Revisiting the CAPM
Challenging the Risk-Return Framework
Market Concentration, Diversification
1 Introduction
The Capital Asset Pricing Model (CAPM), developed by Sharpe (1964), Lintner (1965), and Mossin (1966), remains a cornerstone of modern finance, linking expected returns to risk. It classifies risk into two categories: systematic risk, which stems from market-wide factors and cannot be diversified away, and unsystematic risk, which is asset-specific and can be mitigated through diversification. The CAPM posits that only systematic risk, measured by beta, justifies a return premium, as investors can eliminate unsystematic risk by holding a diversified portfolio, ideally approximating the market portfolio. This principle aligns with broader linear factor models like the Arbitrage Pricing Theory (APT) (Ross 1976), which extends the CAPM by incorporating multiple systematic risk factors while similarly dismissing diversifiable risk under no-arbitrage conditions.
However, the CAPM’s empirical validity has been contested. Banz (1981) documented the size effect, where small-cap stocks outperform CAPM predictions, while Basu (1977) identified the value effect, showing excess returns for stocks with high earnings-to-price ratios. These anomalies spurred the development of multifactor models, such as the Fama-French three-factor model (Fama and French 1993), which augment beta with size and value factors. Beyond these, market concentration has emerged as a critical lens for understanding asset pricing deviations. Hou and Robinson (2006) found that firms in concentrated industries earn higher returns, attributing this to economic rents from market power. Edmans (2009) linked ownership concentration to superior performance, while Choi et al. (2017) showed that institutional investors with concentrated portfolios outperform diversified ones. Neuhann and Sockin (2024) explored how financial market concentration distorts capital allocation, and Bustamante and Donangelo (2017) tied product market concentration to industry returns.
From a theoretical perspective, Magill and Quinzii (1996) argued that incomplete markets—lacking sufficient contingent claims—prevent full risk hedging, challenging CAPM assumptions. Cochrane (1996) emphasized the role of investment-based pricing, while Campbell (1992) critiqued volatility as an incomplete risk measure. Socioeconomic analyses, such as Saez and Zucman (2016), further connect market concentration to wealth inequality, highlighting broader implications. This rich body of literature suggests that market structure and concentration significantly complicate the CAPM’s risk-return framework, necessitating a deeper examination.
2 Main
2.1 Empirical and Mathematical Foundations of Diversification
Diversification’s risk-reducing power is well-established empirically and mathematically. Elton and Gruber (1977) analyzed 3,290 securities, demonstrating that a portfolio of just four stocks markedly reduces variance compared to a single stock, underscoring diversification’s practical utility.
Mathematically, consider an equally weighted portfolio of \(n\) securities. The portfolio variance \(\sigma_p^2\) is given by:
\[ \sigma_p^2 = \frac{1}{n} \bar{\sigma}^2 + \frac{n-1}{n} \bar{\rho} \bar{\sigma}^2 \]
where:
- \(\bar{\sigma}^2\) = average variance of individual securities
- \(\bar{\rho}\) = average correlation between securities
As \(n\) increases, \(\sigma_p^2\) converges to \(\bar{\rho} \bar{\sigma}^2\), indicating that covariance, not individual variance, dominates portfolio risk. When \(\bar{\rho} < 1\), diversification lowers volatility, resembling how higher-order terms in Taylor polynomials diminish to smooth a function or how fractal geometry simplifies irregularities with scale.
2.2 A Critique of Risk as Volatility
The CAPM equates risk with volatility, but this assumption is narrow. Long-term investors may prioritize structural risks—e.g., economic shifts or sector obsolescence—over short-term price swings. A volatile growth stock might be less “risky” to them than a stable but declining asset. Campbell (1992) supports this critique, arguing that volatility oversimplifies the multifaceted nature of risk, a view echoed by behavioral finance perspectives (Shiller 2003).
2.3 Diversification and the Risk-Return Trade-Off
The CAPM ties diversification to the risk-return trade-off, suggesting investors can eliminate unsystematic risk while earning returns proportional to systematic risk exposure. In a stochastic setting, diverse agents (e.g., farmers, energy producers) share idiosyncratic risks, enhancing welfare (Cochrane 2009). Yet, this assumes a broad, competitive market. When the market portfolio—say, the S&P 500—is dominated by a few highly correlated stocks (e.g., tech giants), diversification falters. High \(\bar{\rho}\) reduces variance’s sensitivity to \(n\), undermining the CAPM’s benefits (Grullon, Larkin, and Michaely 2019).
2.4 Market Concentration and the Upper Frontier
In the standard arbitrage-free asset pricing framework, the upper mean-variance frontier assets correlate perfectly (negatively) with the stochastic discount factor (SDF). In concentrated markets, dominant firms with economic moats (Bustamante and Donangelo 2017) act as principal components, compressing the payoff space. For example, if the Herfindahl-Hirschman Index (HHI) measures this dominance or concentration, then a high HHI signals reliance on few assets, limiting diversification. Investors may then seek arbitrage in these stocks, amplifying concentration (Valta 2012).
2.5 Implications for Investors and Market Stability
In concentrated markets, diversification yields to capturing rents from dominant firms. These firms use primary-market capital to reinforce moats, distributing profits rather than fostering competition (Hou and Robinson 2006). Secondary-market trading becomes zero-sum, redistributing wealth without value creation. Early investors in concentrated stocks gain disproportionately, widening inequality (Saez and Zucman 2016) and challenging the CAPM’s traditional data-driven risk-return logic.
2.6 Broader Socioeconomic Consequences
Concentration reduces contingent claim diversity, impairing hedging capacity (Magill and Quinzii 1996). A shock to a dominant sector triggers systemic ripples, increasing instability. This homogeneity shifts markets from managing uncertainty to rewarding market power, exacerbating wealth gaps and contradicting the CAPM’s egalitarian risk-sharing ideal.
3 Conclusion
The CAPM’s diversification-driven risk-return framework faces significant challenges from market concentration. As diversification weakens, investors prioritize rents over risk reduction, simplifying markets into systems dominated by a few firms. This shift threatens stability, equity, and hedging capacity, urging a rethinking of the CAPM and policies to enhance market diversity.