Question

1. For this question, assume the liquidity premium theory.

a. What is the major difference in the assumption about the risk premium between the expectations hypothesis and the liquidity premium theory?

b. Assuming that all future expected short-term interest rates on treasury bills are 2%, determine if the three year treasury note has an annual interest rate of greater or less than 2%. Explain.

c. Commercial paper with maturity of one year is issued by Amazon. Is the annual interest rate on the commercial paper greater than/less than/equal to/or indeterminate as compared to the interest rate on the three year treasury note in part (b)? Explain.

d. If the yield on both one and two year bonds are 4%, would you expect the yield on a one-year T-bill in one year’s time to be higher, lower, or the same as 4%? Explain.

Answer 1

a. The expectations hypothesis assumes that notes, bills and bonds are considered as perfect substitutes of each other by investors. Also,the inflation risk and additional interest rate risk associated with longer maturity treasury securities are not considered by investors.

Liquidity premium theory explicitly assumes that investors are concerned about inflation risk and interest rate risk, and they need a risk premium as a compensation for bearing the extra risk. Therefore,the risk premium of longer-term maturity bonds is high as compared to that of shorter-term maturity bonds.

b. Since future expected short-term interest rates on treasury bills are 2%, then according to the liquidity premium theory, three year treasury note will have an annual interest rate greater than 2% since the risk premium is positive.

c.It is not possible to determine whether the commercial paper issued by Amazon has a lower or higher interest rate than the three year treasury note. The default risk in commercial paper is higher as compared to US treasuries, therefore, a risk premium is needed by the investors for bearing this default risk. Also, the maturity of this commercial paper is one year, which is less than the maturity period of treasury note, therefore, commercial paper has less interest rate and inflation risk, and hence the associated risk premium will be less than the three year treasury note. It will be dependent on the amount of these risk premiums.

d. According to the liquidity premium theory the two year bond will have a higher risk premium as compared to the one year bond so that the investors are compensated for the higher inflation and interest rate risk. Therefore, the expectations hypothesis "yield curve" will slope downwards. This is only possible if the future short-term interest rate is lower than 4%.