Capital Allocation with Value-at-Risk - The Case of Informed Traders and Herding

We scrutinize the use of value-at-risk as a trader's limit in banks in the context of capital allocation. Thus, we compare a bank that has many uninformed traders, each dealing in a separate stock on a perfect capital market, with a bank in which traders receive a noisy signal about the future price of the stock. Additionally, traders are able to deduce some information about the trend of the market by observing the behavior of other traders inside their bank. Each of these traders adheres to an individual value-at-risk limit and, by taking long or short positions accordingly, contributes to the overall risk of the portfolio. In an imperfect market setting informed traders tend to herd in informational cascades. Thus, if capital allocation does not take potential herding into account, the individual trading limits are set too loosely because, due to herding behavior, the returns of the stocks in the resulting portfolios are more often positively correlated than expected.