Value-at-Risk (VaR) Analytics for GBM Portfolios

Students frequently confuse the arithmetic mean return with the drift parameter

\mu

. They often forget the 'drift correction' term

-\frac{1}{2}\sigma^2

, which arises from applying Itô's Lemma to

\ln(V_t)

, leading to an overestimation of the expected value and an incorrect VaR calculation.

Institutional Reference: Advanced Stochastic Processes