Question: Assume that the return R t of a stock has the following log-normal distribution for fixed t: log (Rt) ~ N(, 2 ). Suppose

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

E[R}]?

(d) Is the variance different under these probabilities?

E[R}]?

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