4.22.2005

Q&A: What's the porfolio's duration...

...given the following 3 types of option free bonds?

Bond Price # of Bonds
10%, 5-year $100 40,000
8%, 15-year $84.6275 50,000
14%, 30-year $137.8586 10,000

CppQuant Answer

Portfolio Duration = w(1)D(1) + w(2)D(2) + ... + w(k)D(k), where w(i) is the market value of bond i / market value of the portfolio (each yield must change by 100 basis points for the duration measure to be useful.)

  • Calculate yields for all bonds with Excel's Rate function: turns out yield1 = yield2 = yield3 = 10%
  • Calculate durations for all bonds with MDuration: D1 =MDURATION("jan 01, 2005","jan 01, 2010",10%,10%, 2) = 3.861. Repeat the same for D2=8.047, D3 = 9.168
  • Market Values: m1 = 40,000 * 100 = $4,000,000, m2 = 50,000* 84.6275 = $4,231,375, m3 = 10,000*137.85 = $1,378,586
  • w1 = $4,000,000/$9,609,961 = 41.6%; w2 = $4,231,375/$9,609,961 = 44%; w3 = $1,378,586/$9,609,961 = 14.4%
  • duration = 0.416*3.861 + 0.440*8.047 + 0.144*9.168 = 6.47.

For a 100 bp change in the yield of all three bonds, the porfolio value will change by about 6.47%. For a 50 bp change in the yield of all three bonds, the porfolio value will change by about 3.24% (= 6.47% / 2)

Category: C++ Quant > Debt > Valuation

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