Risk Management Rogue Trader Case

How to tame a rogue trader

In all this exercise, we assume that individuals have a utility function described by the prospect theory (loss aversion, risk averse behavior in gains, risk seeking behavior in losses). A trader is faced with three possible strategies:

- strategy A offers a certain but modest (positive) yield

- strategy B has a higher average yield but incurs the possibility of large gains or large losses

- strategy C has the highest average yield but incurs the possibility of bankruptcy for the bank

1) We consider a trader whose salary is indexed on his P&L (whether positive or negative). Which strategy will the trader prefer?

[pic]

Figure 1

Figure 1 represents the satisfaction (utility) of the trader (y axis) against the P&L of the strategy (x axis). Bu (resp Bd) corresponds to the P&L of strategy B in the “up” (resp. “down”) state. Strategy C is not represented, being similar to B in this case.

The trader prefers strategy A because his aversion to losses makes him prefer a certain small gain over the possibility of having a malus.

2) Same question for a trader incentivized on his gains but bearing no loss if his P&L is negative.

[pic]

Figure 2

This traders bears no cost if the P&L is negative; because his salary increases with the P&L when the P&L is positive and is insensitive to the magnitude of the loss if the P&L is negative, his interest is to adopt the strategy that maximizes the upside possibilities, hence strategy C (see Figure 2).

3) Same question for a trader incentivized on his gains, bearing no loss if his P&L is moderately negative, but bearing a high loss in the case of bankruptcy (e.g. all his fixed salary would have to be repaid if the bank gets bankrupt).

[pic]

Figure 3

This traders bears no cost if the P&L is negative, except if the P&L is so negative that the bank goes bankrupt (strategy C); in this case, the...