Expected Return Frameworks

Before valuing cash flows, you must establish the discount rate — the required rate of return that compensates you for the systematic risk of the asset.

The Capital Asset Pricing Model (CAPM) The Capital Asset Pricing Model (CAPM) formalizes the risk-return relationship for public equities, asserting that investors are compensated only for systematic, non-diversifiable risk (market risk). The required rate of return $E (R_{i})$ for a stock is:

E (R_{i}) = R_{f} + β_{i} (E (R_{m}) - R_{f})

where:

The risk-free rate, anchored to the current yield of short-term U.S. Treasury bills (T-bills), which represents a nominal yield with zero credit risk. For daily statistics, refer to the Treasury’s Daily Treasury Bill Rates.
The asset’s beta, measuring the covariance of the stock’s returns with the broad market relative to the market’s variance:
$β_{i} = \frac{Covariance (R_{i}, R_{m})}{Variance (R_{m})}$
The equity risk premium (ERP), representing the excess return demanded by investors to hold the risky market portfolio rather than risk-free assets. Historically, the U.S. ERP has averaged 4% to 6% above Treasuries.

Under CAPM, idiosyncratic (unsystematic) risk is ignored because a rational investor can diversify it away at zero cost. If a stock’s expected return exceeds its CAPM-derived required rate of return, the security is considered undervalued.

Beyond CAPM: Multi-Factor Models Empirical research has demonstrated that CAPM’s single-beta framework fails to explain a significant portion of historical stock returns. To address this, Eugene Fama and Kenneth French developed the Fama–French Three-Factor Model (1992),⁸⁹ which adds size and value risk factors:

E (R_{i}) = R_{f} + β_{i, 1} (E (R_{m}) - R_{f}) + β_{i, 2} (SMB) + β_{i, 3} (HML)

where:

SMB (Small Minus Big): Captures the size premium — the historical tendency of small-cap equities to outperform large-caps over long horizons.
HML (High Minus Low): Captures the value premium — the outperformance of value stocks (high book-to-market ratio) over growth stocks (low book-to-market ratio).

In 2014, Fama and French expanded the framework to a Five-Factor Model,⁹⁰ incorporating:

RMW (Robust Minus Weak): Captures the quality/profitability premium, showing that firms with high operating profitability generate superior returns.
CMA (Conservative Minus Aggressive): Captures the investment premium, showing that firms that allocate capital conservatively (low asset growth) outperform those that invest aggressively.

Factor investing requires a multi-decade time horizon (often 15+ years); factor premiums can experience extended periods of underperformance, but they provide a highly robust, empirically validated framework for constructing portfolios.

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