4.09.2005

Q: What is the duration/convexity of...

...a 12%, 12-year, option-free bond selling at $125?

A: Duration = (V- - V+) / (2 * V0 * yield_change)

  • yield: with Excel Rate function, Nper = 24, PV=-125, PMT = 12/2, FV=100, which leads to rate= 4.31%. Annualize it one gets 8%.
  • Let yield change be 0.5% (50 bps)
    • for yield = 8.5%: Nper = 24, PMT = 12/2, Rate = (8.5/2)%, FV=100, PV = 126.01 = V+
    • for yield = 7.5%: Nper = 24, PMT = 12/2, Rate = (7.5/2)%, FV=100, PV = 135.20 = V-
  • Duration = (135.20 - 126.01)/(2 * 125 * 0.005) = 7.35

Convexity=(V+ + V- - 2*V0) / (2 * V0 * yield_change^2).

  • Convexity = (135.20 + 126.01 - 2*125) / (2*125*0.005^2) = 17.93

Bonus Points

  • It tells us that for 1% change in the required yield, the bond price will change by approximately 7.35%.
  • For a 10 basis point increase in yield, the approximate percentage price change is -7.35 x 0.001 x 100 = -0.74%
    • Approximate percentage price change = - duration x change in yield x 100
    • the negative sign due to the inverse relationship between price change and yield change - when yields increase, bond prices fall
  • Convexity adjustment takes into account the curvature of the price/yield relationship: convexity x yield_change^2 x 100 = 17.93*0.005^2*100 = 0.04%

Category: C++ Quant > Debt > Valuation

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