### CFA Practice Question

A portfolio manager has bought \$10 million market value of a bond issue that has a duration of 5. Estimate the change in market value for this bond if interest rates change by 50 basis points.
A. \$500,000
B. \$50,000
C. \$250,000
Explanation: Duration is an estimate of the percentage price change of a bond if interest rates change by 100 basis points or 1%. The formula is Approximate Percentage Price Change = - Duration * Change in Yield * 100. In this case, the formula is (-5) * (+/-.005) *100 = +/- 2.5%. Taking 2.5% of \$10,000,000 is \$250,0000 and adding / subtracting that from the original price gives \$10,250,000 / \$9,750,000. The reason for the negative sign on the right-hand side of the original formula is the inverse relationship between price change and yield change. A duration of 5 means that for every 100 basis point change in rates, we estimate the price of the bonds will change in the opposite direction by 5%.

User Comment
steved333 Duration is 100 bp. 5 is for 100 bp, so 2.5 is for 50 bp. \$250k is a multiple of that.
Xocrevilo D = ((change in P)/(P)) x (1/BPM)

5 = ((change in P)/(10m)) x (1/0.005)

change in P = 5 x 50,000 = 250,000
steved333 5*5 is 25. Then it's just a matter of decimal places and multiply by FV
mekc 50 bp = 0.005 = 0.5%
100bp = 1%
dipu617 I don't get it. In the duration formula, there is "2" in denominator!!! That makes the result 500,000. Anybody with an explanation??!!
dand1 You're not asked to use the formula for this one, you are already given the result of it which is 5.
mbuenafe right on xocrevilo.