CFA Practice Question
Assume that you hold a portfolio of bonds as follows:
$5,000,000 par value of 10-year bonds with a duration of 8.047 priced at 84.6275
$1,000,000 par value of 30-year bonds with a duration of 9.168 priced at 137.8586
$6,000,000 of 5-year bonds with a duration of 3.861 priced at 100 (par)
$5,000,000 par value of 10-year bonds with a duration of 8.047 priced at 84.6275
$1,000,000 par value of 30-year bonds with a duration of 9.168 priced at 137.8586
Calculate the duration of the portfolio.
A. 6.0168
B. 5.5683
C. 7.0253
Explanation: The duration of the portfolio is simply the weighted average of the components. Each bond segment is first multiplied by its % of value (par, discount, premium) and then multiplied by its duration. Ultimately each segment is divided by the total % of par portfolio value. In this case, duration = ($6,000,000 x 3.861) / $11,609,961 + ($4,231,375 x 8.047) / $11,609,961 + (1,378,586 x 9.168) / $11,609,961 = 6.0168.
User Contributed Comments 11
| User | Comment |
|---|---|
| Figo | How was the $11,609,961 computed? |
| masha | 11,609,961 = 6,000,000+,4,231,375,1,378,586 (and the latter two are calculated as par value adjusted for discount / premium) |
| eddeb | Portfolio is measured at PV |
| babaj | weighted average |
| jerepast | discount or premium / par |
| twotwo | $11,609,961 = 6,000,000+4,231,375+1,378,586 first value at per $4,231,375 =84.6275*5,000,000 $1,378,586 =137.8586*1,000,000 |
| apiccion | Weigh each bond in the portfolio by its price * par value. Remember duration tells you the % change of the PRICE, so any calculation would need to incorporate price. |
| AUAU | just don't know the discount & premium! |
| mixer | Discount is when price of bond is below par while premuim is when price is above par value |
| shiva5555 | I hate these 3 or 4 trick problems. I always miss one of the tricks. |
| egypt | i think that we have 2 multiply weight by the duration i made this but i have got a difference answer |