk and many more which are reflected in yields of bonds.

Here what it says that if you have higher yield volatility for a GIVEN DURATION it will be more risky. Now keep in mind that Duration itself is an APPROXIMATION which is also related with CONVEXITY measures and its same as +ve or -ve convexity has affects on our duration measures. (GIVEN DURATION is the keyword here)

I still didn't really understand your point quite much it's better if you can be a bit more precise. Though I hope you still understood some

LokiDog2

Ahh, supersunny, you picked out what I dumbfoundedly overlooked. That it is for a GIVEN DURATION. Problem solved. Thanks so much, dude!

leadcfa

I suppose to understand this better, we need to look at the properties of duration (price volatility) first.

All other things constant, the higher the yield, the lower the duration , and vice versa. Also the higher the coupon rate, the lower the duration (less proportion of the total cash flows of the bond is subject to the greater impact of later discount factors as compared to an equivalent bond with a lower coupon). Finally, the longer the term to maturity, the higher the price volatility (duration). You can confirm these properties by using hypothetical numbers varying the coupon, yield or maturity as the case demands.

At least we agreed that the higher the expected yield volatility, the greater the interest rate risk. Now I suppose the issue is that from your observation, you think that since expected higher yield volatility leads to higher interest risk, it should lead to higher duration. But from the pages of the CFAI texts that you referred to earlier, remember that the coupon on the non-investment grade bond generally is expected to be higher as a result of additional risks (as pointed earlier by Supersunny138) than the coupon on the 10-year Treasury note, therefore, by the properties of duration, its duration is expected to be lower.

In conclusion, the bond with the higher yield is expected to have a higher yield volatility, higher interest rate risk, but its duration is expected to be lower as a result of its higher yield (one of the properties of duration).