Assume that the return Rt of a stock has the following log-normal distribution for fixed t:
log (Rt) ~ N(μ, σ2).
Suppose we let the density of log(Rt) be denoted by f(Rt) and hypothesize that μ = .17. We further estimate the variance as σ2 = .09.
(a) Find a function ξ(Rt) such that under the density, ξ(Rt)f(Rt), Rt has a mean equal to the risk-free rate r = .05.
(b) Find a ξ(Rt) such that Rt has mean zero.
(c) Under which probability is it "easier" to calculate
(d) Is the variance different under these probabilities?