Question

Today (10/13/20), the prices on zero-coupon US Treasury STRIPS are as follows: Maturity Price Effective Annual In years (per $1000 in face value) YTM 1 985.000 ______________ 2 952.000 ______________ 3 917.500 ______________ 4 871.442 .0350000 5 821.927 .0400000 Questions: a. What are the yields to maturity for each of these zeros? Fill in the banks above. (3 points, 1 point each) b. You think that short-term interest rates will rise over the next year. In particular, you think that the 1-year and the 2-year rates will be higher than they are currently. If you invest in the two-year now and sell it in one year, will your return be higher or lower than what you could get by investing in the one-year and holding it until maturity? If it depends, what does it depend upon? (5 points)

Answer 1

To find the yields to maturity for each of these zeros, we have to use the zero coupon bond formula:

Zero Coupon Bond Value = F / (1 + r)^t

Here, F = Face Value = $1,000, r = YTM, t = time period (years)

This formula has been used for the years 4 and 5.

This can be verified by putting in the values, for say, 4 years maturity:

871.442 = 1,000 / (1 + r)⁴

On solving, you get r = 0.0350000

Hence proved.

Using this formula to find the YTM of year 1:

985 = 1,000 / (1 + r)¹

r = 0.0152284

Similary, YTM for years 2 and 3 can be calculated.

Ans =

1. r = 0.0152284

2. r = 0.0249000

3. r = 0.0291167