Calculating Volatility and Weights for a Short Portfolio
Summary
A portfolio’s dollar volatility is unchanged when every position is reversed: variance is sign-insensitive, so a short portfolio with the same absolute value as a long portfolio has the same standard deviation. The discussion distinguishes this total risk measure from constituent risk attribution, where a position’s interaction with other holdings can reduce overall portfolio volatility and its contribution may be negative.
For portfolio weights, divide each position by net asset value, including cash, so the weights sum to one. The example shows how a short position can produce a cash weight above one alongside a negative stock weight. The document assumes the covariance matrix is already available and does not walk through calculating portfolio variance from it or address estimation and horizon choices.
Key ideas
- Reversing all positions leaves portfolio variance and standard deviation unchanged.
- A short position can still contribute negatively to portfolio risk attribution through its interactions with other holdings.
- Calculate weights by dividing positions, including cash, by net asset value.
- Weights can be negative for shorts and exceed one for cash while summing to one.
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Full text
# Volatility and weights of a portfolio whose value is negative # Volatility and weights of a portfolio whose value is negative How do you calculate the one day standard deviation (in dollars) for a portfolio that is short $30,000? How do you calculate the weightings to use? I already have the necessary covariance matrix. ## Answer by demully (score 2) https://quant.stackexchange.com/a/58817 The sigma is the same short as if you were long. Imagine you held exactly the opposite portfolio. It stands to reason that volatility of holding both is net zero; and they're -100% correlated. It therefore stands to reason that you have to have the same sigma (for the same value) for them to cancel out thus, as they must. Alternatively, just look at the variance, which will be a sign-indifferent positive, the same as for -30k as for +30k. Where the signs do start to matter is when you have longs and shorts in the portfolio, and you want to start to attribute the portfolio risk amongst its constituents. Then you can indeed have assets with a negative stdev; because their interactions with other constituents represent a net reduction in (expected!!!) volatility. ## Answer by Charles Fox (score 0) https://quant.stackexchange.com/a/48895 Your weights, including cash, should sum to 1. Divide the positions by the portfolio net asset value to get the weights. For example, a \$100 portfolio with a \$50 short position would have \$150 in cash so the weights would be -0.5 and 1.5 for the stock and cash respectively.
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