### CFA Practice Question

Assume that you hold a portfolio of bonds as follows:

\$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 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