To calculate the expected 2-year forward rate, we will use the expectation hypothesis formula, which assumes that the yield on a long-term bond is the average of short-term future rates.

The formula for the forward rate is:

$(1 + Y_{2-year})^2 = (1 + Y_{1-year}) \times (1 + f_{1-year})$

Where:

• $Y_{2-year}$ is the yield for the two-year Treasury bill (6.9% or 0.069).
• $Y_{1-year}$ is the yield for the one-year Treasury bill (7.8% or 0.078).
• $f_{1-year}$ is the expected forward rate for the second year.

Step 1: Rearranging the formula to solve for $f_{1-year}$:

$f_{1-year} = \frac{(1 + Y_{2-year})^2}{(1 + Y_{1-year})} - 1$

Step 2: Plugging in the values:

$f_{1-year} = \frac{(1 + 0.069)^2}{(1 + 0.078)} - 1$

$f_{1-year} = \frac{(1.069)^2}{(1.078)} - 1$

$f_{1-year} = \frac{1.142476}{1.078} - 1$

$f_{1-year} = 1.0597 - 1$

$f_{1-year} = 0.0597$

Step 3: Converting the decimal to a percentage:

$f_{1-year} = 5.97\%$

So, the expected 2-year forward rate is 5.97 (without the percentage sign).

Let me know if you need further details or have any questions!

Additional Questions:

1. How do forward rates help in forecasting interest rates for the future?
2. What assumptions does the expectation hypothesis make about the yield curve?
3. How does the forward rate differ from the spot rate?
4. How might changes in inflation expectations impact forward rates?
5. What are the advantages and limitations of the expectation hypothesis?

Tip:

The expectation hypothesis works under the assumption that investors only care about the average returns over the long term, and not the specific timing of cash flows.