💼 Portfolio Management

CAPM Formula — Capital Asset Pricing Model Explained

The CAPM formula explained: expected return = risk-free rate + beta × market premium. Capital asset pricing model with examples and CFA Level 1 practice.

Key Concepts

Capital Market Line (CML)

CAL using the MARKET portfolio as the optimal risky portfolio. E(R) = R<sub>f</sub> + [(R<sub>m</sub>-R<sub>f</sub>)/σ<sub>m</sub>]σ<sub>p</sub>.

Systematic vs Unsystematic Risk

Systematic (market/non-diversifiable): β measures sensitivity. Unsystematic (company-specific): eliminated by diversification.

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Formulas

From this module

CAPM / SML

E(Ri) = Rf + βi[E(Rm) - Rf]

Where: R<sub>f</sub> = risk-free, β = beta, E(R<sub>m</sub>)-R<sub>f</sub> = market risk premium

Beta

βi = Cov(Ri, Rm) / σ²m

Where: σ²<sub>m</sub> = variance of market returns

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Master Formula Sheet -- Portfolio Management

Utility Function

U = E(R) - ½ × A × σ²

A = risk aversion (A>0: risk-averse)

CAL Equation

E(Rᶜ) = Rᶠ + [E(Rₚ)-Rᶠ]/σₚ × σᶜ

Slope = Sharpe ratio

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Decision Frameworks

Which performance measure to use?

Use when:

  • Sharpe: for well-diversified portfolios (total risk matters)
  • Treynor: for portfolios that are part of a larger diversified portfolio (β matters)
  • Jensen’s Alpha: for measuring active manager skill

Avoid when:

  • Sharpe for poorly diversified portfolios (total risk includes diversifiable risk)
  • Treynor when portfolio is the investor’s entire holdings

Test Your Understanding

R<sub>f</sub>=2%, β=1.2, Market return=9%. CAPM expected return:

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