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Game Theory Applied to Capital Management

https://www.risk.net/our-take/7041081/game-theory-plays-well-for-capital-management

The article mentions how a traditional bank’s capital allocation strategy is flawed given that their current strategies do not maximize their return on capital. When allocating capital among different business desks, banks usually allocate a higher amount of capital to desks that generate a higher return on capital (ROC), and less capital to desks that generate lower ROC. However, these business desks are sometimes highly correlated and sometimes a low capital allocation to one entity could make the other entity suffer. A new strategy must be used in order to consider this correlation and solve this problem. The article introduces a strategy which involves an additional variable that calculates two ratios in each business desk: risk-weighted assets (RWAs) and leverage balance sheet (LBS). The minimum capital requirement for each desk will be the greater of the two ratios. The main issue comes up when considering banks must keep this ratio the same in order to optimize return on capital; therefore, a strategy must be used to analyze which ratio to use (either RWAs or LBS) on each business desk to yield the highest overall return on capital for the bank.

The solution to the allocation problem involves the use of game theory, especially with cooperative games. So far in class, we have discussed players in a game in which they are not allowed to forge any alliances, agreements, or cooperate in any way. Cooperative games are basically a competition between groups of players due to the possibility of external enforcement of cooperative behavior. The strategy is known as Shapley allocation, which is a game theory strategy that has been widely applied in economics and business decision making. First, the strategy assumes each business desk is a player in the game. It consists on attributing a value to each desk in a system where all the desks share costs and gains for their activity. Basically, it measures how much each desk impacts to the overall contribution of the firm. This is done by removing each desk and testing what is the impact on the overall return on capital of the firm. The value attributed at the end of the game serves as a ranking to decide which desks will receive more capital than others. This strategy proved to be a success in this field as they discovered an almost perfect approximation between the Shapley allocation and the maximizing function of RWA and LBS capital to business units.

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