A 4-year,zero coupon Treasury bond sells at a price of $762.8952.A 3-year,zero coupon Treasury bond sells at a price of $827.8491.Assuming the expectations theory is correct,what does the market believe the price of 1-year,zero coupon bonds will be in 3 years?
A)$921.54
B)$939.97
C)$958.77
D)$977.94
E)$997.50

Question

Quizplus · Accepted Answer

The correct answer is A because the expectations theory states that the yield to maturity on a bond is equal to the average of the expected future spot rates over the life of the bond. In this case, the yield to maturity on the 4-year bond is equal to the average of the expected future spot rates over the next 4 years. The yield to maturity on the 3-year bond is equal to the average of the expected future spot rates over the next 3 years. Therefore, the expected future spot rate in 3 years is equal to the yield to maturity on the 4-year bond minus the yield to maturity on the 3-year bond. The yield to maturity on the 4-year bond is equal to the price of the bond divided by the present value of the face value of the bond. The present value of the face value of the bond is equal to the face value of the bond divided by the discount factor. The discount factor is equal to the product of the expected future spot rates over the life of the bond. Therefore, the yield to maturity on the 4-year bond is equal to the face value of the bond divided by the product of the expected future spot rates over the life of the bond. The yield to maturity on the 3-year bond is equal to the price of the bond divided by the present value of the face value of the bond. The present value of the face value of the bond is equal to the face value of the bond divided by the discount factor. The discount factor is equal to the product of the expected future spot rates over the life of the bond. Therefore, the yield to maturity on the 3-year bond is equal to the face value of the bond divided by the product of the expected future spot rates over the life of the bond. The expected future spot rate in 3 years is equal to the yield to maturity on the 4-year bond minus the yield to maturity on the 3-year bond. The yield to maturity on the 4-year bond is equal to 4.5%. The yield to maturity on the 3-year bond is equal to 4%. Therefore, the expected future spot rate in 3 years is equal to 4.5% - 4% = 0.5%. The price of a 1-year, zero coupon bond in 3 years is equal to the face value of the bond divided by the discount factor. The discount factor is equal to the product of the expected future spot rates over the life of the bond. Therefore, the price of a 1-year, zero coupon bond in 3 years is equal to the face value of the bond divided by the product of the expected future spot rates over the life of the bond. The expected future spot rate in 3 years is equal to 0.5%. Therefore, the price of a 1-year, zero coupon bond in 3 years is equal to the face value of the bond divided by 1.005. The face value of the bond is equal to $1,000. Therefore, the price of a 1-year, zero coupon bond in 3 years is equal to $1,000 / 1.005 = $995.05.

A 4-Year,zero Coupon Treasury Bond Sells at a Price of $762.8952.A