Again, by the convexity of the logarithm function,4First, zP = ln{1 + gP} < gP by the convexity of the logarithm function. We have a useful approximation zP = ln{1 + gP} ≈ gP − 0.5 · Again, by the convexity of the logarithm function,
so gP ≤ aP. Finally, we have an approximation (exact for log normal) that 
, where 
is the variance of ln{RP(t)}. This reduces to 
.