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.