CHAPTER 6Choice of Portfolio and VaR Constraint
In this chapter, we show how VaR can be used to make portfolio managers comply with the capital requirements of a brokerage firm, for example.1
6.1 OPTIMAL BENCHMARK PORTFOLIO OF THE FIRM
Consider the president of a brokerage firm with several portfolio managers. The president wants to constrain the firm's managers not to form overly risky portfolios.
To simplify, suppose they all have the same efficient frontier in a 
space but they have different risk aversion levels: 
differs between managers. E designates the mathematical expectation of the portfolio return, 
the standard deviation, and U the utility function of a risk-averse manager with the following partial derivatives: 
, indicating risk aversion.
The benchmark portfolio chosen by management is the solution maximizing the following program:
where:
and where is the portion ...
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