Beyond Beta: When CAPM Isn’t Enough
In the first two articles (first, second), we built the framework of the CAPM: from the fundamental assumptions to beta, up to the Security Market Line. Now it’s time to take a step back and ask ourselves: Does CAPM really work?
The short answer: yes and no.
CAPM is a powerful and still widely used tool, but it has obvious limitations. In this final article, we will explore:
Alpha — the measure of outperformance (or underperformance) compared to CAPM
Empirical Evidence — what works and what doesn’t in the real world
Richard Roll’s Critique — the fundamental problem of the market portfolio
Practical Uses — where CAPM is still useful (and where it isn’t)
Let’s prepare to question everything we’ve built so far. Welcome to the critical side of CAPM.
Alpha: The Measure of Outperformance
If beta measures systematic risk, alpha (α) measures the ability of an investment (or a manager) to beat the market net of the risk taken.
The Formula for Alpha
α = Ri - [Rf + βi × (Rm - Rf)]
Where:
Ri = actual return of the stock
Rf + βi × (Rm - Rf) = expected return according to CAPM
In other words, alpha is the difference between what you achieved and what CAPM predicted you should achieve given your level of risk.
How to Interpret Alpha?
α > 0 → Outperformance. You beat the market net of risk. Well done (or lucky).
α = 0 → Performance in line with CAPM. You got exactly the expected return for your risk.
α < 0 → Underperformance. You did worse than expected. You would have been better off with a passive ETF.
Practical Example
Let’s assume:
Rf = 3%
Rm = 10%
Risk Premium = 7%
β of your portfolio = 1.2
Expected return according to CAPM:
E(R) = 3% + 1.2 × 7% = 11.4%
If your portfolio returned 14%, your alpha is:
α = 14% - 11.4% = +2.6%
Congratulations, you generated positive alpha. But is it skill or luck? That is the million-dollar question.
The Problem of Alpha
Most studies show that:
Positive alpha is rare — most active funds do not beat the market net of fees
Alpha does not persist — those who beat the market one year often do not do so the following year
Alpha can be luck, not skill — it is difficult to distinguish skill from luck in the short term
This is one of the reasons why passive ETFs have been so successful in recent decades.
Empirical Evidence: What Works (and What Doesn’t)
CAPM is elegant on paper, but how does it behave in the real world? The empirical evidence is... complicated.
What Works ✅
The risk-return relationship exists — on average, riskier assets offer higher returns. This is confirmed by the data.
Beta explains some of the variation in returns — not everything, but a significant part.
Diversification works — specific risk can really be eliminated with a well-constructed portfolio.
What Does NOT Work ❌
Beta does not explain everything — there are other factors that influence returns:
Size Effect — small caps tend to outperform large caps (at the same beta)
Value Effect — value stocks tend to beat growth stocks (at the same beta)
Momentum — stocks that have performed well continue to do so in the short term
The beta-return relationship is weaker than expected — in the 70s-80s, several studies showed that the slope of the SML is flatter than CAPM predicts.
Market Anomalies — there are systematic patterns that CAPM fails to explain:
January Effect — January returns are systematically higher
Weekend Effect — Monday returns tend to be negative
Low Volatility Anomaly — less volatile stocks outperform more volatile ones (the opposite of what CAPM predicts!)
The Evolution: Multifactor Models
These limitations have led to the development of more sophisticated models:
Fama-French 3-Factor Model (1992) — adds size and value to the market beta
Carhart 4-Factor Model (1997) — adds momentum
Fama-French 5-Factor Model (2015) — adds profitability and investment
These models explain historical returns better, but they are also more complex and less elegant than the original CAPM.
Richard Roll’s Critique: The Fundamental Problem
In 1977, Richard Roll published a devastating critique of CAPM, known as “Roll’s Critique.” The argument is simple but lethal:
The Market Portfolio is Unobservable
CAPM requires the use of the true market portfolio — which includes all the risky assets in the world: stocks, bonds, real estate, commodities, private equity, art, human capital, etc.
But we cannot observe this portfolio. In practice, we use proxies such as the S&P 500 or the MSCI World. And this creates a problem:
If we use the wrong proxy, all CAPM tests are invalid.
The Implications of Roll’s Critique
We cannot test CAPM — we can only test whether a specific market proxy is mean-variance efficient.
Beta depends on the proxy — the beta of a stock changes depending on the index you use as the “market.”
Empirical results are ambiguous — if CAPM “fails” in tests, is it because the model is wrong or because we used the wrong proxy?
Roll does not say that CAPM is useless, but that it is impossible to verify it empirically in a definitive way.
Practical Uses: Where CAPM is Still Useful
Despite the limitations, CAPM is still widely used. Here’s where:
1. Valuation of the Cost of Equity
Companies use CAPM to estimate the return required by shareholders (ke), fundamental for:
Discounted Cash Flow (DCF) — to assess the intrinsic value of a company
Capital Budgeting — to decide which projects to undertake
WACC — to calculate the weighted average cost of capital
2. Performance Evaluation
Funds and managers are evaluated using alpha and beta:
Sharpe Ratio — excess return per unit of total risk
Treynor Ratio — excess return per unit of systematic risk
Jensen’s Alpha — measure of risk-adjusted outperformance
3. Asset Allocation
CAPM helps build efficient portfolios by combining:
Risk-Free Assets (government bonds)
Market Portfolio (diversified ETFs)
Leverage or De-Leverage depending on risk propensity
4. Benchmark for Passive Investors
CAPM provides the theoretical basis for passive investing: if you can’t beat the market consistently, buy the market(index funds).
Conclusion: Is CAPM Dead? Long Live CAPM
CAPM has obvious limitations:
Its assumptions are unrealistic
The empirical evidence is mixed
The market portfolio is unobservable
There are risk factors that the model ignores
Yet, CAPM is still alive and well. Why?
It’s simple — an elegant formula that anyone can understand and apply
It’s intuitive — it captures the fundamental idea that risk and return are linked
It’s a good starting point — even if not perfect, it provides a useful framework
It’s widely accepted — industry standard for valuations and analysis
As George Box said: “All models are wrong, but some are useful.”
Is CAPM wrong? Probably yes. Is it useful? Absolutely.
And in the end, in finance as in product management, what matters is not theoretical perfection, but practical usefulness.