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?
See Figure 3.
4) Imagine the trader is incentivized on his annual P&L (if positive). Which strategy does he adopt in December in each of the two following cases:
a. His P&L over the first 11 months (January to November) is highly positive
Strategy C is not represented, being similar to B in this case.
In this case, the trader, being risk averse in gains, will prefer to secure a certain bonus with A rather than risking having zero bonus with strategies B or C.
b. His P&L over the first 11 months (January to November) is highly negative
In this case, as the trader does not bear the consequences of his losses, his interest is to adopt a strategy that gives him the chance of having a positive P&L (hence positive bonus) at the end of the year (see Figure 5). C is preferred to B because the downside is the same for the trader (no bonus) while the upside is better with strategy C.
5) Same question as 4):
a. if the trader’s salary is indexed on his P&L (whether positive or negative)
If the P&L over the first 11 months is highly positive, the trader’s risk aversion in gains (and aversion to losses) will prompt him to secure a positive bonus rather than taking the risk of having no bonus or a “malus”, so he will go for strategy A (see Figures 1 and 4).
If the P&L over the first 11 months is highly negative, the trader’s risk seeking behavior in losses will prompt him to seek the possibility of a positive bonus (or no malus) instead of the certainty of a malus, so he will go for strategy C (see...