The equations of an ARCH-in-mean model are shown below:

yt =0 +ht +et et |It1 N(0,ht)

h=+e2 , 0,01 t 1t1 1

Let yt represent the return from a financial asset and let et represent news in the financial market. Now use the third equation to substitute out ht in the first equation, to express the return as

y=+(+e2 )+e t 0 1t1 t

a) If is zero, what do you expect next periods return to be, given information today?

b) If is not zero, what do you expect next periods return to be, given information today? What extra information have you used here to forecast the returns?