The cash prices of 6 -month and 1 -year Treasury bills are...

The cash prices of 6 -month and 1 -year Treasury bills are 94.0 and $89.0 .$ A $1 \frac{1}{2}$ -year, bond that will pay coupons of $\$ 4$ every 6 months currently sells for $\$ 94.84$. A 2 -year bond that will pay coupons of $\$ 5$ every 6 months currently sells for $\$ 97.12$. Calculate the 6 -month, 1 -year, $1 \frac{1}{2}$ -year, and 2 -year spot rates.

Key Concepts

Present Value

Present value is the current worth of a future sum of money or stream of cash flows given a specific rate of return, known as the discount rate. In bond pricing, each future cash flow, including coupon payments and the principal at maturity, is discounted back to the present using the corresponding spot rate, ensuring that the price of the bond reflects current market interest rates.

Treasury Bill Pricing

Treasury bills are short-term government debt instruments issued at a discount to face value. Their pricing does not involve coupon payments; instead, they are sold at a price lower than par and mature at par. The yield of a Treasury bill can be calculated based on the difference between its purchase price and its maturity value, and these yields are fundamental in establishing the initial spot rates in the bootstrapping process.

Spot Rate

A spot rate is the yield on a zero?coupon bond that pays a single cash flow at a specific future time. It represents the rate used to discount a cash flow to its present value for a given maturity, providing a pure measure of time value of money without the effects of interim cash flows such as coupon payments.

Bootstrapping

Bootstrapping is a sequential method used to derive spot rates from the prices of coupon-bearing bonds and other fixed-income securities. This method starts with the shortest maturity instrument (often a Treasury bill) to calculate its spot rate, and then uses that rate to discount cash flows of longer-maturity bonds in order to extract the next spot rate, continuing the process for each subsequent period.

Coupon Bond Pricing

Coupon bond pricing involves determining the bond's present value by discounting its periodic coupon payments and the final principal repayment at maturity using appropriate discount factors or spot rates. This approach reflects the time value of money and is integral to evaluating bond prices relative to prevailing interest rates.

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