Online Portfolio Hedging with the Weak Aggregating Algorithm

In this paper we apply the Weak Aggregating Algorithm to find optimal risk management strategies for financial Market Makers (MMs). Here risk is caused by the market exposure. It is effectively represented by the MM's overall net position, which is the aggregation of all the buy and sell trades carried out by the MM's clients at a given point in time. So-called hedging strategies are used by MMs to manage their risk and reduce market exposure. In essence, the MM actively places trades in order to reduce its overall net position, keeping it within some predefined bounds and as neutral (or flat) as possible. A flatter net position allows the MM to counter any unfavourable price movements which could otherwise incur a significant loss. We apply the Weak Aggregating Algorithm (WAA) to hedging strategies, which are treated as the experts. We combine their hedging decisions with the goal of reducing portfolio risk and maximising profitability, whilst also attempting to smooth out significant drawdowns. We develop a variation of the WAA using discounting and evaluate theWAA on a subset of real life client risk data in three commonly traded Foreign Exchange (FX) currency symbols: EUR/USD, EUR/GBP and GBP/USD. The results show how varying loss parameters and application of discount factors can enable the WAA to give combinations of hedging strategies that can significantly improve profitability and reduce drawdowns as compared to the benchmark of not hedging.