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

Thanks in advance!

  • 1
    $\begingroup$ Looking for something like this? $\frac{d \mathrm{VaR}_q\left(Y+\lambda X\right)}{d\lambda}=E\left[X|Y+\lambda X=\mathrm{VaR}_q\left(Y+\lambda X\right)\right]$ $\endgroup$ Commented Jun 16, 2020 at 18:01
  • 1
    $\begingroup$ Yes, thank you! I also found additional information I needed. $\endgroup$
    – Nick
    Commented Jun 16, 2020 at 23:18


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.