Abstract: In this paper, we consider an optimal portfolio selection method based on maximizing risk-adjusted return on capital(RAROC) of the portfolio. The fractional structure of the objective function maximizing RAROC makes it difficult to be solved. We noticed that in real financial practice, the expected return function and risk function of the portfolio are often homogeneous with the amount of investment. Under some conditions we proved that the problem can be solved by minimizing its denominator in certain constraints. When random return follows normal distribution, it maximizes RAROC problem associated with risk measure, such as Value at Risk(VaR) or Conditional Value at Risk(CVaR), can be reformulated as a problem that minimizes a square root function with linear constraints. The latter problem can be solved by using excising second order cone optimization software.

Key words: optimal portfolio, RAROC, VaR, CVaR, homogeneous