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Bootstrapping Spot Rates from Treasury Security Prices

Article Quant Q&A · Author: Adnanur Rafi Takib
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Summary

The document presents a fixed-income pricing exercise: infer spot rates for successive maturities from the prices of Treasury bills and coupon bonds. The quoted securities include two bills and two bonds that pay coupons every six months. The task is to determine rates at each listed maturity from the cash flows and market prices.

The implied method is sequential bootstrapping. Use the shortest-maturity instrument to infer its discount rate, then apply the known shorter-maturity discount factors to the coupon payments of the next bond. Solve for the remaining maturity discount factor, and repeat for later maturities. The document provides instrument prices, coupon terms, and maturities, but no worked solution, convention for annualizing rates, or stated compounding basis. Accordingly, it poses a calculation rather than demonstrating numerical results; a reader must choose consistent rate conventions and perform the calculations.

Key ideas

  • Spot rates discount individual cash flows at their respective maturities.
  • Short-maturity bill prices provide the first discount factors in a sequential bootstrap.
  • Coupon bond prices can be decomposed into discounted coupon and principal cash flows.
  • Later maturity discount factors can be solved after earlier ones are known.
  • The exercise omits a worked solution and does not specify rate compounding conventions.

Tags

Fixed incomeStatistics
Full text
# Calculation of bond spot rates


# Calculation of bond spot rates












the cash prices of six months and one year treasury bills are \$120 and \$115 respectively. A 1.5 years bond that will pay coupons of \$5 every six months currently sells for \$121. A 2 years bond that will pay coupons of \$5 every six months currently sells for \$ 125. Calculate the six months, 1 year,1.5 years and 2 years spot rates.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.