“Full-scale optimization relies on sophisticated search algorithms to identify the optimal portfolio given any set of return distributions and based on any description of investor preferences (Adler and Kritzman 2007).” Rather than using summary statistics such as mean, variance, and correlation, full-scale optimization utilizes the full sample of returns based on plausible utility functions. Mean-variance optimization assumes either that returns are normally distributed or that investors have quadratic utility. However, asset returns are not exactly normally distributed in practice, and investors are rarely as averse to upside deviations as downside or prefer less wealth to more wealth.

While both approaches to optimization suffer from estimation error, mean variance optimization also incurs approximation error (Adler and Kritzman 2007). While full-scale optimization returns the in-sample optimal portfolio, parametric optimization returns an approximate in-sample optimal portfolio.

Historical returns are used to generate data for full-scale optimization. However, to incorporate an investor’s views regarding expected returns, we adjust the data accordingly.

We include three common expected utility functions – the Power Utility, Kinked Utility, and the S-Shaped Utility functions.

We scale the historical data so to conform with specified return expectations. We assume the risk estimate is the historical experience as it is not possible to adjust the second moment of without altering other moments within the dataset.

**Optimization**

We maximize these equations with enumerated search procedures as there is no closed form solution to the above equations. We use a global search method that generates a population of candidate solutions to an optimization problem and evolves iteratively towards better solutions. The fitness of the candidate solution at each iterative step is evaluated and is mutated or recombined to form a new population. The new population is used in the next iteration of the genetic search. There is the possibility in using a global search that we don’t arrive at the global maximum. In addition, because of the randomness in searching, it is possible for different solutions given different searches.

**Related Articles**

- Adler, T. and Kritzman, M. , Mean-Variance versus Full-Scale Optimisation: In and Out of Sample, Journal of Asset Management, Vol. 7, 5, 302–311, 2007
- Cremers, J., Kritzman, M., Page, S., Optimal Hedge Fund Allocations: Do Higher Moments Matter?, Revere Street Working Papers, 272-13, 2004

Category:Understanding the Software -> Optimization