Why Adding Put Options Can Increase Portfolio VaR

Summary

The document considers a Monte Carlo portfolio analysis in which changing the weights and strikes of put options reduces measures such as expected return and volatility, while Value at Risk sometimes rises. The response says this outcome can be plausible because VaR depends on the shape of the portfolio’s return distribution and the positions combined, rather than on volatility alone.

It recommends inspecting VaR at multiple confidence levels and plotting the simulated return distribution to understand the tail behavior. It also offers an exposure-based explanation: adding puts may improve delta hedging while worsening gamma hedging, depending on the other instruments and portfolio construction. No simulation output, portfolio details, option characteristics, or numerical evidence are included, so the explanation is a diagnostic possibility rather than a demonstrated cause or general rule.

Key ideas

• Lower portfolio volatility does not guarantee lower Value at Risk.
• VaR may respond differently across confidence levels when return distributions have fat tails.
• Plotting simulated returns can help reveal distribution shape and tail behavior.
• Adding put exposure may change delta and gamma hedging in different ways.
• The proposed explanation depends on the portfolio’s other instruments and is not confirmed by reported data.

Tags

# Portfolio with Put Options - VaR, Std. Dev


# Portfolio with Put Options - VaR, Std. Dev












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?

## Answer by boonga (score 1)

https://quant.stackexchange.com/a/71971

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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