Experiment Here is an experiment that demonstrates Ferson’s point (see Ferson, Sarkissian and Simin, Journal of Financial Markets 2 (1), 49-68, February 1999) In this experiment, returns are generated such that cross-sectional differences are entirely due to non-risk reasons. However loadings on the spread portfolio “explain” these differences, so there appears to be a common risk factor

Set-up We want to generate returns that: –Match the (unconditional) cross- sectional average –Have cross-sectional differences that are associated with some non-risk attribute –Have time-varying predictable properties –Have co-movement in returns

Return simulation Sort stocks into 100 portfolios based on first 2 letters of the firm’s name Introduce systematic behavior into returns through simulated excess return r SIM r SIM = μ ACT + δ 0 + δ 1 ’z t-1 + ε SIM

Siimulated return components Constant (grand mean of excess return across portfolios) μ ACT Cross-sectional difference δ 0 –Center at zero –Return difference between highest and lowest = actual value premium, spread equally across portfolios

Simulated return components Predictable time variation –Instruments z t-1 3-month T-bill Dividend yield on S&P500 Expressed as deviations from mean –Coefficients δ 1 Regress HML on z t-1 Centering at zero, spread out each coefficient uniformly across 100 portfolios Rescale to destroy uniformity in coefficients

Simulated return components Residual return –For each portfolio p regress its time series of actual excess return on z t-1, get e P –Regress time series of S&P500 excess returns on δ 1 ’z t-1, get e M –Regress e P on e M, collect slope coefficients in b –Let V(ε) = bb’ + σ 2 I N –Transform e P such that their variances = V(ε)

Risk versus characteristics Researcher looks at returns on the alphabet-sorted portfolios Builds factor-mimicking portfolio AMZ that goes long low-alphabet order (‘A’) firms and goes short high-alphabet order (‘Z’) firms Does 2-pass CSR r sim pt = γ 0 + γ 1 β pM + γ 2 β pAMZ + γ 3 W pt + ξ pt

What would the researcher find?