I’ve just learnt the formula for calculating the effective duration (not complicated, but I need to get used to %, basis point & decimal quicker). I came across the following question: “A 30-year semi-annual coupon bond issued today with market rates at 6.75 percent pays a 6.75 percent coupon. If the market yield declines by 30 basis points, the price increases to $1,039.59. If the market yield rises by 30 basis points, the price decreases to $962.77. Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?” The first thing I noticed was that they were asking for an approximate percentage change in price for a 100 basis point change, when they provided the values for 30 basis point each way (so, from my understanding, 60 basis point change). I took the time to recalculate the values if the market declines by 50 basis point ($1067.37) and rises by 50 basis point ($939.17), and applied the formula: (1067.37-939.17)/(2 * 0.005 * 1000) = 12.8% approx (okay, I made the mistake of using 0.05 instead of 0.005 which gave me the wrong answer), which is one of the answer available. In their solution however, they used the difference of the original values along with 0.003 and arrived to the same answer. So before I go on to assume that approximation goes a long way (and saves a lot of time), can I check if the way I calculated is technically (though unecessarily) the ‘correct’ way to calculate a percentage change in price for 100 basis point? [Or am I misunderstanding something and the fact that I can come to the right answer is fluke]. Thanks.
I get an effective duration of 12.80 using the following forumula: Duration is not a percent. (1,039.59 - 962.77) / 2*.003*1000 “Which of the following choices is closest to the approximate percentage change in price for a 100 basis point change in the market interest rate?” 12.80 = Change P / Change Yield = 12.80*.01 = 12.80%
The “effective duration” gives you just an estimate for the change in bond price. It’s likely to be really good for moves similar to the increment you used to calculate it and get worse the farther out you get (or even the further in you get, maybe). Since you would use it for bonds with options, the accuracy of the calculation depends on things like the gamma of the embedded options, the convexity of the bond without options, and whatever else changes the value of the bond in non-linear ways.
TooNice Wrote: ------------------------------------------------------- > > > In their solution however, they used the > difference of the original values along with 0.003 > and arrived to the same answer. So before I go on > to assume that approximation goes a long way (and > saves a lot of time), can I check if the way I > calculated is technically (though unecessarily) > the ‘correct’ way to calculate a percentage change > in price for 100 basis point? . Hey if us see cfa textbook equity and FI vol 5 pg 489 it says "duration is interpreted as approx price change per 100 basis point change in rate. " This means if we use yield of 30 and compute duration, it still means price change per 100 basis point. Even i got confused here and this is what I understand .
Yeah, I’ve seen that a bunch of times and part of it is that Fabozzi hates the derivative (like calculus kinda derivative) interpretation of duration and CFAI is resolute in not expecting that people have passed high school calculus to be a finance professional (ask me my opinion on that). That means that they write weird stuff like that. In particular, if that’s the definition of duration the duration of a zero is no longer the maturity of the zero. That’s a pretty big probem with that definition.