# Duration

Assume that the price of a bond is currently 102.50. If interest rates increase by 0.5 percent the value of the bond decreases to 100 and if interest rates decrease by 0.5 percent the price of the bond increases to 105.5. Using this information, which of the following is a good estimate of the new bond price if the yield decreases by 1 percent from its current level? A) 108.00. B) 107.87. C) 108.14. D) 109.43.

A, right? (105.5-100)/(2*102.5*0.005)= 5.34=duration=percentage change in bond’s price for 1% change in yield, the new price would be 102.5*1.0534=108.0043

right

I disagree, i would have said D…here’s my reasoning. the price move on a 50bp rate move is down 2.5 vs. up 3…on a larger move, i.e., 100bps, the move up should be more than 3 twice, not less, so north of 108.5…clearly there is a fair amount of convexity to this bond, given the down move is 2.44% and the up is 2.96% on a 50bp move…it seems to me that curvature goes toward the asymptote and that however ridiculous the move seems in price on the up side, it is the only one that hold up to reason (unless it is a callable bond somewhere above 108…that’s my obvious answer choice…does anyone agree with this logic or am i sunk on this one?

petetini, I agree with you… the upside should be more than \$3 from \$105.5. and the only answer true from that is D.

unless it’s a callable bond of course, with a region of negative convexity. Don’t try to be too smart, the question is clearly asking for a duration approach.

So calculate the convexity and see what you get. C = (105.5 + 100 - 2*102.5)/(2*102.5*0.005^2) = 97.6 so adjustment is 97.6*0.005^2 = 0.0024 so that gives us 102.5*(1.0534 + 0.0024) = 108.22 which is more like answer C than D. C is certainly closer than A…

Agreed. But what would you have put in an exam?

On the exam they would tell you to calculate the price using either duration or duration and convexity. Anyway, the question asks what a good estimate would be, not the best estimate. A provides a good estimate and so does B, C, D.

I like the logic, but not the answer…interesting that the fourth option is 107.87, or minus convexity adjustment versus plus…that leads me to believe you are right…but i still like my logic of the answer having to be above 108.5…but i think JoeyD is right Its a BS question.