Unbiased Expectations Theory (Predicting Short-Term Interest Rates)
Expectations theory—often called the unbiased expectations theory—uses current long-term interest rates to infer future short-term rates. It rests on the idea that an investor should be indifferent between:
– Buying a long-term bond today, or
– Rolling over successive short-term bonds whose future yields are uncertain.
If long-term rates reflect investors’ unbiased expectations of future short-term rates, then the yield on a multi-year bond equals the geometric average of anticipated one-year rates over the same horizon.
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Key takeaways
- Expectations theory links long-term yields to expected future short-term yields.
- It assumes investors care only about expected return, not maturity risk.
- The theory can be useful for forming forecasts but often omits term premiums and other real-world factors.
How it works (formula and example)
General relationship for a two-year horizon:
(1 + R2)^2 = (1 + R1_today) × (1 + E[R1_next_year])
Solve for the expected one-year rate next year:
E[R1_next_year] = [(1 + R2)^2 / (1 + R1_today)] − 1
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Example:
– Two-year yield (R2) = 20% → 1 + R2 = 1.20
– One-year yield today (R1_today) = 18% → 1 + R1_today = 1.18
Calculation:
– (1.20)^2 = 1.44
– 1.44 / 1.18 = 1.2203
– Expected one-year yield next year = 1.2203 − 1 = 0.2203 ≈ 22.03%
Interpretation: Given the current yields, the market-implied one-year rate next year would be about 22%.
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Limitations and disadvantages
- Ignores term premiums: Investors may require extra yield to hold longer maturities (liquidity or risk premium), so long-term yields need not equal expected future short rates.
- Sensitive to macroeconomic shocks: Central bank policy changes, inflation surprises, and growth outlooks affect short- and long-term yields differently.
- Overestimation risk: The model can overstate future short rates when it neglects demand/supply imbalances or risk considerations.
- Assumes risk-neutral investors: Real-world preferences for maturity, liquidity, and risk contradict this assumption.
Comparison: Expectations Theory vs. Preferred Habitat Theory
- Expectations theory assumes investors are indifferent to maturity and seek only expected yield.
- Preferred habitat theory recognizes that investors often prefer specific maturities (their “habitat”) and will only move into other maturities if compensated with a risk premium.
Result: Preferred habitat and liquidity-preference models help explain why long-term yields are often higher than the simple expectations-implied path of short rates.
Types of term-structure explanations
- Pure Expectations Theory — long-term rates reflect expected future short rates only.
- Liquidity Preference Theory — adds a positive term premium for longer maturities.
- Preferred Habitat Theory — investors prefer certain maturities and require compensation to shift out of their preferred range.
Practical accuracy and use
Expectations theory provides a clean, mathematical framework to extract market-implied future short rates from the yield curve. It is a useful starting point for analysis and for comparing market expectations to central-bank guidance. However, because it omits term premia and many macro drivers, it should be used alongside other models and qualitative judgment when making investment decisions.
Bottom line
Expectations theory links long-term yields to expected future short-term rates and can produce straightforward market-implied forecasts. Use it as one tool among several, and account for term premiums, policy actions, and macroeconomic risks before drawing firm conclusions.