4. Answer the following questions; Suppose that the current one-year rate (one y

Question

4. Answer the following questions; Suppose that the current one-year rate (one year spot rate) and expected one-year T- bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows; ie-: 6%, iet+1-7%,ift+2-75%,11,t+,-7.85% Using the unbiased expectations theory, calculate the current long-term rates for one, two, three, and four-year maturity Treasury securities. Plot the resulting yields curve. B Suppose we observe the following rates: 11,-10%, i2.-14%, and in+1-10%. If the liquidity premium theory of the term structure of interest rates holds, what is the liquidity premium for year 2 C You note the following yield curve in the The Wall Street Journal. According to the unbiased expectation theory, what is the one-year forward rate for the period beginning two years from today fi,4+2? Maturity Yield one day 2.00% one year 5.50 two years 6.50 three years 9.00

Explanation / Answer

A. Long term rates as per the unbiased expectation theory will be as below:

1 Year = 6%

2 Year = [(1+6%) * (1+7%)]1/2 - 1 = 6.50%

3 Year = [(1+6%) * (1+7%) * (1+7.5%)]1/3 - 1 = 6.83%

4 Year = [(1+6%) * (1+7%) * (1+7.5%) * (1+ 7.85%) ]1/4 - 1 = 7.09%

B. Given that the 1 year rate is 10% and 1 year rate from Year 1 to end of Year 2 is also 10% but the 2 year rate from now is 14% hence the liquidity premium is 4%

C. Let us denote the 1 year forward rate for the period from Year 2 as X. Then we have :

(1+9%)3 = (1+5.50%) * (1+6.50%) * (1+X) ; solving for X, we get X = 15.26%

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