Using the Term Structure to Forecast Interest Rates

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.

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 + i2t)(1 + i2t) -1 = (1 + it)(1 + iet+1) - 1

The Forward Rate

• (1 + i2t)(1 + i2t) -1 = (1 + it)(1 + iet+1) - 1

• (1 + i2t)2 - 1 = (1 + it)(1 + iet+1) - 1

• Solve for iet+1, the forward rate.

– Add + 1 to both sides and divide by (1 + it)

• 1 + iet+1 = (1 + i2t)2 / (1 + it)

– Subtract + 1 from both sides

• iet+1 = (1 + i2t)2 (1

+ it) 1

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.

Adjusted Forward Rate Forecast

• To allow for liquidity premiums in our formula, we subtract it out.

• iet+1 = (1 + i2t - l2t)2

(1 + it)1

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%.

Solution

• iet+1 = (1 + i2t - l2t)2

(1 + it)

• iet+1 = (1 + 0.07 - 0.004)2

(1 + 0.06)

• iet+1 = 7.2%

• You would reject the loan.

1

1