Recall that on a one-year Treasury security the yield is 5.6100% and 8.4150% on a two-year Treasury security. Suppose the one-year security does not have a maturity risk premium, but the two-year security does and it is 0.25%. What is the market’s estimate of the one-year Treasury rate one year from now? (Note: Do not round your intermediate calculations.)

To calculate the market's estimate of the one-year Treasury rate one year from now, we can use the **Expectations Theory of the Term Structure of Interest Rates**. This theory suggests that the yield on a longer-term bond (in this case, a two-year Treasury security) is the average of the short-term rates expected over the life of the bond, plus any risk premiums.

### Step-by-Step Process:

Let:
- \( r_1 = \) current one-year Treasury rate \( = 5.6100\% \)
- \( r_2 = \) current two-year Treasury rate \( = 8.4150\% \)
- \( MRP_2 = \) maturity risk premium for the two-year Treasury bond \( = 0.25\% \)
- \( f_1 = \) the forward one-year rate (this is what we are solving for)

We can express the relationship using the formula:
\[
(1 + r_2)^2 = (1 + r_1)(1 + f_1) + \text{{MRP}}_2
\]
where \( r_2 \) is the two-year yield, \( r_1 \) is the current one-year yield, \( f_1 \) is the forward rate one year from now, and MRP_2 is the maturity risk premium on the two-year security.

We will solve for \( f_1 \), the forward one-year rate.

### Formula Rearranged:
\[
(1 + r_2)^2 - \text{{MRP}}_2 = (1 + r_1)(1 + f_1)
\]
Then, isolate \( f_1 \) and solve it:

Let’s calculate this step by step.

The market's estimate of the one-year Treasury rate one year from now is approximately **11.06%**.

Would you like further details or have any questions? Here are some related questions to consider:

1. How does the Expectations Theory influence interest rate predictions?
2. What factors contribute to a maturity risk premium?
3. How can forward rates help in predicting future interest rates?
4. What are the implications of a high forward rate for the economy?
5. How do interest rate expectations affect investment decisions?

**Tip:** Forward rates are not guaranteed rates but rather market-implied estimates based on current yield curves and expectations of future interest conditions.

Learn how to estimate the one-year Treasury rate one year from now using the Expectations Theory of the Term Structure of Interest Rates. Given a one-year Treasury yield of 5.6100%, a two-year Treasury yield of 8.4150%, and a maturity risk premium of 0.25%, this problem walks you through the calculation step-by-step. Ideal for finance and economics students.

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