1. A bond portfolio manager holds three bonds in her portfolio. Bond 1 has a mar

Question

1. A bond portfolio manager holds three bonds in her portfolio. Bond 1 has a market value of $25,000,000 and a duration of 2, bond 2 has a market value of $13,300,000 and a duration of 8,5, bond 3 has a market value of $32,343,000 and a duration of 13. What is the duration of the portfolio?

2. Consider a 25-year 6% coupon bond priced at 70.357 (par value is $100) with yield to maturity of 9%. Compute the approximate duration for a 10 basis point change in yield (use 0.001 for delta y in the approximate duration formula).

Explanation / Answer

1

Portfolio Duration=(25000000*2+13300000*8.5+32343000*13)/(25000000+13300000+32343000)=8.259969

2

Semi-annual coupons

Price when yield is 9%=70.357

Price when yield falls by 0.1%=71.11049

Price when yield rises by 0.1%=69.61636

So approximate duration=(71.11049-69.61636)/(2*70.357*0.1%)=10.6182

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