OPTIMIZATION MODELS
Optimization models “optimize”, that is, find the best solution to a problem. This is also a technique utilized in a great number of areas, including finance. If you have a certain amount of money to invest and the only important element for you is the yield, you will simply invest all the funds in the highest yielding financial instrument available. However, if you are concerned (as you should be) that such a strategy may carry a high level of risk, you may want to set some restrictions, such as, a minimum or a maximum amount of money to invest in a certain financial instrument; you may also want to set restrictions concerning interest rate levels, volatility of the result, total amount available to invest and others.
When you have more than a couple of restrictions, it becomes very problematic to find the best solution. In this case, many use an operations research tool called linear programming, which finds solutions to linear problems. For example, a portfolio manager may want to find the best portfolio mix according to a set of variables and restrictions. One of the variables may be interest rates, which have to be fixed for every security being considered. The analyst proceeds then to create a tableau, which is basically a matrix where the variables and restrictions are entered.
The problem with this traditional optimization method is that in the real world, things are different. By this we mean that this traditional technique hardly takes into consideration the element of uncertainty present, which must be dealt with in order to generate more meaningful results. In the model we build, we take care to adequately represent the element of uncertainty, by building a simulation model first. For example, while interest rates are fixed in traditional optimization techniques, in our model they represent a probability distribution. This means that the model will look for the best solution, by testing combinations of each one of the possible interest rates entered in the model (instead of only one), and the restrictions set.. This is how the portfolio will be optimized, and the best solution found.
Optimization models can be applied to a great variety of situations. For example, to select the best from various projects being considered when we have a limited budget which does not allow us to carry them all out.