Models and model value in stochastic programming

Finding optimal decisions often involves the consideration of certain random or unknown parameters. A standard approach is to replace the random parameters by the expectations and to solve a deterministic mathematical program. A second approach is to consider possible future scenarios and the decision that would be best under each of these scenarios. The question then becomes how to choose among these alternatives. Both approaches may produce solutions that are far from optimal in the stochastic programming model that explicitly includes the random parameters. In this paper, we illustrate this advantage of a stochastic program model through two examples that are representative of the range of problems considered in stochastic programming. The paper focuses on the relative value of the stochastic program solution over a deterministic problem solution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44253/1/10479_2005_Article_BF02031741.pd

The opportunity set : market opportunities and the effective breadth of a portfolio

The opportunity set (OS) is an ex post measure of the maximum Sharpe ratio for a given universe of assets. As the authors show, the average value of the OS is approximately equal to the square root of portfolio breadth, or the number of assets in a portfolio. The authors thus suggest an interpretation of the OS to be the effective breadth of a portfolio. Effective breadth is higher when the volatility of asset returns is high because such an environment offers investors more opportunities for generating returns, which is tantamount to having greater portfolio breadth. When asset return volatility is lower, the opposite is true; that is, effective breadth is lower and investors are hard-pressed to generate excess returns at any risk level