Average Annual Return Can Be Misleading!

Note: Please read the disclaimer. The author is not providing professional investing advice.

I’ve written before about the importance of not just using average annual rate of return (ROR) as your basis for deciding between your investment options. Standard deviation is also important as it gives you rough upper and lower bounds as to how much any particular yearly return may differ from that average ROR (assuming the future ROR distribution tracks the past).

But there is another way in which the newbie can be lead astray by average annual ROR, especially if the average is an arithmetic mean instead of geometric or annualized. If you find a fund or trading algorithm that has an attractive mean ROR but large standard deviation, you may shrug off that high volatility if your plan is to invest over the long term. Why be concerned about large yearly fluctuations if you’re not planning to move your money for 5 or 10 years? As long as the average annual return is good, so your thinking goes, when I take my money out a decade from now, I will have made a nice profit. The only people who should be concerned with a high yearly fluctuation are those who plan to park their principal for only a year or two, right?

But is that true? Are you perhaps making some assumptions – subconscious even – about what that modest, but adequate average ROR implies? When you see an average ROR of 10%, does your brain think that, though there will be fluctuations from year to year, your ROR on $10,000 after 5 years will roughly be $10,000 x 1.10 x 1.10 x 1.10 x 1.10 x 1.10 or $16,105?

And what is it with those older guys at work who are still complaining about the money they lost by investing in technology stocks during the dot-com bubble? I mean, the market has made some solid gains recently but these guys haven’t let off their belly-aching! Let’s assume they kept their retirement nest eggs fully invested in the technology sector – through thick and thin. Where would they be today? Well, can we approximate it by examining the annual ROR of a technology sector ETF – which should roughly parallel a portfolio invested heavily or mostly in technology stocks?

Technology Sector ROR

So why are they still so bitter? If they had saved up say $100,000 for their retirement and invested only in the tech sector from January 1, 1999 through December 31, 2005, which has an average annual ROR of +0.9% during this period, shouldn’t their investment in January 2006 be worth about:

$100,000 * 1.009 * 1.009 * 1.009 * 1.009 * 1.009 * 1.009 * 1.009 = $106,473?

Granted they haven’t made much money over time but at least they still haven’t lost their nest egg, right? What a bunch of whiners!

But average annual ROR is misleading – because the only way your actual return matches the arithmetic average return (besides when there is no variation from year to year) is if you start off each year with the original principal ($100,000) instead of what was leftover from the previous year . To see how much money they really have today, you need to examine what has happened to their investment on a year-by-year basis.

At the end of 1999, it was worth $100,000 x (1+.651) = $165,100
At the end of 2000, it was worth $165,100 x (1-.419) = $95,923
At the end of 2001, it was worth $95,923 x (1-.233) = $73,573
At the end of 2002, it was worth $73,573 x (1-.382) = $45,468
At the end of 2003, it was worth $45,468 * (1+.387) = $63,064
At the end of 2004, it was worth $63,064* (1+.060) = $66,848
At the end of 2005, it was worth $66,848 * (1-.003) = $66,648

Whoa! This paints an entirely different picture! Even though the technology sector may have an average annual gain of +0.9%, their original principal has dropped by 33%! Now we understand their crankiness and can see why so many people swore off the stock market after the tech bubble burst. We also see why Warren Buffett says rule #1 in investing is not to lose money – and rule #2 is not to forget rule #1! It’s very hard to recover from a large loss.

And we can see how true this is by imagining a hypothetical fund that has returned +50% one year, and -50% the next. Does that make it all even? You make a nice profit in year 1 but then give it all back in year 2 for an average ROR is 0%? Not at all! The reality is $10,000 invested at the beginning of year 1 would be worth $15,000 at the end of the year. And when your $15,000 investment returns -50% during year 2, you’re left with only $7,500 – a 25% loss! The fact of the matter is that in order to break even, a 50% loss has to be followed by a 100% gain! Still feeling comfortable using average annual ROR as your decision basis for picking investments, erstwhile ignoring yearly variance?

Obviously the moral of the story is that an arithmetic average annual ROR can be very misleading and we should do everything possible to avoid ever incurring a large loss. As a minimum we should examine the standard deviation to see how far from the mean a given year may vary probabilistically, and then decide whether we could recover from the loss if indeed we hit a year that is 1 or 2 standard deviations below the mean. And of course, it’s always possible that something unpredictable comes out of left field and serves us up a bad ROR far beyond the 1 or 2 standard deviation range. It is more helpful to use a geometric average rather than arithmetic if we’re truly trying to get a sense of the effective average ROR our money would have grown at historically.

Another way we can protect ourselves is to diversify. If we diversify smartly, we can keep roughly the same average annual ROR as if we were invested in a single stock or fund, but with considerably less variance from year to year.

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