1. Using the Term Structure to Forecast Interest Rates

2. Interest Rate Forecasts Interest rate forecasts are needed when managers of financial institutions have to set interest rates on loans that are promised to customers in the future. We also might want to find the implied forward rate on a bond originating in the future. Specific forecasts of the implied forward interest rate can be generated using the term structure.

3. Expectations Theory According to the expectations theory, the expected return over two periods from investing $1 in a two period bond must equal the expected return from investing $1 in two one period bonds. (1 + i 2t )(1 + i 2t ) -1 = (1 + i t )(1 + i e t+1 ) - 1

4. The Forward Rate (1 + i 2t )(1 + i 2t ) -1 = (1 + i t )(1 + i e t+1 ) - 1 (1 + i 2t ) 2 - 1 = (1 + i t )(1 + i e t+1 ) - 1 Solve for i e t+1, the forward rate. –Add + 1 to both sides and divide by (1 + i t ) 1 + i e t+1 = (1 + i 2t ) 2 / (1 + i t ) –Subtract + 1 from both sides i e t+1 = (1 + i 2t ) 2 (1 + i t ) 1

5. Liquidity Premium According to the liquidity premium hypothesis, investors prefer to hold short- term rather than long-term bonds. Therefore, long-term rates include a liquidity premium to compensate the investor for accepting more risk.

6. Adjusted Forward Rate Forecast To allow for liquidity premiums in our formula, we subtract it out. i e t+1 = (1 + i 2t - l 2t ) 2 (1 + i t ) 1

7. Example Would you be willing to make a one year loan at an interest rate of 8% one year from now? To make a profit, you need to charge one percentage point more than the expected interest rate on a Treasury bond with the same maturity. The liquidity premium is 0.4%, the one year Treasury rate is 6%, and the 2 year Treasury rate is 7%.

8. Solution i e t+1 = (1 + i 2t - l 2t ) 2 (1 + i t ) i e t+1 = (1 + 0.07 - 0.004) 2 (1 + 0.06) i e t+1 = 7.2% You would reject the loan. 1 1