Optimal Value-at-Risk Disclosure

Abstract In 1995, the Basel Accords introduced an alternative method to compute the market risk charge through the use of a risk model developed internally by the financial institution. These internal models, based on the Value-at-Risk (VaR), follow certain rules that are defined under the Basel Accords. From this moment on, risk analysts and financial academics focused their attentions on how to accurately estimate the VaR in order to reduce the regulatory capital. However, considering the market risk framework defined in the Basel Accords, the best strategy to optimize the regulatory capital may not lie in truthfully disclosing an accurate VaR estimation. In this study, we propose to solve, through dynamic programming, for the optimal policy function for disclosing the reported VaR based on the estimated value that minimizes the daily capital charge. This policy function will provide the optimal percentage of the estimated 1-day VaR that should be disclosed, taking into account the impact that this disclosure decision will have in future capital charges, by managing the rules defined in the Basel Accords. Our goal is to prove that truthful disclosure of an accurately estimated VaR is suboptimal. The main results from our investigation show that using the optimal reporting strategy leads to an average daily reduction in the capital requirements of 4.32% in a simulated environment, compared with a normal strategy of always truthfully disclosing the estimated 1-day VaR, and leads to an average daily saving of 7.22% when applied to our S&P500 test portfolio.