Portfolio optimization is the process of choosing the best investment decision across a set

of financial instruments or assets. Investors are faced with a trade-off between risk and expected returns.

Most researchers have considered this problem from one of two perspectives: maximize a portfolio's expected

return for a given risk or minimize a portfolio's risk for a given expected return. In this talk, we consider

a fractional model with a returns over risk ratio that keeps both expected returns and risk flexible simultaneously. The considered model provides us with the optimal investment portfolio for which the expected

returns per unit of risk will be maximized. We demonstrate how to reformulate the basic model as a linear

program. Numerical tests demonstrate that the model is no harder to solve and provides a more balanced

portfolio when compared to previous models.

Based on joint work with J Braun, J Brar, and D Wang.