Experiment

1
Experiment

• Here is an experiment that demonstrates Fersons
  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

2
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

3
Return simulation

• Sort stocks into 100 portfolios based on first 2
  letters of the firms name
• Introduce systematic behavior into returns
  through simulated excess return rSIM
• rSIM µACT d0 d1zt-1 eSIM

4
Siimulated return components

• Constant (grand mean of excess return across
  portfolios) µACT
• Cross-sectional difference d0
• Center at zero
• Return difference between highest and lowest
  actual value premium, spread equally across
  portfolios

5
Simulated return components

• Predictable time variation
• Instruments zt-1
• 3-month T-bill
• Dividend yield on SP500
• Expressed as deviations from mean
• Coefficients d1
• Regress HML on zt-1
• Centering at zero, spread out each coefficient
  uniformly across 100 portfolios
• Rescale to destroy uniformity in coefficients

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Simulated return components

• Residual return
• For each portfolio p regress its time series of
  actual excess return on zt-1, get eP
• Regress time series of SP500 excess returns on
  d1zt-1, get eM
• Regress eP on eM, collect slope coefficients in b
• Let V(e) bb s2IN
• Transform eP such that their variances V(e)

7
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
• rsimpt ?0 ?1 ßpM ?2 ßpAMZ ?3 Wpt ?pt

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What would the researcher find?
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