Question

Suppose you are given the yield curve as follows:

i₁ = 2%; i₂ = 3%; i₃ = 4%; i₄ = 5%. i₅ = 7%, i₁₀ = 10%. These represent the 1-year, 2-year, 3-year and 4-year, 5-year, 10-year bond yields today. Under the pure expectations theory, find a) the expected future one-year rates that will prevail from year 1 to year 2 b) from year 2 to year 3; & c) from year 3 to year 4.

Discuss how financial advisors use the shape of the curve in above questions as part of investment advice.

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Answer 1

Answer )

Under the pure expectation theory the forward rates could be calculated using spot rates of different maturiyu

a) the expected future one year rate after 1 year - let it be F 1,1

we need 1 year and 2 year spot rates

under pure expectation theory

(1+ i2)^2 = (1+i1)*(1+ F 1,1)

solving this we get 4%

b) similary One year future rate prevailing after 2 years from now can be calculated as

( 1+i3)^3 = (1+i2)^2 * (1 + F 2,1)

solving we get F 2,1 = 6.02%

c) Similarly

F 3,1 we can calculate to be 8.05%

We can see that the yield curve is upward sloping ,

with increase in maturity the yield is increasing

the investor can use the strategy of rolling the yield curve

for example, assume a 10-year Treasury yield is 2.46% and a 7-year yield is 2.28%. After three years, the 10-year bond will become a 7-year bond. Because the difference in yield between the 10-year and 7-year is 2.46% - 2.28% = 0.18%, the 7-year bond can rise 0.18% over three years before exceeding the investor’s yield to maturity, that is, 2.46%. Assuming that interest rates stay the same, this positive roll means that the price of the bond will go up as time passes. The roll-down return is the amount that interest rates can rise over a specified time period before the current yield exceeds an investor’s YTM. If the investor sells the bond, he will get more than he paid for it, in addition to the coupon payments already received. In effect, the investor earns money by rolling down the yield curve.