An Analysis of VaR-based Capital Requirements

Abstract

We study the dynamic investment and reporting problem of a Financial institution subject to capital requirements based on self-reported VaR estimates, as in the Basel Committee's Internal Models Approach (IMA). We characterize the solution of this problem using martingale duality and parametric quadratic programming techniques. With constant price coefficients, we show that optimal portfolios display a local three-fund separation property. VaR-based capital requirements induce financial institutions to tilt their portfolios towards assets with high expected return (and high systematic risk), but result nevertheless in a decrease of the overall risk of trading portfolios. In general, an institution may optimally under-report or over-report its true VaR, depending on its risk aversion and the stringency of capital requirements. Overall, we find that capital requirements determined on the basis of the IMA can be very effective not only in curbing portfolio risk but also in inducing truthful revelation of this risk.