Contrary to what we are led to believe, investors can only spend compound returns, not average returns. Nevertheless, the average returns are so often mentioned by those seeking to promote an investment approach. This practice can often mislead investors who don't understand how money is made and lost over a period of time, due to compounding, in markets that move up in one year and down in the next.

There are two factors that can have a significant impact on the realized returns experienced by investors: the dispersion of returns and the impact of negative returns. Read on to discover the impact these factors could have on your portfolio, and how you can use this knowledge to gain higher compound returns and avoid the negative side of compounding.

### Back to Basics

First, let's review the mathematics used to calculate simple and compound averages. The simple return is the mathematical average of a set of numbers. The compound return is a geometric mean, or the single percentage, usually annual, that provides the cumulative effect of a series of returns. The compound return is the mathematical calculation describing the ability of an asset to generate earnings (or losses) that are then reinvested and generate their own earnings (or losses).

Let's say you invested $1,000 in the Dow Jones Industrial Average (DJIA) in 1900. The average annual return between 1900 and 2005 for the DJIA is 7.3%. Using the annual average of 7.3%, an investor has the illusion that $1,000 invested in 1900 would become $1,752,147 at the end of 2005 because $1,000 compounded annually at 7.3% yields $1,752,147 by the end of 2005.

However, the DJIA was 66.08 at the beginning of 1900 and it ended at 10717.50 in 2005. This results in a compound average of 4.92%. In the market, you only receive compound returns, so $1,000 invested at the beginning of 1900 in the DJIA would result in only $162,547 by the end of 2005. (To keep things simple and relevant to the discussion, dividends, transaction costs and taxes have been excluded.)

What happened? There are two factors that contribute to the lower results from compounding: dispersion of returns around the average and the impact of negative numbers on compounding.

### **Dispersion of Returns**

As the returns in a series of numbers become more dispersed from the average, the compound return declines. The greater the volatility of returns, the greater the drop in the compound return. Some examples will help to demonstrate this. Figure 1 shows five examples of how the dispersion of returns impacts the compound rate.

The first three examples show positive or, at worst, 0% annual returns. Notice how in each case, while the simple average is 10%, the compound average declines as the dispersion of returns widens. However, half the time the stock market moves up or down by 16% or more in a year. In the last two examples, there were losses in one of the years. Note that as the dispersion in returns grows wider, the compound return gets smaller, while the simple average remains the same.

Figure 1

This wide dispersion of returns is a significant contributor to the lower compound returns investors actually receive.

### **Impact of Negative Returns**

It is obvious that negative returns hurt the actual returns realized by investors. Negative returns also significantly impact the positive impact compounding can have on your total return. Again, some examples will demonstrate this problem.

In each of the examples in Figure 2, a loss is experienced in one year and the compound average return for the two years is negative. Of particular importance is the percent return required to break even after the loss. As the loss increases, the return required to break even grows significantly as a result of the negative effect of compounding.

Figure 2

Another way to think about the impact of negative returns on compounding is to answer this question, "What if you invested $1,000 and in the first year you earned 20%, and then lost 20% the following year?" If this up and down cycle continued for 20 years, it would create a situation that is not that different from what occurs in the market. How much would you have at the end of 20 years? The answer is a disappointing $664.83 – not exactly something to brag about next time you're at a party.

The impact of dispersion of returns and negative numbers can be deadly to your portfolio. So, how can an investor overcome the dark side of compounding and achieve superior results? Fortunately, there are techniques to make these negative factors work for you.

### **Overcoming t****he Dark Side of Compounding**

Successful investors know that they must harness the positive power of compounding while overcoming its dark side. Like so many other strategies, this requires a disciplined approach and homework on the part of the investor.

As academic and empirical research has shown, some of a stock's price movements are due to the general trend of the market. When you are on the right side of the trend, compounding works for you, both in up markets as well as down markets. Therefore, the first step is to determine whether the market is in a secular (long-term or multi-year) bull or bear trend. Then invest with the trend. This also holds true for shorter term trends that take place within the secular trends.

During bull markets it is fairly easy to do well - the common quip is correct, "a rising tide floats all boats." However, during a bear or flat market, different stocks will perform well at different times. In these environments, winning investors seek stocks that offer the best absolute returns in strong sectors. Investors must become good stock pickers rather than just investing in a diversified portfolio of stocks. In such cases, using the value approach to investing can have excellent results. It can also be useful to learn to short the market when the trend is down. Another strategy is to use bonds to build a ladder that provides a relatively safe return that can be used in a weak stock market environment.

During weak markets, when negative compounding can substantially harm your portfolio, it is even more important to employ proven capital management techniques. This starts with trailing stops to minimize losses and/or capture some profit from an investment. Another important technique is to rebalance your portfolio more frequently. Rebalancing capitalizes on short-term cycles in the financial markets. By selling part or all of the top performers in one asset class or sector, it provides capital to invest in new promising opportunities. A variation of this strategy is to sell part of your position when you have a quick gain to capture some profit and move the stop to or above your entry price. In every case, the investor is actively seeking to offset the negative side of compounding or even work with it.

### **The Bottom Line**

Overcoming the dark side of compounding requires that an investor be an active manager of his or her portfolio. This requires learning the skills needed to recognize market trends, find appropriate investment opportunities and then employ proven capital management techniques. Overcoming the negative side of compounding and beating the market can a very satisfying experience, after all, it's your money that's at stake.