4.02.2005

Q: Is there an arbitrage opportunity...

...given the following market data for $1000 par bonds?

Year .5 1.0 1.5 2.0
Market Price $900 $900 $900 $900
Coupon 10% 10% 10% 10%
Spot Rate 15% 16% 15% 14%

CppQuant Answer

One should buy the 2 year Treasury, strip the coupons and principal, and sell at the spot rates for a risk free profit of $30.67. The conclusion is based on discounting each cash flow at the prevailing spot rate.

  • Period 1 = 50 / (1+15%/2) = 46.51
  • Period 2 = 50 / (1+16%/2)^2 = 42.87
  • Period 3 = 50 / (1+15%/2)^3 = 40.25
  • Period 4 = 1050 / (1+14%/2)^4 = 801.04
  • Total cash flow PV = Period 1 + Period 2 + Period 3 + Period 4 = $930.67 > $900

Bonus Points

  • Reconstitution of strips also occurs when the strips in the market are priced less than the bond (will continue until the bond price does not vary materially from the arbitrage-free value.)

Category: C++ Quant > Debt > Valuation


The conclusion is based on the act that the implied YTM on the 2-year bond is higher than any individual spot rate. Using Excel's Rate function with Nper = 4, PV = -900, FV = 1000, PMT = 50, one gets rate = 8.03% * 2 = 16.06%.

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