An investor is indifferent to the maturities of securities, as long as the yield

Question

An investor is indifferent to the maturities of securities, as long as the yields are the same. Today, a security with one year to maturity has a known yield of 6.20%, and a security today with three years to maturity has a yield of 8.47%. If the investor decides to invest in the security with one year to maturity today and a security with two years to maturity one year from today, what yield would the two year security one year from today have to be for this strategy to equal the yield of the security with three years to maturity today (i.e., what is the forward rate of a security with two years to maturity, one year from today)?

9.62%

9.76%

9.81%

9.98%

9.62%

9.76%

9.81%

9.98%

Explanation / Answer

Rate for 3 year = 8.57%

Rate for 1 year = 6,20%

Now according to forward rate theory, let rate be r%

(1 + 8.57%)3 = (1 + 6.20%) * (1 + r%)2

1.279763 = 1.0620 * (1 + r%)2

(1 + r%)2 = 1.20505

1 + r% = 1.205050.5

1 + r% = 1.09774

r% = 9.76%

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