Fine-Tuning Your Risks By Dirk Vandycke

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In this second of a two-part series on managing risk, we look at how to overcome the disadvantages of diversification. (Read Part 1) In part 1, it became clear that we need to bring profits and total return into the equation to evaluate the effects of diversification. However, it’s necessary to look beyond its common risk-lowering incentive and gain a more holistic view of diversification. While the advantages on the risk side are beneficial to all traders, from expert to layman, you mustn’t be blind to the disadvantages, mostly on the profit side. Diversification will spread risk, and hence lower it, but at the cost of averaging your returns. Let’s see if we can put this knowledge into practice.

Diversification vs. Concentration

Statistical expectancy tells us we have more control over the average size of winners and losers than over how frequently they occur. But frequency plays a role in profitability, so instead of trying to increase the numbers of winners while decreasing the number of losers, perhaps you should shift your focus to minimizing the size of losers and maximizing the size of winners. Cutting losses and riding winners is mathematically represented by expectancy. Shifting your resources so you have fewer winners will tend to concentrate your portfolio instead of spreading it. But how do you maximize profits with fewer winners? One way to do that is to add to winning positions, which would accelerate the speed of your winners and bring you higher profits. You can take an even bigger piece of the portfolio pie as a consequence.

Geometrical growth or power laws in mathematics tell us that diversification decreases average returns. Say you have nine winners of 2% and one winner of 30%. Average return in such a case would be a meager 4.50% using the following calculation:

That one big winner increases the average return of the 2% winners by only 1.15%. If diversification didn’t decrease average and overall return, or if the effect is negligible, it means that the original returns must be similar. In such a case, the only thing diversification did was perhaps increase transaction costs, which contributed to lowering the return. If diversification is counterproductive to expectancy, then concentration could be a valid option. To determine if it is a valid option, I ran a Monte Carlo simulator on a database of thousands of stocks. I monitored the performance of these stocks over the last decade and over different market conditions.

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The Test Portfolios

Each test included a portfolio of 13 randomly selected stocks over a specific time period, with the initial capital divided between all stocks. I had the computer run two copies of each portfolio. One was the homogenous diversified portfolio, which acted as a reference for comparison purposes. The other copy of the portfolio, the pruning portfolio, pruned the diversification and gradually morphed into a portfolio containing just one stock. The pruning portfolio placed a three ATR trailing stop for all positions. Once a position was stopped out, the cash from that position would get distributed evenly over the remaining holdings in the portfolio, thus adding to your positions. Eventually, there would only be one position holding 100% of all portfolio resources. Once this last position was stopped out, I compared the net return of both portfolios. The time period used was dictated by when the last stock of the pruning portfolio was stopped out.

Here Are The Results

The average return of all test portfolios is depicted in Figure 1. Each of the gray lines on the chart represents the average equity curves of all 13 portfolio holdings. Note that some stocks stayed in the portfolio longer than others. The solid red line is the equity curve of the pruning portfolio and the dashed green line represents the homogenous diversified portfolio. Clearly, concentrating funds by holding onto the winners seems to be the superior method. Note also that the return on the pruning portfolio is higher by 2.36% than that of the homogenous diversified portfolio. It may seem like a small edge, but the pruning portfolio had to make several artificial costs during the concentration process.

FIGURE 1: HOMOGENOUS DIVERSIFIED PORTFOLIO VS. PRUNING PORTFOLIO. The gray lines show the average returns of each of the stocks up to the point at which they got stopped out. The solid red line represents the pruning portfolio whereas the dashed green line represents the homogenous diversiﬁed portfolio.

Keep in mind that a concentrated portfolio can start with three or four stocks and have only one exit, which would reduce your transaction costs. Realistically, you would probably encounter fewer costs in the pruning portfolio than in the reference portfolio, and that would increase the return of the pruning portfolio.