Interpreting Asset Risk Contributions in Long-Short Portfolios

Summary

The document asks how to interpret covariance-based asset risk contributions when portfolio weights include both longs and shorts and sum to zero. It contrasts the usual calculation, based on portfolio weights multiplied by the return covariance matrix, with the intuition that increasing the position associated with the largest volatility contribution should raise portfolio volatility. In a long-short portfolio, however, these values can be negative, making that rule unclear.

The question also distinguishes marginal risk contribution from sensitivity of portfolio volatility to an asset’s own volatility, but supplies no answer or worked example. It therefore identifies a useful portfolio risk question rather than presenting a method. In particular, the sign of a covariance-based contribution depends on both the position and its relationship to the rest of the portfolio; the document leaves unresolved how to translate that measure into weight changes for a volatility target.

Key ideas

• Covariance-based asset contributions can be negative in a long-short portfolio.
• The portfolio is dollar neutral, with long and short weights summing to zero.
• The document asks how to use asset risk contributions when adjusting weights to a volatility target.
• It raises a distinction between marginal risk contribution and sensitivity to an asset’s own volatility.

Tags

# How to adjust an assets position to target volatility in a long-short portfolio?


# How to adjust an assets position to target volatility in a long-short portfolio?












I have a portfolio of weights $\mathbf{x}$ where some positions in $\mathbf{x}$ are short s.t. $\Sigma_i x_i=0$ (dollar neutral).

The standard way to estimate the volatility contribution per asset is by using $\mathbf{x}'\Sigma$ where $\Sigma$ is the covariance matrix of asset returns. From this, I would look at the asset with the largest vol-contribution and increase (decrease) its position to increase (decrease) my portfolio volatility to target a specific volatility.

This works in a long only portfolio where $x_i > 0 \, \forall i$, however it can yield negative values in a long-short portfolio. How would I use / interpret the form $\mathbf{x}'\Sigma$ in terms of volatility contribution per asset to adjust weights in a long-short portfolio to target volatility?

I found this post quite useful in giving some background, but I am confused as to the difference in "marginal risk contribution" and "sensitivity of the portfolio volatility with respect to an assets volatility", especially in how it relates to a long-short portfolio.

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