CHAPTER The Risk and Term Structure of Interest Rates 129 The interest rate on the five-year bond would be 8% int it + i te+ + i et + + + i te+ (n - 1) n lnt where it year interest rate 5% i et + i et + i et + i et + year interest rate 6% year interest rate 7% year interest rate 8% year interest rate 9% l5t liquidity premium 1% n number of years Thus i5t = 5% 6% 7% 8% 9% 1% 8.0% If you did similar calculations for the one-, three-, and four-year interest rates, the one-year to five-year interest rates would be as follows: 5.0%, 5.75%, 6.5%, 7.25%, and 8.0%, respectively Comparing these findings with those for the pure expectations theory, we can see that the liquidity preference theory produces yield curves that slope more steeply upward because of investors preferences for short-term bonds Let s see if the liquidity premium and preferred habitat theories are consistent with all three empirical facts we have discussed They explain fact 1, that interest rates on different-maturity bonds move together over time: a rise in short-term interest rates indicates that short-term interest rates will, on average, be higher in the future, and the first term in Equation then implies that long-term interest rates will rise along with them They also explain why yield curves tend to have an especially steep upward slope when short-term interest rates are low and to be inverted when short-term rates are high (fact 2) Because investors generally expect short-term interest rates to rise to some normal level when they are low, the average of future expected short-term rates will be high relative to the current short-term rate With the additional boost of a positive liquidity premium, long-term interest rates will be substantially above current short-term rates, and the yield curve would then have a steep upward slope Conversely, if short-term rates are high, people usually expect them to come back down Long-term rates would then drop below short-term rates because the average of expected future short-term rates would be so far below current short-term rates that despite positive liquidity premiums, the yield curve would slope downward The liquidity premium and preferred habitat theories explain fact 3, that yield curves typically slope upward, by recognizing that the liquidity premium rises with a bond s maturity because of investors preferences for short-term bonds Even if