Risk Premia

A valid risk premium must be grounded in a structural or behavioral reason for its persistence. Structural premia arise from bearing undiversifiable macroeconomic risks (e.g., equity premium compensates for consumption risk). Behavioral premia stem from persistent investor biases (e.g., value premium from over-extrapolation). Without a sound economic narrative, a factor is likely a statistical artifact.

• Structural: Compensation for covariance with bad times (recession, liquidity crisis)
• Behavioral: Exploitation of cognitive errors (anchoring, loss aversion)
• Hybrid: Momentum combines initial underreaction with eventual overreaction

A robust risk premium manifests across diverse markets and time periods, not just in a single country or decade. The value premium, for instance, has been documented in US equities, international developed markets, and emerging markets. Pervasiveness reduces the probability that the observed return is a sample-specific anomaly.

• Out-of-sample test: Evidence in multiple independent markets
• Asset class breadth: Exists in equities, fixed income, currencies, and commodities
• Temporal stability: Persistent over distinct economic regimes

The premium should not depend on a single, fragile definition. For example, the value factor can be measured by book-to-price, earnings-to-price, or cash-flow-to-price ratios. A premium that vanishes with minor definitional tweaks is likely overfitted. Robustness implies the signal is capturing a genuine underlying phenomenon.

• Multiple proxies: Various fundamental metrics yield similar results
• Parameter stability: Not sensitive to rebalancing frequency or weighting scheme
• Survivorship: Persists after accounting for delisted and bankrupt firms

The premium must be capturable after accounting for real-world transaction costs, market impact, and liquidity constraints. A theoretical premium concentrated in micro-cap stocks with high turnover may be unattainable in practice. The gap between paper returns and realized returns defines the strategy's capacity.

• Capacity: Maximum AUM before alpha is arbitraged away
• Turnover: Lower turnover reduces slippage and tax drag
• Short-side feasibility: Availability and cost of borrowing securities

Risk premia are not constant income streams; they exhibit significant cyclicality and can experience prolonged drawdowns. The value factor, for example, suffered a severe drawdown from 2017–2020. Understanding the correlation of drawdowns across factors and their relationship to macroeconomic regimes is critical for portfolio construction.

• Regime dependence: Performance varies with growth, inflation, and volatility
• Correlation clustering: Drawdowns often coincide during liquidity crises
• Recovery profile: Mean-reversion speed after underperformance troughs

The premium's historical average excess return must be statistically distinguishable from zero. A common threshold is a t-statistic greater than 2.0. However, due to multiple testing bias—researchers testing thousands of factors—higher hurdles like a t-statistic above 3.0 or the deflated Sharpe ratio are necessary to control the false discovery rate.

• t-stat > 2.0: Basic threshold for significance
• t-stat > 3.0: Adjusted threshold accounting for data mining
• Deflated Sharpe Ratio: Penalizes for the number of untested variations

A risk premium captured by buying assets that appear cheap relative to their fundamentals and selling those that appear expensive. The classic metric is the book-to-price ratio, though modern implementations use composite measures including earnings yield and cash flow yield. The premium is often attributed to the higher distress risk and longer duration of value firms, which require compensation. Academic research by Fama and French established value as a core equity factor alongside market beta and size.

A risk premium based on the empirical tendency for assets that have performed well in the recent past to continue outperforming in the near future, and vice versa. Typically measured over a 6-12 month lookback window excluding the most recent month. The premium is attributed to behavioral biases like investor herding and delayed overreaction, as well as risk-based explanations involving growth rate shocks. Momentum is observed across asset classes including equities, currencies, and commodities.

A risk premium captured by going long assets with high carry and shorting assets with low carry. Carry is the return an investor earns if spot prices remain unchanged. In currencies, this is the interest rate differential; in commodities, it is the roll yield from futures curve structure; in fixed income, it is the term spread. The premium compensates investors for bearing the risk of sudden price reversals during crash events, which can produce severe drawdowns.

The empirical observation that portfolios of low-volatility stocks tend to generate higher risk-adjusted returns than high-volatility stocks, contradicting traditional CAPM predictions. Possible explanations include leverage constraints forcing investors seeking high returns into volatile stocks, and the lottery preference of retail investors. The anomaly is robust across global markets and persists even after controlling for value and size factors.

A phenomenon where many investors pile into the same factor-based strategies, compressing expected returns and increasing the risk of a sharp, correlated drawdown when the trade unwinds. Crowding can be measured through metrics like pairwise correlation of hedge fund returns, valuation spreads reaching extreme levels, and increased factor volatility. The quant quake of August 2007 and the value factor drawdown of 2018-2020 are canonical examples of crowding-induced crashes.