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Answer: Under liquidity preference, the expected future six-month spot rate, E[S(2.0, 2.5)], is 3.00%
First compute the 6-month forward rate from 2.0 to 2.5 years using the continuously compounded zero rates: \[ f(2.0,2.5) = \frac{2.5\cdot 2.00\% - 2.0\cdot 1.75\%}{0.5} = \frac{5.00\% - 3.50\%}{0.5} = 3.00\% \] - Under **pure expectations theory**, the forward rate equals the expected future spot rate, so **3.00%** is plausible. - Under **liquidity preference theory**, investors require a positive liquidity premium for longer maturities, so the forward rate should be **greater than** the expected future spot rate. Therefore the expected future spot rate should be **less than 3.00%**, making **2.40%** plausible, but **3.00%** not consistent with a positive liquidity premium. - Under **preferred habitat/market segmentation**, many shapes are possible, so **3.15%** could be possible. Thus the least likely statement is **B**.
Author: Manit Arora
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Q-3. 715.3. Consider the following upward-sloping but smooth zero rate curve:
| Maturity (yrs) | Zero Rates (CC) |
|---|---|
| 0.50 | 1.00% |
| 1.00 | 1.25% |
| 1.50 | 1.50% |
| 2.00 | 1.75% |
| 2.50 | 2.00% |
There are various theories that attempt to explain the factors that determine the shape of the zero rate curve. If the above zero curve is observed, each of the following theories is plausible EXCEPT which of the following theories is the LEAST LIKELY to be true, if only because it does not comport with the observed zero curve?
A
Pure expectations, the expected future six-month spot rate, E[S(2.0, 2.5)], is 3.00%
B
Under liquidity preference, the expected future six-month spot rate, E[S(2.0, 2.5)], is 3.00%
C
Under liquidity preference, the expected future six-month spot rate, E[S(2.0, 2.5)], is 2.40%
D
Under preferred habitat (market segmentation), the expected future six-month spot rate, E[S(2.0, 2.5)], could be 3.15%
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