Question

The following information applies to the next 6 questions.

Suppose that the stripped U.S. Treasury bonds were priced as follows in Jan 2015:
	Maturity (years)	Price
	1	96.1538
	2	90.7029
	3	83.9619

What is the estimated 1-year spot interest rate for Treasury securities?

What is the estimated 2-year spot interest rate for Treasury securities?

		3%
		4%
		5%
		6%
		7%

What is the estimated 3-year spot interest rate for Treasury securities?

		3%
		4%
		5%
		6%
		7%

What is the estimated forward interest rate for the 1-year period starting 1/1/2016?

		3%
		4%
		5%
		6%
		7%

Suppose there is a 3-year 10% coupon T-bond with annual coupon payment.  Based on the above stripped U.S. Treasury bond prices, what should be the price of the 10% coupon bond if there is to be no arbitrage opportunities. Assume the par value is $1,000.

		1,036.53
		1,041.33
		1,052.27
		1,065.17
		1,110.44

QUESTION 81

1. What is the yield to maturity of the above 3-year 10% T-bond?

   		4.87%
   		5.88%
   		6.33%
   		6.57%
   		7.78%

Answer 1

What is the estimated 1-year spot interest rate for Treasury securities?

1 year spot rate, S1 = FV / P1 - 1 = 100 / 96.1538 - 1 = 4.00%

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What is the estimated 2-year spot interest rate for Treasury securities?

2 year spot rate, S2 = (FV / P2)^1/2 - 1 = (100 / 90.7029)^1/2 - 1 = 5.00%

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What is the estimated 3-year spot interest rate for Treasury securities?

3 year spot rate, S3 = (FV / P3)^1/3 - 1 = (100 / 83.9619)^1/3 - 1 = 6.00%

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What is the estimated forward interest rate for the 1-year period starting 1/1/2016?

F12 = (1 + S2)² / (1 + S1) - 1 = (1 + 5%)² / (1 + 4%) - 1 = 6%

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Suppose there is a 3-year 10% coupon T-bond with annual coupon payment.  Based on the above stripped U.S. Treasury bond prices, what should be the price of the 10% coupon bond if there is to be no arbitrage opportunities. Assume the par value is $1,000.

Coupon = 10% x 1,000 = 100

Price = 100 / (1 + S1) + 100 / (1 + S2)² + (100 + 1,000) / (1 + S3)³ = 100 / (1 + 4%) + 100 / (1 + 5%)² + 1,100 / (1 + 6%)³ = $  1,110.44

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What is the yield to maturity of the above 3-year 10% T-bond?

YTM = RATE (Period, PMT, PV, FV) = RATE (3, 100, -1110.44, 1000) = 5.88%