Homework Answers
Under expectation theory,
I0,3 = (I0,1 + I1,2 + I2,3) / 3
where I0,3 = 3 year interest rate under expectation theory = 7%
I0,1 = Expected interest rate for 1 year = 5%
I1,2 = Expected interest rate for year 2 at the end of year 1 = 6%
I2,3 = Expected interest rate for year 3 at the end of year 2
Hence, 7% = (5% + 6% + I2,3) / 3
Hence, I2,3 = Expected interest rate for year 3 at the end of year 2 = 3 x 7% - 5% - 6% = 10%
Under liquidity premium theory:
Interest rate under liquidity premium theory = Interest rate under expectation theory + liquidity premium
Hence, 10% = 7% + Liquidity premium
Hence liquidity premium for the third year = 10% - 7% = 3%
No, the gap between interest rate as per expectation theory and liquidity premium theory will widen further in the fourth year as the liquidity premium increases with time to maturity. Hence as time to maturity increase, the divergence between the two will be more.
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