Return Predictability and Stock Market Crashes in a Simple Rational Expectations Model



6.6 The Price of the Market Portfolio

The price of the market portfolio at date t, St ,is

St = £ exp(rf (t - s))E[DsΦt,sDt) + exp(-rf h)E(dpDt+ eΦt,t+hDt)
s=t

= A £ exp(r, (t - s)) £ Dtв

exp[(1 - δtV(s - t))1D - δiβσD,/2)]

N

+A exp(-rf h) £ Dt(1 -δi)βi dp1 -δi

exp[(1 - δi)dh{μD - [(1 - δi)d - 1]⅛/2)]
with

A-1 ≡ Y D-δitBt,t

Bis ≡ βi dp-δiexp[zd(t + h - s)D - [δzd + 1]σD/2)]

25



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