 # Duration overestimates what?

Please explain: With respect to an option-free bond, when interest-rate changes are large, the duration measure will overestimate the: A) associated change in the bond’s rating. B) final bond price from a given increase in interest rates. C) increase in a bond’s price from a given increase in interest rates. D) fall in a bond’s price from a given increase in interest rates. Thanks S

You should think about this more because it’s the essence of convexity which is a really important investment concept.

i think D… wats the answer btw?

saurya_s Wrote: ------------------------------------------------------- > Please explain: > > With respect to an option-free bond, when > interest-rate changes are large, the duration > measure will overestimate the: > > A) associated change in the bond’s rating. > Interest rate chanages don’t cause changes in bond ratings (rating agencies do). > > B) final bond price from a given increase in > interest rates. > No because option-free bonds have positive convexity and convexity is always a good thing for the owner of a bond. Using duration alone, you will say that you will get beaten by an interest rate increase more than you actually will. > > C) increase in a bond’s price from a given > increase in interest rates. > That’s about the same statement as B) > > D) fall in a bond’s price from a given increase in > interest rates. > This is correct as explained above. > > Thanks > S

Is it true only when the bond is trading at discount? S

No, all non-callable bonds have positive convexity.

Joey, I meant the overestimation of fall (as calculated by duration ignoring convexity)- will it be there only if bond is trading st discount? Similarly, underestimation of price increase (as calculated by duration ignoring convexity) will only be when the bond is trading at premium? Thanks S

Saurya, the duration estimation of a decrease in bond price from an increase in interest rates will always over estimate the fall for a noncallable bond. As Joey noted, this is the essence of convexity. Just think of the Price-Yield graph of an option free bond. The duration is the slope of the line at the current yield point. So regardless if the bond is trading at a premium/par/discount, the duration estimate for any change (increase or decrease) in interest will underestimate the price of the bond. think visually of a tangent line to the price curve to help cement the idea.

or underestimate the increase in bond price from a given decrease in yield!

Huh, I looked at B as a bonds final price is usually par, so that is false. A doesn’t make sense, and rates increase, prices decrease, so it has to be D, not C. I need to look at that convexity stuff again and again…

Great point Char-Lee. I personally always go back to price/yield graph with this type of questions. Over/underestimation is easy to notice from the graph.

It’s D Duration underestimates price when there is a large change in the yield aka overestimates the fall in price

D is the only thing that makes sense. Remember that duration is a measure of a bond’s price’s sensitivity to a change in rates. Modified duration is (% change in value / % change in rate) for small changes in the rate. Remember that convexity is a concept related to duration and is infact the change in duration with respect to rates. Convexity accounts for the fact that a bond’s price actually drops less for a given rise in yields than it would rise for a drop in yields of the same magnitude. Without convexity - duration only - the drop is over-estimated. Thus D is the answer. One way to remember this is to remember that convexity is usually positive and benefits the investor. The investor benefits from the price dropping less than it would rise for the rate changes of the same magnitute. Convexity is negative only in cases where the bond becomes unattractive as the rates drop - this is the case when the lower rate makes it more likely that the bond will be called. Since the bond in the question is option-free, this does not apply and the answer is D.