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Maximizing Sharpe Ratio == Shorting Volatility

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Calculating beta of a portfolio with short stock positions? I am doing a project where I need to calculate the beta of a portfolio my group created that has regular stocks and stocks in a shorts position. How would I go about calculating the beta of the stocks in a short position, and do I use those in the weight of each individual stock in the portfolio?

Yep go with this. This would be the most appropriate method if we're just considering theoretical correlations with a benchmark. In application, reality gets messy i.

Beta Definition - zuwywakybobu.web.fc2.com

As a more theoretical measure of systematic risk consider that relationships frequently change. For example, consider a beta post-merger announcement or market drawdowns short-squeeze but this is irrelevant with diversification.

Yea, I started thinking about all the stuff you listed and was like, yea this isn't a very realistic fit, but I was pretty sure it would work, crudely. Imagine that you had a stock which was exactly the same as a short position in another stock realistically would probably be an ETF, but doesn't matter for argument's sake. The only thing to change in that equation is r, translating to -r, and by property of covariance, becomes -Cov r,rm etc Hence, treat the short position as if it had a negative beta and plug it into the same equations you normally would.

For most stocks this brings your overall portfolio beta closer to zero, exactly as you would expect becuase a portfolio of long stocks and their corresponding shorts positions would have to have beta of zero. Use of this site constitutes acceptance of our User Agreement and Privacy Policy.

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