May

1

"Couldn't you just buy a portfolio of stocks that outperformed random?" That question was posed over dinner by an individual investor who had never taken a statistics course and had no real idea of random. He also had no idea over how long one should compare the performances. But he held the belief that today's financial weather is a function of yesterday's financial weather, and in his own way was looking for a way to make it work. Individual investors believe in autocorrelation even if they don't know what it is; they do not believe in the random walk.

The question caught us off-guard because we did not know the answer. We had always compared performance to the market indices as the obvious benchmarks. We were not enamored with the idea, but as professionals we had no choice but to learn the answer.

We have taken the 500 largest capitalization stocks* and their 1-day rates of change. Then we have randomized the signs of those rates of change. For example, if stock A had a gain of 0.32 percent on a particular day, the study would for each observation randomly attribute that day's performance as a positive 0.32 percent or a negative 0.32 percent. Keeping the absolute value of the percentage change and randomizing the sign preserves the volatility of each particular stock.

We then produced 1,000 such random results for each of those stocks over the last 10 years.

Next, on a moving basis (with varying lookback periods) we compared the actual performance of each stock to its collection of random results. We then ranked each by the percentage of the actual above or below the random collection. For example, if at a given time, the actual performance of stock B was better than 850 of the 1,000 random runs, then stock B was given a ranking of 85. If, over the same period, stock C ranked 80, then stock B was deemed to be stronger than stock C. Thus the stocks were compared first to themselves and then to each other.

We then simulated trading results as follows: we purchased a collection of stocks that ranked highest on a given day, allocating funds equally. The collections varied from as few as 5 assets to as many as 50. There was no attempt to rebalance the portfolio. For example, if 3 stocks dropped off the list, then we simply divided up the sales proceeds equally to the 3 new stocks entering the list. This was to keep the strategy operationally possible. We know that total daily rebalancing is more profitable (we have tested it), but it requires transactions in every held asset every day that is onerous for all but a few professionals. The actual strategy seems simple, but is annoyingly time consuming because of the number of calculations involved.

There was no attempt to institute stops. Stocks were never "sold"; they were simply replaced. This avoided the toughest decision in investing: when to sell.

We performed this work over a number of "lookback" periods. In the link below we have illustrated results over a semi-annual period (126 market days). Since ranking over a lookback period is more reflective of the middle of the period, we were essentially comparing quarterly price performance, which we felt mimicked either actual or expected quarterly earnings performance.

If stock price behavior is random, the strategy will not perform well.

Our preference is to compare performance on a reward-to-risk ratio. That is, we take the average annual rate of return and divide that by the maximum drawdown over the period. The S&P 500 Index on a total return basis returned a 9.26 percent average annual rate of return and experienced a 47.41 percent peak-to-valley drawdown, thus its reward-to-risk ratio is .1953. However as you will see, the choice of performance yardstick is moot, as the results are totally one-sided.

Of the 46 collections studied, the average annual return was 27.39%, while the average maximum drawdown was 45.15%. The average reward-to-risk ratio of the collections was 0.6076. More importantly however, is that all of the collections bested the S&P. There was not one that underperformed the market.

Although the results are fairly uniform some vague generalities can be made, which will not be surprising: The fewer the number of assets chosen, the higher the return and more volatile the performance. The greater the number of assets chosen, the closer that performance will come to mimicking the overall market.

These are not enviable results, but they are significantly better than the market. This study raises the bar for asset rotators. Most compare their performances to a buy and hold strategy of the indices. However, now we would postulate that these are new benchmarks for an asset rotator to beat prior to claiming any expertise.

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* The list included deceased stocks (e.g. Enron, Worldcom, etc.) to prevent survival bias. Thus at times the list consisted of more than 500 stocks.


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