# Capital budgeting problem

### From Glossary

In its elementary form there is a fixed amount of capital, say , that can be allocated to any of investments. Each investment has a minimum level, say , and a maximum level, say . The expected return on investment is a function, , where is the level of the -th investment opportunity (). Risk is measured by a standard deviation from the expected return, say . The problem is to maximize total expected return, subject to a *budget constraint*: , and a *risk constraint*: , where and are parameters. The returns on the investments could be correlated. Then, if is the variance-covariance matrix, the risk constraint is quadratic: . (Also see the portfolio selection problem.)