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Hello I am interested in portfolio optimization . Previously I when I have done portfolio optimization I would take the historical returns of a stock and use them to perform a mean variance optimization, however I was just recently introduced to the idea of using the implied volatility of options to perform a mean variance optimization because option implied volatility is forward looking unlike historical volatility . I would like to know if I were to use implied volatility to solve this problem how would I go about doing this . Would I take the for example one year of future volatility of different stocks and put that into a mean variance optimization instead of taking the historical returns of different assets and putting them into a mean variance optimization problem ?

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There are some subtleties / difficulties.

  1. Implied volatiliy, which depends on the strike of a vanilla option, is only a forward looking measure in the sense that it can be regarded as the risk-neutral expectation of break-even delta-hedging profit and loss of a vanilla option of strike $K$ which is delta hedged to expiration using a constant volatility. If this sounds complicated that's because it is. I suspect that many that use implied volatility as optimisation input use the ATM implied volaitlity as input. You could do that, but whether it's the logically right thing to do? I don't think so. Some would say using ATM implied volatility "is not even wrong".

  2. I would not use therefore implied volatility, which depends on strike, as a forward looking volatility measure. Better, or at least logically more sound, would be to use for instance some GARCH (or variations of GARCH) output for future realised volatility. Another possibility would be to use the volatility swap price as input, which is the risk-neutral expecation of future realised volatility. Both of these do not depend on strike of vanilla option.

  3. The tenor of the GARCH estimate / volswap strike should depend on your optimisation horizon. If you are optimising for the next week, use a one week estimate, and so forth.

  4. Then, what correlation are you going to use? As far as I know there is no liquid market for implied correlation. You could use historical correlations, or some other statistical (forward looking) estimate for correlation.

It's not an easy thing, in my opinion no clear-cut answers, and more often than not an art rather than science.

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