Can you walk me through the normal VaR formula with a concrete example?

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AcadiFi · Accepted Answer

For a portfolio with mean return mu and standard deviation sigma over the horizon, the normal VaR at confidence level c is VaR = -(mu + z * sigma) * V, where z is the negative quantile of the standard normal at (1-c) and V is portfolio value. For a one-day horizon with mu roughly zero, the formula collapses to VaR = -z * sigma * V, or equivalently |z| * sigma * V where |z| is 1.645 at 95% and 2.326 at 99%. Worked example: a $50M equity book with daily volatility 1.4% and zero drift. The 99% one-day VaR equals 2.326 * 0.014 * $50M = $1.628M. If we include a positive drift of 0.05% daily, relative VaR remains 2.326 * 0.014 * $50M but absolute VaR becomes (2.326 * 0.014 - 0.0005) * $50M = $1.603M. Common mistakes: using z=1.96 (two-tailed 95%) instead of 1.645, forgetting that the negative sign in the formula turns the quantile into a positive loss, and mixing percent volatility with fractional volatility. For multi-asset portfolios, sigma comes from w'Sigma w where w is the weight vector and Sigma the covariance matrix; the formula structure stays the same. Always confirm units — annual vol must be scaled to the horizon — and decide absolute or relative VaR before writing the sign.

Can you walk me through the normal VaR formula with a concrete example?

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