Question

6.

Assume that the preferred habitat theory holds and that the one-year spot rate is 5.50% per annum nominal and that the 18-month spot rate is 5.25% per annum nominal. Assuming that investors have a preferred investment horizon of 18 months and semi-annual compounding and that the expected six-month rate in one year’s time is 5.75% per annum nominal, what is the risk premium for 18 month bonds?

Group of answer choices

0.50%, as there is too little demand for 18 month bonds relative to 12 month bonds

-0.85%, as there is too much demand for 18 month bonds relative to 12 month bonds

1.00%, as there is too little demand for 18 month bonds relative to 12 month bonds

-0.50%, as there is too much demand for 18 month bonds relative to 12 month bonds

-1.00%, as there is too much demand for 18 month bonds relative to 12 month bonds

Answer 1

In order to solvethe probelem, consider the following example

using similar logic,

with a spot rate of 5.5% (compounded semi annually), yield on the 12 month bond would be = $ (1+(0.055/2))^2 = 1.05575

with a spot rate of 5.25% (compounded semi annually), yield on the 18month bond would be = $ (1+(0.0525/2))^3 = 1.080803

1.080803/1.05575 = $ 1.023756

hence the yield on 18 month rate is same as if the investor received one year spot rateof 5.5% over the first year and 2.375 % over the next 6 months.

but the given expected 6 month rate is 5.75% annual = 2.875% semi annual.

risk premium = forward rate - expected rate = 2.375-2.875 = -0.500%

Note according to preferred habitat theory, 18 month bonds are preferred over 12 month bonds and hence demand for 28monthbons re higher.

Ans: -0.50%, as there is too much demand for 18 month bonds relative to 12 month bonds