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I did a Monte Carlo simulation to evaluate my portfolio. I used different Strikes and Weights for the Put options. Now to my problem: All statistical measures (like expected return, volatility) decrease if I put more weight in my put option. This makes sense, however the Value at Risk doesnt align! Since I am basically capping my tail risk, I would expect VaR to decrease as well. However for certain Strike prices as I increase the weight invested in my put, VaR increases as well. (see the table below)

Does this make sense?

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    $\begingroup$ Can you describe your portfolio and your options? Do you just tail hedge an equity position by buying put options? Which strikes do you use? $\endgroup$ Commented May 12, 2024 at 16:10
  • $\begingroup$ Does you var increase as the put strikes increase? I.e they have more delta. $\endgroup$ Commented Sep 9, 2024 at 23:37

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You are likely to have a fat tail in the distribution of possible returns. What does your 95% VaR look like? 90% VaR? Could you even plot histogram of your returns.

very plausible to increase VaR as you weigh up on the options, it depends on what the other instruments are in the portfolio, let's say you are decently delta hedged but become poorly gamma hedged as you increase your weightings on your put.

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