Consider the expectations theory of the term structure of interest rates. A downward sloping yield curve indicates that investors expect short-term interest rates to

Question

BlackTom AI · Accepted Answer

Under the expectations theory of the term structure, long-term yields equal the average of current and expected future short-term rates, so a downward slope implies expected future short rates are lower than current short rates.

1) Relevant concepts
- Expectations theory: the n‑period yield equals the arithmetic average of the current short rate and the expected short rates over the remaining (n−1) periods (ignoring risk premia).
- Yield curve slope: comparison of short-term yield (y1) and longer-term yield (yn) reveals market expectations about future short rates.

2) Step-by-step reasoning
- For a 2‑period (two-year) example the expectation relationship is: y2 = (r1 + E[r2]) / 2, where r1 is today’s one‑period rate and E[r2] is the expected one‑period rate next period.
- If the yield curve is downward sloping, y2 < r1.
- Substitute: (r1 + E[r2]) / 2 < r1.

3) Intermediate algebraic steps
- Multiply both sides by 2: r1 + E[r2] < 2 r1.
- Rearranged: E[r2] < 2 r1 − r1 = r1.
- Therefore E[r2] < r1: the expected future short rate is lower than today’s short rate (a decrease).

4) Why the correct answer is correct
- The arithmetic derivation shows directly that a lower long-term yield relative to the current short rate requires expected short rates to fall. More generally, if the n‑period yield is below the current short rate, the average of expected future short rates must be below the current short rate, meaning investors expect a decrease.

5) Why other choices would be incorrect
- “Increase”: would correspond to an upward‑sloping yield curve (longer yields higher than short yields), implying expected increases in short rates.
- “Stay the same” (flat curve): if long and short yields were equal, the market expects future short rates to remain roughly unchanged.
- “Uncertain”: under the pure expectations theory the slope gives a direct expectation; uncertainty or other interpretations arise only when adding liquidity or term premia (other theories), but the question specifies the expectations theory.

6) Conclusion
Therefore, under the expectations theory a downward sloping yield curve indicates investors expect short-term interest rates to decrease in the future, matching the provided answer: "Decrease in the future."

Consider the expectations theory of the term structure of interest rates. A downward sloping yield curve indicates that investors expect short-term interest rates to单项选择题

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