Welcome to Rational Expectations Theory!
Hello there! Welcome to one of the most intriguing parts of the CM2 syllabus. If you’ve ever wondered why markets react so quickly to news, or why beating the market is notoriously difficult, you’re in the right place. Rational Expectations Theory is a cornerstone of modern financial economics. Don't worry if the logic feels a bit abstract at first—we’re going to break it down into simple, bite-sized pieces that make complete sense in an actuarial and investment context.
1. What are Expectations?
In economics, an expectation is simply a forecast about what will happen to a variable in the future (such as future asset prices, interest rates, or inflation). Because investment decisions depend on expected future cashflows, how market participants form these expectations is critical.
Adaptive vs. Rational Expectations
Before rational expectations, economic models relied on adaptive expectations:
1. Adaptive Expectations: Backward-looking. Individuals base forecasts solely on past values, adjusting their expectations only after observing a forecast error. If inflation was 2% last year, they expect 2% next year. This implies people make systematic, predictable errors when conditions change.
2. Rational Expectations: Forward-looking. Economic agents form forecasts using all available information, including past data, current knowledge, and an understanding of the underlying economic model.
2. The Rational Expectations Hypothesis (REH)
The Rational Expectations Hypothesis assumes that economic agents do not make systematic forecasting errors. Formally, let \( X_{t+1} \) be the variable to be realised at time \( t+1 \), and let \( \Omega_t \) represent the information set available at time \( t \). The rational expectation is the mathematical conditional expectation:
\( E[X_{t+1} | \Omega_t] \)
The actual outcome can be written as the expected value plus an error term \( \epsilon_{t+1} \):
\( X_{t+1} = E[X_{t+1} | \Omega_t] + \epsilon_{t+1} \)
Under REH, the forecast error \( \epsilon_{t+1} \) satisfies two key properties:
- Zero mean: \( E[\epsilon_{t+1} | \Omega_t] = 0 \). Forecasts are unbiased on average.
- Orthogonality (uncorrelated with information): The error term is completely uncorrelated with any variable in \( \Omega_t \). If it were correlated, agents could have used that relationship to improve their forecast!
Important: Rational \(\neq\) Perfect Foresight
Rational expectations does not mean investors can see the future. Random shocks occur. However, errors are unpredictable noise rather than persistent, exploitable bias.
3. The Efficient Markets Hypothesis (EMH)
When the Rational Expectations Hypothesis is applied to financial markets, it forms the foundation of the Efficient Markets Hypothesis (EMH). An efficient market is defined as one in which asset prices fully and instantaneously reflect all available information.
Because prices adjust immediately to reflect the information set \( \Omega_t \), no investor can consistently earn abnormal (risk-adjusted) returns. The definition of 'all available information' leads to the three classical forms of EMH (formulated by Eugene Fama):
A. Weak Form EMH
Information set (\( \Omega_t \)): Consists only of all past market trading data, such as historical security prices, returns, and trading volumes.
Implication: Current asset prices already reflect all information contained in past prices. Successive price changes must therefore be independent random variables (a random walk or martingale difference process).
B. Semi-Strong Form EMH
Information set (\( \Omega_t \)): Includes all publicly available information. This encompasses past price history plus financial statements, company announcements, economic data, news reports, and published analyst forecasts.
Implication: Asset prices adjust immediately and unbiasedly as soon as public information is released. No analysis of public data can yield consistent abnormal profits.
C. Strong Form EMH
Information set (\( \Omega_t \)): Encompasses all information whatsoever, both public and private (insider information).
Implication: Security prices instantly reflect even monopolistic private information held by corporate insiders or management. No one—not even corporate directors—can earn abnormal risk-adjusted returns.
4. Consequences for Investment Management
The validity of each form of EMH has profound implications for how institutional investors and actuaries design investment strategies:
1. Implications of Weak Form for Technical Analysis:
Technical analysis (chartism) attempts to predict future price movements by studying patterns in past prices and trading volume (e.g. moving averages, head-and-shoulders patterns). If the weak form holds, technical analysis is completely useless for generating abnormal returns, as past patterns contain zero unpriced information.
