Below are the yield rates for different maturities (rates on the yield curve)

Maturity

1-year

2-year

3-year

Rates

6%

5%

4%

Based on the expectation hypothesis, what is the expected future interest rate between year 1 and year 2?

(please answer in %. If the answer is 8.05%, then in the box, write 8.05)

Question

Below are the yield rates for different maturities (rates on the yield curve)

Maturity

1-year

2-year

3-year

Rates

6%

5%

4%

Based on the expectation hypothesis, what is the expected future interest rate between year 1 and year 2?

(please answer in %. If the answer is 8.05%, then in the box, write 8.05)

BlackTom AI · Accepted Answer

Under the expectations hypothesis, the n-year spot rate reflects the geometric average of expected future one-year rates. For two years, (1 + S2)^2 = (1 + S1) · (1 + f1), where S1 is the current 1-year spot rate, S2 the current 2-year spot rate, and f1 the expected one-year rate between year 1 and year 2.

Given S1 = 6% = 0.06 and S2 = 5% = 0.05, solve for f1:

1) Compute (1 + S2)^2:
(1.05)^2 = 1.1025

2) Divide by (1 + S1):
1.1025 / 1.06 = 1.0400943396

3) Subtract 1 to get f1:
f1 = 1.0400943396 − 1 = 0.0400943396 ≈ 0.04009434

4) Convert to percent and round:
f1 ≈ 4.00943396% → 4.01%

Why this is correct: the expectations hypothesis implies the multi-year spot rate equals the compounded product of current and expected future short rates; therefore the forward one-year rate must satisfy the geometric relation above. Using that relation yields 4.01%.

Why other simple approaches are incorrect:
- Taking an arithmetic average ((6% + 5%)/2 = 5.5%) ignores compounding and the hypothesis’ multiplicative structure.
- Subtracting yields or using linear interpolation misstates how multi-period returns compound.
- Interpreting rates as continuously compounded would require different formulas; here the standard discrete annual compounding formula is appropriate given one-year periods.

Conclusion: The expected interest rate between year 1 and year 2 is 4.01%, matching the provided answer.

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