Sometimes, the historical data on returns and variances may be poor predictors of how investments will perform in the future. In this case, the scenario approach to portfolio optimization may be used. Using this technique, we identify several different scenarios describing the returns that might occur for each investment during the next year and estimate the probability associated with each scenario. A common set of investment proportions (or weights) is used to compute the portfolio return ri for each scenario. The expected return and variance on the portfolio are then estimated as:

Where ri is the portfolio return for a given set of investment proportions under scenario i and Si is the probability that scenario i will occur. We can use Solver to find the set of investment proportions that generate a desired EPR while minimizing the VPR. Given the following scenarios, find the investment proportions that generate an EPR of 12% while minimizing theVPR.

Returns Windsor 0.14 Flagship Templeman 0.09 0.12 0.15 0.18 0.16 T-Bills 0.07 0.06 0.08 0.07 0.06 Probability 0.10 0.10 0.10 0.10 0.14 0.09 0.25 0.18 0.33 0.15 4