Portfolio returns: Compound vs Average Returns

In last Tuesday's blog we addressed the issue of what actually goes into calculating portfolio returns. We began by looking at how variations in input parameters can affect the calculation. But that's only one half of the story. Today we'll address the other half: how return values vary depending on the calculation method.

Compound versus average returns
There are two basic methods of calculating the returns in a portfolio--by averaging or compounding-- and understanding the difference between them is crucial to your investment approach and also in comparing fund returns. Contrary to what you might think, you can only spend compound returns, not average returns, but it's the average return that is typically given in fund prospectuses. To understand why this is true, we'll have to look at both methods of portfolio calculation.

Average returns
The average return is nothing more than the arithmetic average of individual returns. This is a simple calculation: average return = sum of all returns/number of returns. For example, if a portfolio returns 10% in each of three consecutive years, the average return is 10% ((10%+10%+10%)/3). The same return can also be achieved by the following portfolio returns: 15%, 25% , and -10%. However, their compounded returns are not the same which we'll see in a minute.

Compound returns
The compound return is a geometric mean that takes into account the cumulative effect of a series of returns. It describes an asset that is reinvested at the same time interval (typically on an annual basis) along with its earnings (or losses). This is what mutual funds do. I won't confuse you with the mathematical formula for compounding, but you can try if for yourself using this handy compounding calculator.

Let's look at a real example of the difference between these two methods of calculation. Suppose you had invested $1 in the Dow way back in 1900. The average annual return of the Dow from 1900 to 2005 was 7.3%. So, by compounding your 7.3% gains annually from 1900 to the end of 2005 you'd expect to have realized $1,752, right? Wrong! If you look at a chart of the Dow, you'll see that it began at 66 in 1900 and ended 2005 at 10717.

Doing the reverse calculation, you'll find that the effective compound interest rate on the gain was really only 4.92% instead of 7.3%. Using the 4.92% as the compounding basis, your 1900 buck would now only be worth $163 by the end of 2005. That's 90% less than using the average Dow value of 7.3%!

What's going on? Why is there such a huge discrepancy in returns? There are two reasons to account for this: dispersion of returns and negative returns.

Dispersion of returns
In finance, dispersion can be thought of as how far the real returns are from the average return. For you statistical wonks, dispersion is related to the standard deviation (the volatility). Thus, the more volatile the portfolio, the greater the dispersion.

The following chart below dramatically illustrates the effect of dispersion on several portfolios with the same $10,000 starting value and the same average return of 10%.


What this table means to you, the investor, is that the compound returns of more volatile portfolios can be significantly lower than the stated average return.

Negative returns
Negative returns is the other factor that can have a major impact on returns. Particularly important to investors is how much their portfolios will have to gain after a downturn. Let's look at the following table:


You can see that the amount that a portfolio has to increase just to get back to break-even magnifies as the amount of loss increases. A portfolio loss of even 30% can take many years to finally recover, and that's not including the time-loss of money—ouch!

Steps you can take to avoid these problems
First of all, it pays to keep an eye on your portfolio. The strategy of buy-and-hold is essentially dead unless you're a teenager and can wait 40-50 years for your portfolio to recover. In bull markets, buying strong stocks in strong sectors (“best of breed” as Cramer would call them) is a popular strategy. In bear markets, going into cash or cash-type of investments (treasuries, high-grade bonds) will spare your portfolio the effect of a large negative return. If you own stocks, set stop losses, and stick to them. If you don't like shorting in bear markets, you can still participate by buying put options or inverse ETFs; however, there's nothing wrong with preserving cash. Unless you have a high net worth or a lot of disposable income, it's best for average investors to avoid placing a large portion of their portfolios into riskier assets such as speculative stocks. This reduces the effect of dispersion, but it can also reduce overall returns, too.

Summary
I hope you've found this article useful. The important thing to remember is that the average return is no indication of how well your money will do in a particular fund. The size of negative returns plus the dispersion of returns are the two factors that will impact your money the most and it's the compound return that tells the real story.

In upcoming articles I'll look at ways the investor can use market timing and portfolio optimization techniques to minimize the effects of negative returns and dispersion.

Channeling Stock Portfolio Update
Long pick SOHU hit its price target and sold for $50.03. An updated chart will be displayed later. There were a couple of typos in the weekend chart which are corrected. Also, the stop loss values are changed to reflect the higher channel value if the stock entry was a short and the lower channel value of the entry was a long as opposed to using the average true range. I feel this gives the trade more time to develop. Time will tell if this is a better stop loss criterion.