Consider a one-year certificate of deposit (CD) paying 4 percent interest and a two-year CD that pays 6 percent. The different rates imply that investors are expecting interest rates to rise in a year's time; otherwise they would be nearly equal. This future rate implied by the difference is called the forward rate. The forward rate in this case is the rate on a one-year CD 12 months from now. When added to the current one-year 4 percent CD, it will make the total return equal to that of the two-year 6 percent CD. Calculating this forward rate can be done with a relatively simple equation using the current rates of return, or spot rates.
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Write out the formula for forward rates: Value of longer investment = (value of shorter investment) x (forward rate + 1)
Compute the value of the investments after interest payments using the same amount of principal. In this example, the final value of $100 in the 6 percent two-year CD is:
100 x 1.06 x 1.06, which can also be written as 100(1.06)^2 = $112.36 Note: ^2 means to the second power.
The final value of $100 in the one-year 4 percent CD is:
100 x 1.04 = $104
Plug the values into the equation in Step 1 and solve for the forward rate. In this example:
112.36 = 104 x (forward rate + 1)
forward rate = (112.36 / 104) - 1 = .0803, or 8.03 percent
Check your work by computing the value of $100 in a one-year CD at 4 percent rolled into a one-year CD at 8.03 percent. This should equal the value of a two-year CD at 6 percent.
104 x 1.0803 = $112.35, which is almost the amount computed above for the two-year CD. Had we not rounded the forward rate to 8.03 percent, the values would be equal.
When calculating the values of the investments in Step 2, use the correct method of compounding interest (annual, semi-annual, continuous) for the particular investment. The forward rate should use this method as well.
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