A factor is a common driver of asset returns. Economic growth, inflation, market returns and investment styles can explain why several securities move together. A loading measures an asset's sensitivity to the factor. A factor that explains covariance need not earn a nonzero risk premium. Distinguish a statistical source of co-movement from a priced exposure that investors require compensation to hold.
Risk premiums depend on when an asset pays. Losses in states where investors most need wealth are particularly costly. Assets that perform well in those states can command higher prices and lower expected returns. A factor need not affect every asset equally, or even every asset class, to matter for a particular portfolio.
The capital asset pricing model (CAPM) considers a single investment horizon, mean-variance investors and common beliefs about returns and covariances. Its standard version assumes frictionless trading and borrowing or lending at the risk-free rate. These assumptions lead investors to combine the same efficient risky portfolio with a risk-free asset. Market clearing makes that risky portfolio the value-weighted market portfolio.
Common mistakes
- Calling every common exposure a priced factor. Covariance explanation and expected-return compensation are different claims.
- Pricing only the mean payoff. The SDF example's assets have equal expected payoffs but prices of $95 and $98 because their state dependence differs.
- Changing benchmarks only in the numerator. A factor alpha needs a matching risk measure. The 0.275 ratio in Example 4 mixes definitions.
Bottom line
- Common factors need not all be priced; premiums compensate specified exposures.
- CAPM links expected return to market beta under restrictive assumptions.
- SDF valuation weights payoffs by both state probability and marginal value.
- Benchmark choice, horizon and risk denominator determine the measured alpha and ratio.
Exam shortcut
Write the benchmark and horizon beside every performance input. Use the same market premium throughout a factor comparison. For construction questions, separate the forecast adjustment from the holdings constraint, then compare the expected improvement with the cost of implementing it. When a return record looks unusually strong, check omitted factors and nonlinear payoffs before attributing it to skill.
The full lesson (about 4,816 words, 32 min read) adds 9 worked examples, all 6 common mistakes, a self-check, free in the app.
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