Interest rates on 2-year Treasury securities are currently 5.00%, while 5-year Treasury securities yield 10.00%. If the pure expectations theory is correct, what does the market believe that 3-year securities will be yielding 2 years from now?
The pure expectations theory suggests that the future interest rates on securities can be predicted based on the current yield curve. According to this theory, investors form their expectations about future interest rates independently of any risk premiums.
To determine the market's belief about the yield on 3-year securities 2 years from now, we need to look at the yield curve's pattern and calculate the expected yield.
Here's how we can approach it step by step:
1. Start with the information given:
- Interest rate on 2-year Treasury securities = 5.00%
- Interest rate on 5-year Treasury securities = 10.00%
2. Calculate the average annual interest rate increase implied by the yield curve. To do this, we can compute the annual interest rate increase between the 2-year and 5-year securities:
- Average annual interest rate increase = (10.00% - 5.00%) / (5 - 2) = 5.00% / 3 = 1.67%
3. To find the expected yield on the 3-year securities, we need to add the average annual interest rate increase (1.67%) to the 2-year interest rate (5.00%). This will give us the market's belief about the yield on 3-year securities 2 years from now:
- Expected yield on 3-year securities = 5.00% + 1.67% = 6.67%
Therefore, according to the pure expectations theory, the market believes that 3-year securities will be yielding 6.67% 2 years from now.