Value at risk in dollars vs. log returns

I have a quick question about this remark in Tsay's book "Analysis of Financial Time Series" (3rd edition).

He says that $$\text{dollar VaR} = \text{Value} \times \text{log return VaR}$$ and that $$\text{Value} \times [\exp(\text{log return VaR}) - 1]$$ is an approximation to that.

Based on how quantiles transform, it seems to me that it should be the other way around!

Eq (7.1) for completeness

Thanks for your help!

1 Answer

I think you are right. What he calls the approximation is the correct amount, the other is an approximation.