• Global Frameworks: CFA Level 1 (Portfolio Management), CIMA Financial Strategy (F3).

1. The Market Portfolio and the Capital Market Line (CML)
Under the strict equilibrium conditions of the Capital Asset Pricing Model (CAPM)—where all investors possess identical expectations, have access to perfect information, and face no transaction costs—the tangency portfolio becomes the Market Portfolio (M). This portfolio contains every risky asset in the global economy, weighted by its market value.
When the CAL uses the true market portfolio, it is renamed the Capital Market Line (CML):

E(R_p) = R_f + ((E(R_M) – R_f) / σ_M) · σ_p
  • Limitation: The CML can only evaluate the expected returns of total, fully diversified portfolios because it uses total risk (σ) as its risk metric. It cannot price individual stocks or inefficient portfolios.

2. The Security Market Line (SML)
Individual risky assets contain unsystematic risk, which can be diversified away. Therefore, the market only prices systematic risk, measured by Beta (β):

βi = Cov(R_i, R_M) / σ_M^2 = ρ{i,M} · (σ_i / σ_M)

Graphing expected return against Beta creates the Security Market Line (SML), which applies to all individual assets, portfolios, and asset classes:
Expected Return E(R)
      ▲
      │                             / Security Market Line (SML)
      │                            / 
      │         * Undervalued     /   (Alpha > 0)
      │          ───────►        /
      │                         /
      │                        / ◄─────── * Overvalued (Alpha < 0)
      │                       /
      │                      /
  Rf  ├─────────────────────* (Market Portfolio, Beta = 1.0)
      │                    /
      └───────────────────┴────────────────────────► Systematic Risk (β)

  • Alpha (α) Generation: If an asset is mispriced, it will drift off the SML.
    • An asset plotted above the SML is undervalued (α > 0); it offers too high a return for its risk. Analysts should buy it.
    • An asset plotted below the SML is overvalued (α < 0); it offers too low a return for its risk. Analysts should sell it.

3. Multifactor Models: Fama-French and Carhart
Empirical research shows that the single-factor CAPM cannot explain all market returns. This led to multi-factor models that isolate specific market premiums:
  • Fama-French Three-Factor Model: Expands on CAPM by adding size and value factors:

    E(R_i) = R_f + β_i1 (R_M − R_f) + β_i2 (SMB) + β_i3 (HML)
  •  

  •
    • HML (High Minus Low): Explains the historical premium of value stocks (high book-to-market ratios) over growth stocks.

    SMB (Small Minus Big): Explains the historical premium of small-cap stocks over large-cap stocks.

  • Carhart Four-Factor Model: Adds a momentum factor (WML – Winners Minus Losers), which captures the tendency of an asset’s recent performance trend to persist in the near term.
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