# What is the differential Value-at-Risk?

I am currently working on a Machine Learning Project, implementing portfolio optimization algorithms according to different risk measures. I have found sufficient information on Sharpe Ratio optimisation, but not on Value-at-Risk.

My question is: What is the equation for differential VaR - the derivative taken with respect to a first-order exponential moving average decay rate?

It should be comparable to the differential Sharpe Ratio proposed by Moody & Safell. This formula was already discussed in: What’s the derivative of the sharpe ratio for one asset? Trying to optimize on it for a model

• Looking for something like this? $\frac{d \mathrm{VaR}_q\left(Y+\lambda X\right)}{d\lambda}=E\left[X|Y+\lambda X=\mathrm{VaR}_q\left(Y+\lambda X\right)\right]$ Jun 16 '20 at 18:01
• Yes, thank you! I also found additional information I needed.
– Nick
Jun 16 '20 at 23:18