# Spot and Forward Rates embedded in treasury bond prices: calculate cash & profit

A) What spot and forward rates are embedded in the following treasury bonds? The price of one-year (zero coupon) treasury bills is 93.46 percent. Assume for simplicity that bonds make one annual payment. Hint: Can you devise a mixture of long and short positions in these bonds that gives a cash payoff only in year 2? In year 3?

Coupon (%) Maturity (years) price (%)

4 2 94.92

8 3 103.64

B). A three-year bond witha 4 percent coupon is selling at 95.00 percent. Is there a profit opportunity here? If so, how would you take advantage of it?

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#### Solution Preview

A. In all cases, recall that the price of a bond is the discounted value of its flow of payments. Let's assume for simplicity that all bonds have a face value of 100.

The Treasury bill will then pay 100 in a year. Its price now is 93.46. Since the value of this bond is the discounted value of its flow of payments (there is only one payment, one year from now), we have that:

93.46 = 100/(1+r1)

Where r1 is the spot one-year interest rate. From this equation, we get:

1+r1 = 100/93.46

r1 = 0.07 (rounded)

So the spot one-year interest rate is 7%.

In order to calculate the implied interest rate for the next year, we use the second bond. Since the face value is 100 this bond pays 4 one year from now and 104 (coupon + face value) two years from now. Again, we use the bond value formula and isolate the interest rate from there:

94.92 = 4/(1+r1) + 104/[(1+r1)(1+r2)]

We ...

#### Solution Summary

The solution presents a very detailed explanation of how to profit with treasury bonds. The calculations are included.