Correlation and Risk in Portfolios of Short Single-Stock Put Options

Summary

The document poses a portfolio construction question about equally weighting short put positions by option price across different stocks with a shared maturity. The author describes Monte Carlo results in which portfolios involving more highly correlated underlyings show a higher value, then questions the intuition that low correlations would be preferable because they create more independent chances of expiring out of the money.

The text does not define precisely what “portfolio value” measures, provide simulation assumptions, or give an answer. It therefore does not establish which correlation structure is preferable. A useful analysis would need to distinguish expected premium or payoff from risk measures such as loss probability and tail loss, and specify the dependence model, strikes, and underlying distributions. The document highlights a relevant dependence question for short-option portfolios but supplies no evidence beyond the author's stated simulation observation.

Key ideas

• The question concerns a price-weighted portfolio of short puts on multiple stocks with a common maturity.
• The author reports that higher underlying correlations produced a higher simulated portfolio value.
• The suggested benefit of low correlations is more independent outcomes, but this intuition is not resolved.
• The document does not define its value metric, simulation assumptions, or preferred correlation structure.
• Portfolio conclusions depend on the payoff measure and the model for underlying dependence.

Tags

# Portfolio of single stock short put options: which correlation structure preferrable?


# Portfolio of single stock short put options: which correlation structure preferrable?












Let's say you want to have a equally-weighted (in terms of the option price) portfolio of short put options on various stocks with the same maturity.

Running Monte-Carlo simulations, it seems that choosing options with a highly correlated stock as an underlying results into a higher value of my portfolio.

Intuitively, I would have guessed that correlations close to zero would be preferable, because then we would have more independent bets which are more likely to be not executed at maturity.

Any ideas what correlation structure should be preferred?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.