Seasonality in Equilibrium Stock Returns: A Dynamic Perspective on SAD

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Seasonality in Equilibrium Stock Returns A
Dynamic Perspective on SAD

• Xifeng Diao Maurice Levi
• U of Calgary UBC
  

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Motivation

• Saunders (1993), Hirshleifer and Shumway(2003)
• Sunshine/Daylight (measured by cloudiness) ? Mood
  ? Bias ? Returns (low returns on rainy days)
• Kamstra, Kramer, and Levi (KKL, 2003)
• Sunshine/Daylight (measured by length of day) ?
  SAD ? Risk Aversion ? Returns (high returns on
  short days)
• The implication of seasonal risk aversion for
  returns
• Static effect higher risk aversion in fall and
  winter ? higher required returns in fall and
  winter
• Dynamic effect risk aversion decreases in winter
  and spring ? price ? ? high realized returns in W
  and Sp
• Which effect dominates? Not clear in previous
  study

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This Papers Contribution

• Dynamic effect should dominate
• Our model shows that it is the change, not the
  level, of daylight or risk aversion that
  determines the pattern of SAD-induced seasonal
  returns (Winter, Spring gt Summer, Fall)
• Others
• Concavity (diminishing marginal impact of
  daylight WgtSp, SugtF)
• Cross-sectional differences (size, beta, STD)
• Empirical Evidence

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The Model

• Assets
• Zero net supply of bond, rf normalized to 0.
• A single risky asset with a terminal payoff DT,.
• dDt / Dt µD dt sD dBt
• Agent
• A representative agent with CRRA utility
• Objective function Max E U(WT)

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Equilibrium Returns

• Return from time t to td
• log (Std / St)
• (?t-0.5) sD2d (?t ?td)sD2(Tt-d)
  sD(BtdBt)
• where ? risk aversion.
• Concavity ?t -g(lt), where lt is length of day
  at t, and g(lt) is concave.

Dynamic Term
Variance Term
Static Term
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Summary of Implications

• Winter gt Spring gt Summer gt Fall
• Cross-sectional
• Risk riskier firms have larger amplitudes
• Size smaller firms tend to have more ownership
  by individual investors, who are more susceptible
  to behavioural factors

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Quarterly Excess Returns (1962-2000)
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Quarterly Excess Returns (Size Deciles)
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Comparing Different Hypotheses
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AR-GARCH-M Model
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Size/Risk and Seasonality Amplitude
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Summary

• Theory
• Dynamic Effect Should Dominate W,SpgtSu,F
• Concavity Effect WgtSp SugtF
• Further Inferences
• Cross-sectional Differences Size/Risk
• Tests
• Strongly supportive (size premium is even
  reversed in fall)