Extending the Market Risk Estimation Horizon - An Optimization Approach

Economic Capital estimation for market risk requires a bank to extend its estimate of risk based on a smaller time horizon, n, which is generally one or ten days to a longer horizon, N, which is generally one year. This would require modeling of the possible changes in the portfolio over the horizon and calculation of the corresponding impact on the long-term loss distribution. Once the long-term distribution has been determined, Economic Capital can be estimated using diffrent risk measures. The standard method used for extending Economic Capital based on a commonly used risk measure, Value-at-Risk (VaR), from n days to N days is scaling it up by a factor of sqrt (N/n). We adopt a different approach for extending the loss distribution. Rather than making assumptions regarding the nature of portfolio loss distributions across time and the risk measures used, we arrive at optimal portfolio instrument weights relevant to the risk behavior of the trading desk historically. This would require solving for optimal portfolio selection given the risk behavior of the desk and can potentially incorporate various other constraints like limits on positions and portfolio amounts