Final answer:
The yield on a 3-year Treasury security today, based on the pure expectations theory and given interest rates, is approximately 2.966%.
Step-by-step explanation:
Based on the pure expectations theory, which states that long-term interest rates are the average of current and expected short-term interest rates, we can calculate the yield on a 3-year Treasury security.
Knowing the current yield on a 1-year Treasury security is 2% and it is expected to be 2.7% the following year and 3.2% the year thereafter, we can use these expectations to determine the yield for the 3-year Treasury.
The formula to calculate this average yield over the three years would be:
3-Year Treasury Yield = (Current 1-Year Yield + Next Year's Expected 1-Year Yield + Following Year's Expected 1-Year Yield) / 3
Plugging the given yields into the formula yields:
3-Year Treasury Yield = (2% + 2.7% + 3.2%) / 3
3-Year Treasury Yield = 2.966%
Therefore, the yield on a 3-year Treasury security today is approximately 2.966%.