 # duration question

Given the following two pairs of price and yield (price, yield): (94.064, 8.3%) and (98.469, 7.7%), the effective duration of the bond is: A) 7.63. B) 4.34. C) 2.75. D) 27.53.

I approximated the middle price p0 = avg = 96.2665 then using (p_ - P +) / ( 2 * p0 * delta r) = (98.469 - 94.064) / (2 * 95.2665 * .003) = 7.63 Choice A.

that’s correct, cpk123.

I’ll go with A. I can’t remember the exact formula now, Something like V± V-/2(V0)(delta y) but from just a quick estimate : %change in price=duration*change in yield (roughly without accounting for convexity) ((94.064-98.469)/98.469 )* 100= -4.47% = % change in price 4.47%/.6% = 7.46 …so I get A?

cool I am right. Thanks.

LongonCFA, Yes you are correct as long there is no option 7.47 on exam. I heard that CFAs who set up questions are really good in coming up with wrong “correct” answers.

Goel_ar, but sometimes there are q’s where you’ll save some precious time just by estimating things, like LongOnCFA’s done above. (though I’m not saying that computation of the original formula is big here :))

I’m with libra here. Suppose that the one-sided increment was lots different than the two-sided increment. That would mean that the left and right increments are way different which would mean something like the bond has some really short-dated embedded option or something. That would mean that effective duration is not particularly relevant which means that it would be a lousy question. One-sided is faster and gets you where you need to go.

how realistic is this question? I mean for a bond price to change with the same amount, (in money) if the yield goes up or down with an equal %amount that would mean that the bond would be situated on a specific point on the convexity curve. do you guys agree/dissagree?

That doesn’t happen here…

why not? cpk123 approximated the initial price as being the average of the to extremes that means that for equal changes in yield there are equal changes in the dollar amount

No it doesn’t - check it out by drawing a graph. If the bond price has positive convexity, the line whose slope is the duration crosses the curve at the two points and is in the interior between those two yields.

you are incorrect, florinpop. cpk123 did a good job approximating duration. however, bond prices don’t change by the same amount for equal increase and decrease of the yeild. look at example of a plain zero-coupon bond. if yields go down by 1% bond prices will increase more than they decrease if yields go down by 1%. convexity coefficient helps compensate a portion of that.

So are you telling me that if the yield changes from 8% to 8.3% the bond price should change(absolute value) by the same amount as if the yield changes from 8% to 7.7%?

No that should almost never happen unless you work really hard at making it so…

maratikus I didn’t say the problem was not solved right I was just asking how realistic that is since it implies exactly what you said a change in yield downward or upward creates the same change in price that would happen only if the bond yield would be in a particular spot on the curve.that was what I am trying to find out

florinpop in the absence of any other information for this question, how else are you supposed to arrive at an answer? There is no maturity provided. If that were provided, using the Bond function, and either of 8.3 or 7.7 Coupon rate could have been determined and then use that and the 8% YTM To arrive at the P0 price. In this case, in the absence of anything else, the avg was the only price you could arrive at.

but Joey by solving the problem the way ckp123 did wouldn’t you imply that?

correct cpk123 i agree with your answer but I had something else on my mind. i’m not judging your answer just try to understand better these concepts. I understand that is the way to solve the problem with the data given

florinpop, I’m glad that you question how others approach solving the problem. i posted the initial question because there are multiple approaches. My solution didn’t involve estimating the middle point, I just estimated duration roughly using the two points. Good discussion!