Question

a) A treasury STRIPS with 13 years until maturity has a face value of $10,000.   It’s trading at a price of $4,131. What’s the YTM of the STRIPS?

b) Suppose the real rate is 2% and the inflation is currently at 2.5%.   What will you expect the yield on the treasury bills?  

c) A coupon bond with 5 years to maturity has a face value of $1,000 and a coupon of $40 a year.   It’s trading at a price of $950.   What’s the coupon rate and current yield?

Answer 1

Answer a.

Par value = $10,000
Current price = $4,131
Time to maturity = 13 years
Semiannual period = 26

Let semiannual YTM be i%

$4,131 = $10,000 / (1 + i)^26
(1 + i)^26 = 2.420721
1 + i = 1.0346
i = 0.0346 or 3.46%

Semiannual YTM = 3.46%

Annual YTM = 2 * 3.46%
Annual YTM = 6.92%

Answer b.

Nominal return = (1 + Real return) * (1 + Inflation rate) - 1
Nominal return = (1 + 0.02) * (1 + 0.025) - 1
Nominal return = 1.0455 - 1
Nominal return = 0.0455 or 4.55%

Answer c.

Coupon rate = Annual coupon / Face value
Coupon rate = $40 / $1,000
Coupon rate = 0.04 or 4.00%

Current yield = Annual coupon / Current price
Current yield = $40 / $950
Current yield = 0.0421 or 4.21%