Question

The yield on 1-year Treasury securities is 6%, 2-year securities yield 6.2%, 3-year securities yield 6.3%, and 4-year securities yield 6.5%. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities:

a. A 1-year security, 1 year from now
b. A 1-year security, 2 years from now
c. A 2-year security, 1 year from now
d. A 3-year security, 1 year from now

Answer 1

To forecast the yields on the given Treasury securities using expectations theory and geometric averages: a) 1-year security, 1 year from now = 6.1%, b) 1-year security, 2 years from now = 6.15%, c) 2-year security, 1 year from now = 6.25%, d) 3-year security, 1 year from now = 6.4%.

Step-by-step explanation:

To forecast the yields on the given securities using the expectations theory and geometric averages, we need to consider the pattern of increasing yields over time. Based on the given information, we can observe that the yields on Treasury securities are increasing gradually:

• The yield on 1-year Treasury securities is 6%
• The yield on 2-year Treasury securities is 6.2%
• The yield on 3-year Treasury securities is 6.3%
• The yield on 4-year Treasury securities is 6.5%

a. A 1-year security, 1 year from now:
Using the geometric average, we can calculate the forecasted yield as the square root of the product of the current yield (6%) and the next year's yield (6.2%).
Forecasted yield = √(6% * 6.2%) = 6.1%

b. A 1-year security, 2 years from now:
Using the geometric average, we can calculate the forecasted yield as the square root of the product of the current yield (6%) and the yield after two years (6.3%).
Forecasted yield = √(6% * 6.3%) = 6.15%

c. A 2-year security, 1 year from now:
Since the yield on a 2-year security is not given, we can assume that the yield will continue to increase at the same rate as the previous years.
Forecasted yield = Previous Yield + (Rate of Increase * Number of Years)
Rate of Increase = (Yield of Next Year - Yield of Current Year) / Number of Years
Forecasted yield = 6.2% + ((6.3% - 6.2%) / 2) = 6.25%

d. A 3-year security, 1 year from now:
Since the yield on a 3-year security is not given, we can assume that the yield will continue to increase at the same rate as the previous years:
Forecasted yield = Previous Yield + (Rate of Increase * Number of Years)
Rate of Increase = (Yield of Next Year - Yield of Current Year) / Number of Years
Forecasted yield = 6.3% + ((6.5% - 6.3%) / 3) = 6.4%