Equity Trading Markets

The three-factor model (market beta, size, value) explains over 90% of the cross-sectional variation in portfolio returns, vastly outperforming the single-factor CAPM.

The value premium (HML factor) averages approximately 4.4% per year historically, but has been shrinking since publication, raising questions about whether it was a genuine risk premium or a statistical artifact that was arbitraged away.

A strategy of buying past 6-month winners and selling past 6-month losers earns approximately 1% per month over the subsequent 6-12 months on US stocks 1965-1989, after controlling for systematic risk. This momentum effect persists across size quintiles and is not explained by the Fama-French three-factor model.

Stocks with the worst 3-year prior returns (losers) outperform stocks with the best 3-year prior returns (winners) by approximately 25 percentage points over the subsequent 5 years, consistent with investor overreaction. Prior losers earn about 19.6% more per year than prior winners.

A three-factor model including market return, size (SMB), and book-to-market (HML) factors captures most cross-sectional variation in US stock returns, with HML loading capturing value premium of approximately 4-5% per year. The model explains 90%+ of variance in diversified portfolio returns.

High investor sentiment predicts lower subsequent returns for difficult-to-arbitrage stocks (small, young, unprofitable, distressed) and higher returns for the same stocks when sentiment is low. A one-standard-deviation increase in beginning-of-year sentiment predicts a 2.4% lower annual return for speculative stocks.

Several technical patterns (head-and-shoulders, double tops/bottoms, broadening patterns) exhibit statistically significant conditional return distributions different from the unconditional distribution, suggesting informational content in technical analysis. However, after accounting for data snooping, results are weaker.

When arbitrageurs face capital constraints and performance-based investor withdrawals, they may reduce positions when prices move against them, allowing anomalies (momentum, value) to persist even with sophisticated investors present. Arbitrage is thus limited and anomalies can be self-reinforcing in the short run.

In a competitive market with one informed insider and a market maker, the informed trader's private information is incorporated gradually into prices through trading. Market depth (lambda) is constant and inversely related to the amount of private information, meaning more informed trading leads to less liquid markets.

VIX spikes correspond to sharp market declines (average VIX increase of 6.6 points on days S&P 500 falls more than 3%) and mean-reverts quickly after spikes. High VIX readings historically precede above-average subsequent market returns, supporting its use as a contrarian sentiment indicator.

Evidence from event studies supports semi-strong form efficiency — prices adjust rapidly to public information such as stock splits and earnings announcements. Weak-form efficiency is broadly supported by the absence of profitable filter rules. Strong-form efficiency fails: corporate insiders earn abnormal returns.

The efficient frontier of risky assets traces the minimum-variance portfolio for each level of expected return. Diversification reduces portfolio variance whenever assets are less than perfectly correlated. The optimal portfolio for any investor lies on the efficient frontier, with the specific point determined by risk tolerance.

In equilibrium, expected asset returns are linearly related to systematic risk (beta relative to the market portfolio). Only systematic risk is priced; idiosyncratic risk is not because it can be diversified away. This provides the theoretical foundation for the Sharpe ratio as the appropriate measure of risk-adjusted performance.

The put-call ratio is one of six indicators (along with closed-end fund discount, NYSE share turnover, IPO volume/returns, dividend premium) that form a composite investor sentiment index. High sentiment predicts lower subsequent returns for difficult-to-arbitrage stocks (small, young, volatile, unprofitable). The sentiment effect is most pronounced in the cross-section, not just the aggregate market.

The CBOE VIX (computed from S&P 100 implied volatilities) serves as a forward-looking fear gauge: spikes in VIX reliably precede periods of equity market turbulence. The put-call ratio and VIX are complementary sentiment measures — put-call ratio captures directional investor positioning while VIX captures expected market volatility.