Assume that the return R t of a stock has the following log-normal distribution for fixed t:

Question:

Assume that the return R_t of a stock has the following log-normal distribution for fixed t:

log (Rt) ∼ N(μ, σ²)

Suppose we let the density of log(R_t) be denoted by f (R_t) and hypothesize that μ = 0.17.We further estimate the variance as σ² = 0.09.

(a) Find a function ξ(R_t) such that under the density, ξ(R_t) f(R_t), R_t has a mean equal to the risk-free rate r = 0.05.

(b) Find a ξ(R_t) such that R_t has mean zero.

E[R²_t]

(d) Is the variance different under these probabilities?

Distribution
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