The price of a zero-coupon bond with maturity 1 year is $943.40. The price of a zero-coupon bond with maturity 2 years is $898.47. For this problem, express all yields as net (not gross) rates. Assume the face values of the bonds are $1000.
What is the yield to maturity of the 1 year bond?
What is the yield to maturity of the 2 years bond?
Assuming that the expectations hypothesis is valid, what is the expected short rate in the first year?
Assuming that the expectations hypothesis is valid, what is the expected short rate in the second year ?
Assuming the liquidity preference theory is valid and the liquidity premium in the second year is 0.01, what is the expected short rate in the second year?
Assuming that the expectations hypothesis is valid, what is the expected price of the 2 year bond at the beginning of the second year?
What is the rate of return that you expect to earn if you buy the 2 year bond at the beginning of the first year and sell it at the beginning of the second year?
1.
Price of 1 year zero coupon bond = 943.40
face value = 1000
price = face value / ( 1 + S1)^1
where S1 is yield for 1 year
So
943.40 = 1000 / ( 1+S1)^1
so
S1 = 6%
2.
Price of 2 year zero coupon bond = 898.47
face value = 1000
price = face value / ( 1 + S2)^2
where S2 is yield for 2 year
So
898.47 = 1000 / ( 1+S2)^2
so
S2 = 5.5%
3.
Expected short rate for 1st year = S1 = 6%
4.
Expected short rate for 2nd year = 1f1
(1+S2)^2 = (1+S1)^1 * ( 1+1f1)
so
1f1 = 5.0024%
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