The implications of value-at-risk and short-selling restrictions for portfolio manager performance

Fulbert Tchana Tchana; Georges Tsafack

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Using a framework where portfolio managers maximize their expected utility under asymmetric information, we introduce one of the most common restrictions (VaR constraint) faced by portfolio managers and provide an analytical solution to this complex problem.
Analyzing this solution with realistic values of parameters and comparing with the solution to a similar problem (already solved by Gendron and Genest, Journal of Finance, 1990) where managers face a short-selling restriction, we establish the following results: i) In volatile market, the VaR constraint will have a stronger impact than the short-selling restriction on the manager performance; ii) In this situation, aggressive managers will be more affected by the VaR constraint; iii) While the short-selling restriction tends to evenly affect all managers, the VaR restriction has a stronger impact on managers with good information quality.
These results suggest that sophisticated investors will see their performance more affected by VaR constraint than short-selling restriction.

Abstract

After the recent financial crisis and the tightening of the regulation processes, portfolio managers regularly face strong restrictions, with complex implications for their performance. This paper provides a framework to analyze the performance of a portfolio manager under a value-at-risk (VaR) constraint, in a Markowitz setup. Using appropriate parameters, we calibrate the model for a manager with private information and compare the effect of VaR and short-selling (SS) constraints on the relationship between the expected portfolio return and the market return. We find that, in a more volatile market, the VaR restriction will have a greater effect on manager performance than the SS restriction. The VaR constraint also strongly affects a manager with high-quality information, while the SS restriction only moderately affects a manager with any level of information quality. Regarding their attitude toward risk, an overly aggressive manager will find their overall performance more affected by the VaR constraint.

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