Question

Problem 9-14 Treasury STRIPS (LO3, CFA1)

U.S. Treasury STRIPS, close of business November 15, 2015:

Maturity	Price			Maturity	Price
November ’16		99.471		November ’19		95.035
November ’17		98.782		November ’20		92.570
November ’18		96.827		November ’21		89.342

a. Calculate the quoted yield for each of the STRIPS given in the table above. (Input all amounts as positive values. Do not round intermediate calculations. Enter your answers as a percent rounded to 3 decimal places.)

b. Does the market expect interest rates to go up or down in the future?

Answer 1

a). Price of STRIP = Face Value / (1 + r)ⁿ

STRIPS are semi-annually compounded.

For November '16:

99.471 = 100 / [1 + (y/2)]²

[1 + (y/2)]² = 100 / 99.471

1 + (y/2) = [1.0053]^1/2

y/2 = 1.0027 - 1

y = 0.0027 * 2 = 0.0053, or 0.53%

For November '17:

98.782 = 100 / [1 + (y/2)]⁴

[1 + (y/2)]⁴ = 100 / 98.782

1 + (y/2) = [1.0123]^1/4

y/2 = 1.0031 - 1

y = 0.0031 * 2 = 0.0061, or 0.61%

For November '18:

96.827 = 100 / [1 + (y/2)]⁶

[1 + (y/2)]⁶ = 100 / 96.827

1 + (y/2) = [1.0328]^1/6

y/2 = 1.0054 - 1

y = 0.0054 * 2 = 0.0108, or 1.08%

For November '19:

95.035 = 100 / [1 + (y/2)]⁸

[1 + (y/2)]⁸ = 100 / 95.035

1 + (y/2) = [1.0522]^1/8

y/2 = 1.0064 - 1

y = 0.0064 * 2 = 0.0128, or 1.28%

For November '20:

92.570 = 100 / [1 + (y/2)]¹⁰

[1 + (y/2)]¹⁰ = 100 / 92.570

1 + (y/2) = [1.0803]^1/10

y/2 = 1.00775 - 1

y = 0.00775 * 2 = 0.0155, or 1.55%

For November '21:

89.342 = 100 / [1 + (y/2)]¹²

[1 + (y/2)]¹² = 100 / 89.342

1 + (y/2) = [1.1193]^1/12

y/2 = 1.0094 - 1

y = 0.0094 * 2 = 0.0189, or 1.89%

b). Note that the term structure is upward sloping; the expectations hypothesis then implies that this reflects market expectations of rising interest rates in the future.