Control of Brokerage Margins

In this paper we analyze financial risk from the point of view of a brokerage company, who exposes itself to risk by lending assets or money to its clients for allowing short-selling or leveraged operations (firm-wise risk). We develop analytical models for control of firm-wise risk, by defining both specific margin factors for single assets and a global margin factor that takes into account the overall riskiness of a complex portfolio. In the first part of this work we derive a model to evaluate leverage factors, by linking them with the probability for the client’s portfolio value to go below a certain safety threshold, using Value-at-Risk and Expected Shortfall approaches. Further, we present optimization models based on these two approaches in order to determine the optimal leverage factors. In the second part, we present a model for margin control based on the concept of marginal availability. A global margin factor considering the overall riskiness of a complex portfolio is derived, and we show the effectiveness of the approach also when dealing with portfolios containing options.