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Risk Attribution

​​​​​​​​​​​​​Philippe Grégoire
Hervé van Oppens

 

In this article, we propose a methodology to measure the effective contribution to the total risk and to the tracking error due to asset allocation or selection. We demonstrate that the portfolio historical volatility is explained, first by the assets’ volatility and correlation (as for the marginal contribution to risk) and second by the holding’s volatility (portfolio’s turnover). The results highlight that what matters for effective risk contribution is the time series of contribution to return (holdings at each period times periodic return). Applying these results to effective contribution to tracking error (TE) shows that what matters is the time series of excess return times weight differences. This result is different from marginal contribution to the TE, which depends solely on time series of excess return and not on changes in portfolio’s holdings. Our results in risk attribution give an exact decomposition of portfolio’s total risk and TE that complement the return attribution analysis. Exact decomposition refers to the fact that the sum of contributions is exactly equal to the portfolio’s volatility and TE.

In this article, we propose a model for risk attribution that explains the difference between the risk of a portfolio and its strategic asset allocation. A first version of the risk attribution model explains the changes in the risk profile by allocation, diversification and selection decisions. The second version is more intuitive as it attributes the risk, first to tactical allocation decisions and, second to the stock picking. The changes in the correlations or the contribution to the overall risk of the portfolio are measured by a term called ‘diversification effect’.  Risk attribution contributes to a better understanding of the sources of performance as it links up the source of active returns to active risk.

In this article, we propose an attribution model for a leveraged or hedged portfolio

that is in line with Brinson et al. The model takes into account the effect of futures in allocation, displays a selection effect that is due solely to securities and not futures, measures the leverage effect, and, finally, isolates the return that is caused by an imperfect correlation between futures and the underlying asset class.

Strategic

Asset Allocation

& Risk Attribution

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Philippe Grégoire
Philippe Vandooren

 

Performance Attribution for Portfolios that Trade Futures Contracts

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Philippe Grégoire
Yves Hennard