This paper evaluates the financial efficiency of the private pension system investment portfolio throughout the period 2006-2011 in Peru. We find that an investment portfolio is financially efficient when it delivers the smallest Sharpe ratio relative to the market ratio. We estimate the optimal portfolio under a robust Non-Parametric Shrinkage approach that considers all relevant restrictions that may affect the optimization procedure. Our results suggest that the administrators of the Peruvian private pension system have not reached financial efficiency in any of the three types of pension funds.