Question

5. Assume the following interest rates

Current Rate on a 1-year bond due in 2019: 4%

Expected Rate on a 1-year bond due in 2020: 5%

Expected Rate on a 1-year bond due in 2021: 6%

Expected Rate on a 1-year bond due in 2022: 4%

Expected Rate on a 1-year bond due in 2023: 2%

a. According to the expectations theory for the yield curve, what would be the current rate on a 3-year bond due in 2021? Show work.

b. According to the expectations theory for the yield curve, what would be the current rate on a 5-year bond due in 2023? Show work.

c. Graph and explain the yield curve. Explain how and why it might be upward sloping and when it might be downward sloping. Explain.

d. How might the liquidity preference theory change your results? Explain.

e. How might risk premiums change your results? Explain.

PLEASE GIVE DETAILED ANSWER, not Repeat answers that have already been posted! Thank you:)

Answer 1

NOTE: The current rate for the 1-year bond is the one-year spot rate. All other rates, the expected rate of a one-year bond due in 2020 is the one-year forward rate one-year from now, the expected rate of a one-year bond due in 2021 is the one-year forward rate two-years from now and so on. The pure expectations theory would be used to determine the spot rate curve for different maturities from the forward rates given.

(a) Two Year Spot Rate = (1+r2)^(2) = [(1+r1) x (1+f1)]  

r2 = (1.092)^(1/2) - 1 = 0.04498 or 4.498 %

Three Year Spot Rate = (1+r3)^(3) = (1+r2)^(2) x (1+f2)

(1+r3)^(3) = (1.04498)^(2) x (1.06)

r3 = 0.04996 or 4.996 %

(b) Four Year Spot Rate = (1+r4)^(4) = [(1+r3)^(3) x (1+f3)]

r4 = [(1.04996)^(3) x (1.04)]^(1/4) - 1 = 0.04746 or 4.746 %

Five Year Spot Rate = (1+r5)^(5) = [(1+r4)^(4) x (1+f4)]

r5 = [(1.04746)^(4) x (1.02)]^(1/5) - 1 = 0.04191 or 4.191 %

(c)

As is observable the spot rate curve first moves up, reaches a peak at intermediate maturities and then starts climbing down at longer maturities. In this it mimics the behaviour of the expected rate trend which rises from 4% to reach 6% at intermediate maturity and then climbs down to 2 % for longer maturities. This observation is in sync with the pure expectations hypothesis which states that short-term interest rates are a predictor of long-term interest rates.

(d) The liquidity preference theory states that longer maturity bonds should have higher interest rates as compared to shorter maturity bonds because investors inherently prefer highly liquid investments such as cash and cash equivalents over fixed income investments such as a bond. This, in turn, implies that investors would demand greater returns for holding the relatively illiquid bonds for a longer duration of time as compared to holding them for a shorter duration. Hence, by this theory, short-term bonds should pay low interests and the same should progressively increase as the maturity of the bond goes up. The spot rate curve derived in part(c) is erroneous if one follows the liquidity preference theory as that curve climbs down for longer maturities. The spot rate curve should be upward sloping throughout if one were to follow the liquidity preference theory.