How to show volatility in Stock index < individual Stock?Hi, I am working on this subject using Option Pricing but I can't seem to relate the them together as well as using CAPM.Please could someone guide me around this?Thx!

A stock index is a portfolio of individual stocks, some stocks may be more volatile than the index and others may less volatile. What Harry Markowitz and others showed over forty years ago is that, if the constituient stocks in a portfolio are less than perfectly correlated, the volatility of the portfolio is less than a simple weighted average of the individual volatilities. You can find these results in any intro finance or portfolio theory text. This is something rather different than what you have suggested.The same logic about less than perfect correlation between assets led Sharpe and others to believe that diversifiable risk should not receive compensation. Rather, only systematic or non-diversifiable risk is relevant. Add a couple of convenient assumptions and you eventually get to the CAPM. Any intro finance text should show you this as well.Regarding options, Robert Merton showed that an option on a portfolio is less valuable than a portfolio of options. See his 1973 paper titled “Theory of Rational Option Pricing” in the Bell Journal of Economics for the proof.

This is something rather different than what you have suggested.Correct me if I am wrong, are you implying that volatility in stock index is higher or lower now than say as compared to a typical stock?I know now that it depends on the correlation between the stock and the market. But my main concern here is how do I show all these using option pricing?Thx for the troubles!

Buy calls on the Dow, sell calls on the equivalent number of shares in each of the Dow 30 companies, and see what your net position is.