Treasury Bond Dealer | Spot Rates, Bond Price, and Decision Making

Treasury Bond Dealer Observations

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Question

A Treasury bond dealer observes the following Treasury spot rates from the spot rate curve: 1-year 7.40%, 2-year 7.00%, and 3-year 6.3%. The bond dealer also observes that the market price of a 3-year 8% coupon, 100 par value bond is $103.95. Based on this information, the dealer should:

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Explanations

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A. B. C.

Explanation

To determine the appropriate course of action for the Treasury bond dealer, let's analyze the situation step by step:

  1. Calculate the present value of the bond's cash flows: The 3-year 8% coupon bond has a face value (par value) of $100, a coupon rate of 8%, and a coupon payment frequency of annual. The coupon payments are $8 per year (8% of $100).

Using the spot rates provided, we can discount each cash flow to its present value:

  • Year 1 coupon payment: $8 / (1 + 7.40%)^1 = $7.46
  • Year 2 coupon payment: $8 / (1 + 7.00%)^2 = $7.19
  • Year 3 coupon payment and face value: $8 / (1 + 6.30%)^3 + $100 / (1 + 6.30%)^3 = $7.82 + $82.92 = $90.74

The sum of these present values is $7.46 + $7.19 + $90.74 = $105.39.

  1. Compare the calculated present value with the market price: The market price of the 3-year 8% coupon bond is given as $103.95. Comparing this with the calculated present value of $105.39, we observe that the market price is lower than the bond's intrinsic value.

  2. Determine the appropriate course of action: Based on the information provided, the dealer should take advantage of the undervalued bond and buy it in the open market. By purchasing the bond for $103.95, which is below its intrinsic value of $105.39, the dealer can profit from the price discrepancy.

Option A, "buy the 8% coupon bond in the open market, strip it, and sell the pieces," is the correct answer. "Stripping" refers to separating the bond's cash flows into individual components (zero-coupon bonds) and selling them separately. This strategy allows the dealer to profit from the difference between the market price and the intrinsic value of the bond.

Option B, "sell the 8% coupon bond short and buy the component cash flow strips with the proceeds," is not appropriate in this case because selling the bond short would involve borrowing and selling a bond the dealer doesn't own. This action would be more suitable if the dealer believed the bond was overvalued.

Option C, "do nothing since the 8% bond is selling for its arbitrage-free price," is incorrect because the market price is below the bond's intrinsic value, indicating an opportunity for profit through arbitrage.

In summary, the dealer should buy the undervalued bond in the open market, strip it into its individual cash flow components, and sell them separately to profit from the price discrepancy.

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