Value at Risk Bounds for Portfolios of Non-normal Returns

by Elisa Luciano of the University of Turin and ICER, Turin, and
Marina Marena of the University of Eastern Piedmont and ICER, Turin

April 1, 2001

Abstract: This paper studies Value at Risk (VaR) bounds for sums of stochastically dependent random variables, i.e. portfolios of correlated financial assets. The bounds hold under no restrictions on the dependence or on the marginal distributions of returns. An improvement of the bounds is given for positive (quadrant) dependent returns (random variables). Both sets of bounds are computed for portfolios of 6 international indices. Backtesting confirms the usefulness of the approach, even with respect to other shortcuts, such as the normality assumption. For small portfolios, bounds are not over conservative.

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