Question

Suppose you observe the following term structure for treasury securities: maturity yield 1 year 2 years 3 years 4 years 5 years 6.0% 6.2 6.4 6.5 6.5 assume that the pure expectations theory of the term structure is correct. (this implies that you can use the yield curve provided to "back out" the market’s expectations about future interest rates.) what does the market expect will be the interest rate on 1-year securities, 1 year from now? what does the market expect will be the interest rate on 3-year securities, 2 years from now? calculate these yields using geometric averages.

Answer 1

The market expects the interest rate on 1-year securities, 1 year from now, to be approximately 6.1%. The market also expects the interest rate on 3-year securities, 2 years from now, to be approximately 6.47%.

Step-by-step explanation:

The market's expectation for the interest rate on 1-year securities, 1 year from now, can be calculated using the geometric average of the yields for the 1-year and 2-year securities. Since the yield for the 1-year security is 6.0% and the yield for the 2-year security is 6.2%, the calculation would be:

((1 + 0.06) * (1 + 0.062))^(1/2) - 1 = 0.061

Therefore, the market expects the interest rate on 1-year securities, 1 year from now, to be approximately 6.1%.

Similarly, the market's expectation for the interest rate on 3-year securities, 2 years from now, can be calculated using the geometric average of the yields for the 3-year and 4-year securities. Since the yield for the 3-year security is 6.4% and the yield for the 4-year security is 6.5%, the calculation would be:

((1 + 0.064) * (1 + 0.065))^(1/2) - 1 = 0.0647

Therefore, the market expects the interest rate on 3-year securities, 2 years from now, to be approximately 6.47%.