3. Let Rt denote the simple monthly return and assume that
Rt ~ iid N(µ,ó ). Consider
the 2-period simple return
Rt (2) = (1+ Rt )(1+ Rt −1) −1.
a. Assuming that cov(Rt , Rt −1) = 0 , show that E[Rt Rt −1] = µ 2 .
Hint: Use cov(Rt , Rt −1 ) = E[Rt Rt −1 ] − E[Rt ]E[Rt −1].
b. Show that E[R (2)] = (1+ µ)2 −1
c. Is Rt (2) normally distributed? Why or why not?
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