7. Forward Rate a. Determine the forward rate for various one-year interest rate

Question

7. Forward Rate                

                    a. Determine the forward rate for various one-year interest rate scenarios if the two-year interest rate is 8 percent, assuming no liquidity premium. Explain                    the relationship between the one-year interest rate and the one-year forward rate while holding the two-year interest rate constant.                

                    b. Determine the one-year forward rate for the same one-year interest rate scenarios described in question (a) while assuming a liquidity premium of 0.4                    percent.                

                    Does the relationship between the one-year interest rate and the forward rate change when considering the liquidity premium is considered?                

                    c. Determine how the one-year forward rate would be affected if the quoted two-year interest rate rises; hold constant the quoted one-year interest rate as                    well as the liquidity premium. Explain the logic of this relationship.                

                    d. Determine how the one-year forward rate would be affected if the liquidity premium rises and if the quoted one-year interest rate is held constant. What if                    the quoted two-year interest rate is held constant? Explain the logic of this relationship.                

                    9. Debt Security Yield                

                    a. Determine how the appropriate yield to be offered on a security is affected by a higher risk-free rate.                

                    Explain the logic of this relationship.                

                    b. Determine how the appropriate yield to be offered on a security is affected by a higher default risk                

                    premium. Explain the logic of this relationship.

Explanation / Answer

a)As the one-year interest rate rises, the forward rate declines. The one-year forward rate is zero once the one-year interest rate is equal to the two-year interest rate, and it becomes negative if the one-year interest rate exceeds the two-year interest rate. The forward rate is reduced when using higher levels of a one-year interest rate, holding a two-year interest rate constant. The smaller the differential between the two-year and one-year interest rates, the lower is the interest rate in the second year that is needed so that the combination of the two one-year rates are equal to the two-year rate.

b)The general relationship between the one-year interest rate and the one-year forward rate still holds.

c)The forward rate increases for higher levels of a two-year interest rate. The greater the differential between the two-year and one-year interest rates, the greater is the interest rate in the second year that is needed so that the combination of the two one-year rates are equal to the two-year rate.

d) The forward rate is reduced for higher levels of the liquidity premium, holding the one-year and two-year interest rates constant. The higher the liquidity premium, the greater the proportion of the interest rate differential (two-year rate minus one-year rate) that is due to interest rate expectations, and the lower is the one-year forward rate.

9)

a)The appropriate yield to be offered on a security would need to be increased if the risk-free rate rises. A higher yield would be necessary to place the security, as investors still want a particular premium above the risk-free rate.

b)The appropriate yield to be offered on a security would need to be increased if the default premium on the security increased, because the investors would require a higher return to compensate for the higher default risk.

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