THE DIRTY SECRET OF OPTIMIZATION

Since the early studies of Markowitz, researchers have used optimization methods to determine the ideal weights of stock and bond portfolios. Today there are excellent optimization software programs such as the Zephyr AllocationADVISOR software used in this study. But researchers have to use common sense in their applications.

Consider a simple optimization experiment. So far we have represented U.S. stock portfolios with a single index, either a large-cap index or an all-cap index. Suppose that the portfolio consists of different indexes for growth and value stocks and for small-cap stocks. As discussed in early chapters, many portfolios are divided along style and size dimensions. Often a portfolio will have separate allocations for large-cap growth and large-cap value as well as small-cap growth and small-cap value. Some portfolios go even further by adopting nine different allocations, with value and growth being augmented with an allocation to core and with small and large being augmented with an allocation to mid cap. It’s interesting to investigate how optimization programs would allocate such portfolios.

For the experiment, a four asset portfolio will be compared with a two asset portfolio that contains a single U.S. stock index. The two asset portfolio consists of the Barclays Aggregate index and Russell 3000 all-cap index only. In the four asset portfolio, the U.S. stock allocation will be divided in three segments, large-cap growth and ...

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