The formula for lognormal Value at Risk (VaR) is: $\text{Lognormal VaR} = W_0 \times (1 - e^{\mu - z \times \sigma})$

Given the data:

• Initial Portfolio Value ($W_0$) = $85 million
• Mean geometric return ($\mu$) = 12% or 0.12
• Standard deviation ($\sigma$) = 32% or 0.32
• Confidence level = 95%, which corresponds to a standard normal $z$-value of 1.645 (or 1.65).

First, calculate the exponent: $\mu - z \times \sigma = 0.12 - (1.645 \times 0.32)$ $`$0.12` - 0.5264 = -0.4064 $$

Next, calculate the exponential term: $e^{-0.4064} \approx 0.666044$

Finally, calculate the VaR: \text{Lognormal VaR} = 85 \times (1 - 0.666044) = 85 \times 0.333956 \approx \`$28.38`6 \text{ million}

Therefore, the closest answer is `$28.39` million.