Required returns and factor exposures

Learning goals

• Explain capm expectations using mechanisms and limitations.
• Explain return regression using mechanisms and limitations.
• Explain multiple risk sources using mechanisms and limitations.

Draft · approximately 35 minutes, excluding further revision.

CAPM expectations

CAPM expresses expected equity return as the risk-free rate plus beta times the market risk premium; beta measures covariance exposure, not total volatility.

The market model is a statistical regression of realized asset returns on market returns with an intercept and residual; its intercept is not mechanically the CAPM risk-free rate.

Return regression

Beta depends on estimation frequency, sample, benchmark and firm leverage; historical precision does not guarantee a stable future exposure.

Idiosyncratic residual risk can be diversified under the model, whereas shared factor exposure remains; holding many similar exposures can preserve substantial systematic risk.

Multiple risk sources

Multifactor models distinguish exposures to several systematic drivers; factor definitions and correlations matter when interpreting contributions or designing a hedge.

Arbitrage-pricing reasoning connects expected returns to systematic exposures under assumptions; it does not identify every economically appropriate factor automatically.

Estimate beta from synchronized returns

Use fictional monthly market returns0%,2%,4% and stock returns1%,2%,6%. Means are2% and3%. Sum of cross deviations=0.001 and market squared deviations=0.0008, so slope beta=1.25 and intercept=0.03−1.25×0.02=0.005. Predicted stock returns are0.5%,3%,5.5%; residuals are0.5%,−1%,0.5%.

This tiny regression illustrates the computation only. A production estimate needs a defensible sample, synchronized currencies and periods, corporate-action adjustments, outlier review and uncertainty assessment. A multifactor regression may change the market coefficient when omitted exposures correlate with the market; historical alpha is not automatically exploitable expected alpha.

Formula and assumptions

E(Ri)=Rf+βi[E(Rm)−Rf]; Ri=α+βRm+ε

Original applied case: Required returns and factor exposures

1. Use risk-free 3%, beta 1.2 and expected market premium 5%, all for the same horizon.
2. CAPM required return=3%+1.2×5%=9%.
3. This is an expected required rate under a model; actual one-year return can differ sharply.

Errors to catch

• Do not assume: CAPM beta is identical to total standard deviation.
• Do not assume: The market-model intercept must equal the risk-free rate.
• Do not assume: Historical beta never changes.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org
• Reference · www.investor.gov