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Portfolio Theory and Quantitative Investment / CAPM and Equilibrium Models

CAPM: The Security Market Line and Beta Pricing

The Capital Market Line describes equilibrium returns for efficient portfolios — those lying on the tangent from the riskless rate to the market frontier. But most securities and most portfolios are not efficient. An individual stock has idiosyncratic risk that cannot be eliminated except by holding the full market. Yet the market must somehow price that stock. What determines its equilibrium expected return?
The CAPM answers with the Security Market Line (SML): every asset's equilibrium expected excess return is proportional to its beta with the market portfolio. Idiosyncratic risk earns nothing, because diversification is costless and any investor can eliminate it. Only systematic risk — the covariance of the asset with the market — is rewarded:
Rˉi−RF=βi(RˉM−RF)(SML)\bar{R}_i - R_F = \beta_i(\bar{R}_M - R_F) \tag{SML}

This equation is arguably the most used formula in applied finance. Every WACC calculation, every cost-of-equity estimate, every hurdle rate in a corporate investment decision, and every benchmark-relative return decomposition starts from this one equation. The alpha in active management is defined as the deviation from this line: the return a portfolio earns above what its beta predicts. Understanding where the SML comes from — and what it assumes — is the foundation for interpreting when it fails.

Learning objectives. By the end of this note you should be able to:
  • state the Security Market Line equation and identify each term;
  • explain why beta — not total variance — is the relevant risk measure in equilibrium;
  • plot the SML and interpret the positions of individual securities relative to it;
  • compute a stock's required return using the CAPM, given market risk premium and beta;
  • explain the no-arbitrage logic behind the SML (securities off the line get arbitraged back on);
  • define Jensen's alpha and compute it from the SML.

In this lesson

  1. From CML to SML: beta as the relevant risk measure
  2. The Security Market Line
  3. Interpreting the SML
  4. Jensen's alpha
  5. Alternative form: the covariance-SML
  6. The characteristic line

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