THE ECONOMICS OF MONEY,BANKING, AND FINANCIAL MARKETS 168

136 PA R T I I APP LI CAT IO N Financial Markets Forward Rate A customer asks a bank if it would be willing to commit to making the customer a one-year loan at an interest rate of 8% one year from now To compensate for the costs of making the loan, the bank needs to charge one percentage point more than the expected interest rate on a Canada bond with the same maturity if it is to make a profit If the bank manager estimates the liquidity premium to be 0.4%, and the one-year Canada bond rate is 6% and the two-year bond rate is 7%, should the manager be willing to make the commitment? Solution The bank manager is unable to make the loan because at an interest rate of 8%, the loan is likely to be unprofitable to the bank i where in 1t *n 1t int *1t n e t n = two-year bond rate liquidity premium one-year bond rate liquidity premium number of years 11 + in + 1t - *n + 1t2n + 11 + int - *nt2n - 0.07 0.004 0.06 Thus i et = 11 + 0.07 - 0.00422 + 0.06 - = 0.072 = 7.2% The market s forecast of the one-year Canada bond rate one year in the future is therefore 7.2% Adding the 1% necessary to make a profit on the one-year loan means that the loan is expected to be profitable only if it has an interest rate of 8.2% or higher S U M M A RY Bonds with the same maturity will have different interest rates because of three factors: default risk, liquidity, and tax considerations The greater a bond s default risk, the higher its interest rate relative to other bonds; the greater a bond s liquidity, the lower its interest rate; and bonds with tax-exempt status will have lower interest rates than they otherwise would The relationship among interest rates on bonds with the same maturity that arises because of these three factors is known as the risk structure of interest rates Four theories of the term structure provide explanations of how interest rates on bonds with different terms to maturity are related The expectations theory views long-term interest rates as equalling the average of future short-term interest rates expected to occur over the life of the bond; by contrast, the segmented markets theory treats the determination of interest rates for each bond s maturity as the outcome of supply and demand in each market in isolation Neither of these theories by itself can explain the fact that interest rates on bonds of different maturities move together over time and that yield curves usually slope upward The liquidity premium and preferred habitat theories combine the features of the other two theories and by so doing are able to explain the facts just mentioned They view long-term interest rates as equalling the average of future short-term interest rates expected to