# To Optimize or Not Optimize

One question that clients sometimes ask is, “Are IFA’s portfolios optimized?” It’s a fair question.  That word “optimization” is thrown around somewhat loosely, and it certainly sounds like a good thing.

Optimization is performed using three pieces of data.

1. An asset’s time period by time period return (for example annual or monthly).
2. An assets standard deviation.
3. An asset’s correlation with other assets.

Using those three pieces of information a computer program can determine the best portfolio an investor could have held during the time period under analysis. By best, we mean the specific combination of assets that would have yielded the highest returns at a certain standard deviation.

The perils of optimization exercises are obvious.  First, they are very time period dependent.  The optimal portfolio from 1990 to 2000 would be very different then the optimal portfolio from 1980 to 1990, which would be different again from the optimal portfolio from 1980 to 2000.

Secondly, the optimization exercise will tend to concentrate a portfolio in the one, two, or three asset classes that have performed the best in the period under analysis.

To illustrate let’s look at an example. The general framework for IFA’s portfolios was suggested in 1991 by DFA as an example of a globally diversified investment (see ifabt.com for description of the history on the IFA Index Portfolios and this pdf for an explanation of the evolution of the allocations and of the stitching together of indexes and live funds over time).

Because 1991 was the decision point, in our example we’ll optimize a portfolio of DFA based indexes from 1958 to 1990 for the standard deviation of a Index Portfolio 90.  We’ll then see how this portfolio performs from 1991 through 2007. In both instances we’ll compare with Index Portfolio 90 and draw lessons based on the comparison.  The total time period under review here is 50 full years, from 1958 through 2007.

At a standard deviation equivalent to a Index Portfolio 90, the optimal portfolio of indexes includes:

1. 24.3% Large Cap US Value
2. 43.53% International Small Value
3. 13.93% Emerging Small Cap
4. 18.24% One-Year Fixed Income
 Optimal Portfolio 90 Allocation (base on 1958-1990 time frame)

This optimal portfolio would have produced an average return between 1958 and 1990 of 17.6% with a standard deviation of 19.7%. By comparison, IFA portfolio 90 during the same time period produced a return of 13.76% with the same standard deviation.

 Figure A

Now we examine how the optimized portfolio and IFA Index Portfolio 90 compare during the subsequent 17 years, from 1991 to the present.  Again we start this analysis in 1991 because that’s the year in which the general framework for the IFA Index Portfolios was first worked out.

From 1991 to 2007, the optimized portfolio had returns of 11.62% and a standard deviation of 14.69%.  Index Portfolio 90 on the other hand has returns of 13.96% and a standard deviation of 13.69%.  Portfolio 90 had higher returns and less risk then the optimized portfolio in the subsequent time period.

 Figure B

This example shows the peril of portfolio optimization.  From 1958 to 1990 the best performing asset class on a risk return basis was International Small Cap Value.  Based on past returns the investor would have loaded up on that asset class at the exclusion of others. However, during the subsequent period Domestic Small Cap Value performed much better.  How was an investor in 1990 to know whether domestic or foreign Small Cap Value would do better?  The truth is, they couldn’t know. The only prudent strategy would be to hold both and rebalance periodically based on market movements.

So, to answer the initially posed question, “Are IFA’s Index Portfolios optimized?” The answer is no. Instead IFA’s Index Portfolios don’t make bets on one or two asset classes, whether foreign or domestic, that have performed exceptionally well over some time period.  We hold foreign, domestic, and emerging markets. We hold large and small companies, and we hold REITs and fixed income. We tilt the portfolios towards the small and value risk factors that reward patient investors with higher risk adjusted returns, we rebalance the portfolios to keep investors at a consistent risk exposure and we tax loss harvest taxable investors when the opportunity arrives.

For a similar perspective, see this excerpt from the Seekingalpha article Testing Forward Looking Asset Allocation

"The challenge of ‘optimizing’ a portfolio by calculating the efficient frontier is that you need to have estimates for the expected returns and standard deviations of all available asset classes, as well as the correlations between them. Where do you get such data? A simple minded approach to this problem is simply to use historical data. This leads to poor results, in general, if you manage a real portfolio simply by looking backwards in this manner. William Bernstein performed an experiment in which he created asset allocations based on trailing data in which he optimized historical returns with a risk constraint over a series of time periods. In other words, he calculated the efficient frontier using historical data and then allocated a model portfolio so that it was on the efficient frontier. He found that a portfolio managed in this way generated a substantially lower return than a simple static allocation with annual rebalancing, in which the portfolio was spread between the major asset classes ('The Intelligent Asset Allocator', P. 70). The under-performance occurs because asset allocation using historical data simply tends to over-weight the portfolio to the assets that have performed well in that specific period. This tends not to work well going forward (e.g. out-of-sample)."
http://seekingalpha.com/article/101125-testing-forward-looking-asset-allocation