From Risk to Return: The CAPM Mechanism
In the first article, we laid the groundwork: CAPM distinguishes between systematic risk (the one that counts) and specific risk (the one you can eliminate). But how do you concretely measure the systematic risk of a stock? And how does it translate into an expected return?
This is where two fundamental concepts come into play: beta and the Security Market Line (SML). These tools transform CAPM from an elegant theory into an operational model, usable to evaluate whether an investment is correctly priced by the market.
If the first article was the theory, this is the operating manual.
Beta: The Measure of Systematic Risk
Beta (β) is the beating heart of CAPM. It measures the sensitivity of a stock to market movements.
How Does Beta Work?
β = 1 → The stock moves exactly like the market. If the market goes up by 10%, the stock goes up by 10%.
β > 1 → The stock is more volatile than the market. A β of 1.5 means that if the market goes up by 10%, the stock tends to go up by 15%.
β < 1 → The stock is less volatile than the market. A β of 0.5 means that if the market goes up by 10%, the stock only goes up by 5%.
β = 0 → The stock is not correlated with the market (e.g., a risk-free bond).
β < 0 → The stock moves in the opposite direction to the market (rare, but possible with some assets like gold).
How is Beta Calculated?
Beta is calculated with the formula:
β = Cov(Ri, Rm) / Var(Rm)
Where:
Cov(Ri, Rm) = covariance between the returns of the stock and those of the market
Var(Rm) = variance of market returns
In practice, beta measures how much a stock tends to move along with the market. It’s a statistical regression: take the historical returns of the stock and the market, and see how correlated they are.
Practical Examples of Beta
Tesla (β ≈ 2.0) → Very volatile stock, amplifies market movements. When the market goes up, Tesla flies. When it goes down, it crashes.
Coca-Cola (β ≈ 0.6) → Defensive stock, less volatile than the market. People drink Coca-Cola even in a recession.
Utilities (β ≈ 0.5-0.7) → Stable sectors, not very sensitive to economic cycles.
Tech Growth (β ≈ 1.3-1.8) → Cyclical and volatile sectors, amplify market movements.
The Security Market Line (SML): Pricing Risk
If the Capital Market Line (CML) describes efficient portfolios, the Security Market Line (SML) describes individual stocks and their expected return as a function of beta.
The formula for the SML is the classic CAPM formula:
E(Ri) = Rf + βi × [E(Rm) - Rf]
Where:
E(Ri) = expected return of stock i
Rf = risk-free rate (e.g., yield on 10-year US Treasuries)
βi = beta of stock i
E(Rm) - Rf = market risk premium
What Does the SML Tell Us?
The SML is a straight line that starts from the risk-free rate and rises with a slope equal to the market risk premium. Each stock should be positioned on this line based on its beta.
Stocks on the SML → Are correctly priced by the market.
Stocks above the SML → Are undervalued (offer more return than they should for their risk).
Stocks below the SML → Are overvalued (offer less return than they should for their risk).
Numerical Example
Let’s assume:
Rf = 3% (risk-free rate)
E(Rm) = 10% (expected market return)
Risk Premium = 7% (10% - 3%)
Let’s calculate the expected return of two stocks:
Stock A (β = 1.5):
E(RA) = 3% + 1.5 × 7% = 3% + 10.5% = 13.5%
Stock B (β = 0.8):
E(RB) = 3% + 0.8 × 7% = 3% + 5.6% = 8.6%
If Stock A offers an expected return of 15%, it is undervalued (it’s above the SML). If it offers only 12%, it is overvalued (it’s below the SML).
Beta and SML in Practice: How to Use Them
CAPM and SML are powerful tools for:
Evaluating whether a stock is correctly priced — compare the CAPM expected return with the one implied in the market price.
Building portfolios with the desired risk — combine stocks with different betas to obtain the risk/return profile you are looking for.
Calculating the cost of equity — companies use CAPM to estimate the return required by shareholders (fundamental for DCF).
Comparing investments with different risks — CAPM gives you a common yardstick to evaluate different assets.
Limitations of Beta (Spoiler Alert)
Beta is elegant, but not perfect:
It’s based on historical data — the past doesn’t always predict the future.
It varies over time — a company’s beta can change with its strategy, leverage, sector.
It depends on the market index chosen — different betas if you use S&P 500, MSCI World, or other benchmarks.
It doesn’t capture all the risks — there are factors (size, value, momentum) that CAPM ignores.
But despite these limitations, beta remains one of the most used tools in finance. It’s simple, intuitive, and robust enough for most applications.
Conclusion: CAPM at Work
With beta and the SML, CAPM becomes operational. It’s no longer just theory: it’s a tool for making concrete investment decisions.
In the next (and last) article in the series, we will address the concept of alpha, the empirical evidence of CAPM, and the most important criticisms, including the devastating one from Richard Roll.
Spoiler: CAPM is not perfect, but it is still incredibly useful.