2. Implications of Semi-Strong Form for Fundamental Analysis:
Fundamental analysis involves analysing company accounts, industry dynamics, competitive advantages, and economic trends to identify 'underpriced' or 'overpriced' stocks. If semi-strong efficiency holds, fundamental analysis cannot beat the market because market prices adjust to new information faster than an active analyst can trade on it.
3. Active vs. Passive Investment Management:
If markets are semi-strong or strong-form efficient, active portfolio management (stock picking and market timing) simply incurs research expenses and transaction costs that drag performance below the market benchmark. The rational policy is therefore passive management (such as investing in broad index-tracking funds), keeping costs low and holding a well-diversified portfolio tailored to the investor's risk tolerance.
5. Empirical Evidence: For and Against the EMH
A. Evidence Regarding the Weak Form
Evidence supporting weak form:
- Serial correlation tests: Autocorrelations of day-to-day or week-to-week stock returns are generally close to zero, supporting the random walk hypothesis.
- Filter rule tests: Trading rules based on past price movements (e.g. buy if a share rises by \( 5\% \)) do not outperform a simple buy-and-hold strategy once transaction costs are deducted.
Evidence against weak form (Anomalies):
- Momentum effect: Over intermediate horizons (3 to 12 months), past winners tend to continue outperforming past losers.
- Long-term reversal: Over 3- to 5-year horizons, extreme past losers tend to outperform extreme past winners.
- Calendar anomalies: Statistically significant return patterns have been documented at specific calendar dates, such as the 'January effect' (higher small-cap returns in January) and the 'day-of-the-week effect' (historically lower returns on Mondays).
B. Evidence Regarding the Semi-Strong Form
Evidence supporting semi-strong form:
- Event studies: Studies analysing major news events (e.g. earnings announcements, stock splits, dividend changes, takeover bids) show that share prices adjust within minutes or hours without significant persistent drift.
- Mutual fund performance: On average, actively managed mutual funds fail to beat passive index benchmarks on a risk-adjusted basis, especially after deducting management fees and transaction expenses.
Evidence against semi-strong form (Anomalies):
- Post-earnings announcement drift (PEAD): Following an earnings surprise, stock prices often continue to drift in the direction of the surprise over subsequent weeks, suggesting underreaction.
- Fundamental anomalies: Strategies sorting stocks by accounting metrics systematically earn abnormal returns not explained by standard risk models—for instance, the size effect (small-cap stocks outperforming large-cap stocks) and the value effect (stocks with low price-to-earnings or high book-to-market ratios outperforming growth stocks).
- Speculative bubbles and crashes: Rapid asset price surges disconnected from fundamentals (e.g. dot-com bubble) and sudden crashes (e.g. October 1987) suggest limits to market rationality.
C. Evidence Regarding the Strong Form
Evidence supporting strong form:
- Professional fund managers and institutional investors with proprietary resources generally fail to outperform the market consistently over the long run.
Evidence against strong form:
- Insider trading: Studies show corporate insiders (directors, senior executives) systematically earn significant abnormal profits when trading shares of their own firms before public news announcements.
- Specialist/market-maker profits: Parties with privileged order-book access often achieve superior risk-adjusted returns.
Conclusion: Empirical testing overwhelmingly rejects the strong form of the EMH in its strict sense.
6. Summary of Key Concepts
- Rational expectations: Forecasts use all available information (\( \Omega_t \)) and errors are random with zero expected value.
- Weak form EMH: \( \Omega_t \) is past price and volume data. Technical analysis cannot generate abnormal returns.
- Semi-strong form EMH: \( \Omega_t \) is all public information. Fundamental analysis cannot generate abnormal returns; favours passive investment.
- Strong form EMH: \( \Omega_t \) is all information (public and private). Even insider trading cannot generate abnormal returns (empirically refuted).
- Empirical consensus: Markets are broadly weak-form and substantially semi-strong-form efficient, but anomalies (momentum, value effect, PEAD) and behavioral biases show efficiency is not absolute.