6. Let Yt be a stock’s return in time period t and let Xt be the inflation rate during this time period. Assume the model Yt = β0 + β1Xt + δσt + at, (14.30)

where at = t

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1+0.5a2 t−1. (14.31)

Here the t are independent N(0, 1) random variables. Model (14.30)–

(14.31) is called a GARCH-in-mean model or a GARCH-M model.

Assume that β0 = 0.06, β1 = 0.35, and δ = 0.22.

(a) What is E(Yt|Xt = 0.1 and at−1 = 0.6)?

(b) What is Var(Yt|Xt = 0.1 and at−1 = 0.6)?

(c) Is the conditional distribution of Yt given Xt and at−1 normal? Why or why not?

(d) Is the marginal distribution of Yt normal? Why or why not?