Following are the yields on selected Treasury securities:
$\begin{array}{cc}
\text { Maturity } & \text { Yield } \
\hline \text { 2 years } & 1.6 \% \
\text { 3 years } & 2.2 \
\text { 4 years } & 2.4
\end{array}$
?Using the expectations theory, compute the expected one-year interest rate in Year 3. That is, compute the rate that is expected to exist only during Year 3. (Base your answer on an arithmetic average rather than a geometric average.)
A)2.2%
B)1.6%
C)3.4%
D)1.9%
E)3.0%

Question

Quizplus · Accepted Answer

The expectations theory suggests that the yield of a longer-term bond is an average of the short-term interest rates that are expected to occur over the bond's life. To find the expected one-year interest rate in Year 3, we can use the yields given for the 2-year, 3-year, and 4-year securities. The formula to calculate the expected rate in Year 3 (E3) is based on the idea that the average yield of a 3-year security is the average of the expected rates in Years 1, 2, and 3, and similarly for the 2-year and 4-year securities. Given:- 2-year yield = 1.6% (average of Year 1 and Year 2 rates)- 3-year yield = 2.2% (average of Year 1, Year 2, and Year 3 rates)- 4-year yield = 2.4% (average of Year 1, Year 2, Year 3, and Year 4 rates)We can set up the equations as follows, where E1, E2, and E3 are the expected rates for Years 1, 2, and 3, respectively:1. $E1 + E2 = 2 \times 1.6\% = 3.2\%$2. $E1 + E2 + E3 = 3 \times 2.2\% = 6.6\%$3. $E1 + E2 + E3 + E4 = 4 \times 2.4\% = 9.6\%$We are solving for E3, the expected rate in Year 3. From the first two equations, we can find E3 by subtracting the sum of E1 and E2 from the total for the first three years:$E3 = 6.6\% - 3.2\% = 3.4\%$Therefore, the expected one-year interest rate in Year 3 is 3.4%.

Following Are the Yields on Selected Treasury Securities ?Using the Expectations Theory, Compute the Expected One-Year Interest Rate