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# Low Charges And High Volatility: How To Erase Your Returns

“Variance drain”, also called volatility drag, is the fundamental principle that between two portfolios with identical starting values and identical average returns, the portfolio with the greater variance will result in substantially lower total wealth.  As such, with medium to long-term financial planning, managing the variance of your asset base is of great importance.

For example, ever wonder how a leveraged ETF can claim to provide almost exactly 2X or 4X the daily performance of its underlying index, but then the long term performance is similar to or worse than the underlying index?…

Whilst there is some math involved, we’ll keep everything as simple as possible, as it is crucial for all investors to be familiar with the underlying concepts.  We will briefly define a couple of statistics terms, and then explain with examples how the terms relate to your investments, and how variance can drain returns from your portfolio.

Aprimary method to characterize a fund’s risk is with the variation (volatility) of its returns. This is typically measured with the investment’s standard deviation or its “variance”.

Standard deviation is a basic term in descriptive statistics.  If an investment’s average return is 10% and the standard deviation is 15%, this means that two thirds of the time the investment has returned between -5% and 25% (10 average, plus 15 and minus 15).  For example: in any ten year period, for about 7 of the years the portfolio experienced returns between -5% and +25% each year, with the remaining ~3 years experiencing greater or lesser returns.

## Variance Drain – What Is “Variance” In Investing?

Variance involves a little bit more math, and as such is not as simple to work with. Standard deviation tends to be easier because it is expressed in the same units as the average, whereas variance is expressed in squared units.  We do not want to lose anyone here, so the concept behind summing the square rooted squares does not need to be discussed in this article… As a summary, using Variance and Standard Deviation ensures an accurate measure of the level of volatility by treating positive and negative data points with equal measure.

What does all this really mean to me?  The reason it’s important to learn these basic statistics terms is not only to understand what people are actually referring to when speaking about volatility, but also to take it one step further and understand the real implications of these terms on your returns. Unless an investor is close to retirement then ordinarily you are looking at a long investment time-line ahead. Even if an individual likes to focus on a short time-frame and break things up into short-term plans, unless they are at the very end of their working life they are still facing about a half-dozen short-term plans. When we look at the big picture, we are almost always faced with medium to long-term investment horizons. At which point, we must strongly consider the impact of variance drain on returns.

Average returns are nice, but as variance drain illustrates, too much volatility can erase a sizeable portion of our gains. Let’s look at a couple of examples illustrating this effect.

First, a simple example with extreme numbers:

A
stock is purchased for \$200. At the end of the first year, its price is \$400 (100% gain). In the second year, the stock price drops to \$200 (50% loss).

2-year Arithmetic Average Return:   25%         (100% – 50%) / 2

2-year Geometric Return:     0%         \$200 (final value) – \$200 (starting value)

As you can see, focusing only on the average returns can leave much to be said about the actual performance.  Of course, the above is an extreme example. Real world applications of this concept are much more subtle, but in the long run could still have a quantifiable impact.

Now a more realistic example comparing two \$100,000 portfolios over a 10-year period:

Portfolio A
consists of 15% in a core bonds fund and 85% in a MSCI World Index (equity) tracker (rebalanced approx. once a year if the 15/85 ratio becomes out of line). This strategy is passive.

Portfolio B consists of an actively maintained portfolio consistent with a 10-year time horizon, requiring time and attention to manage downside risk and volatility as markets change throughout the 10 years. This strategy is active.

After the 10 years are up, Portfolio A and B, net of all costs of implementing each strategy, both have the same exact arithmetic average returns: 9% per year.

Portfolio A initially rejoices at achieving the same average returns as the active portfolio.  However, over the 10 year period Portfolio A experienced the full ups and the full downs of the market, and underwent a variance of 19%.  Portfolio B managed the downside risk and volatility, experiencing a variance of 10%.

Although they both had identical average returns, the actual end result is:

Portfolio A:  \$193,641

Portfolio B:  \$238,793

As is evident, even if a particular strategy aims to produce similar average returns if it must endure the inevitable periodic market downswings, it is less likely to be able to make up for it in the good years.  Such volatility will drag down (variance drain) the long term actual growth.

## Examples Of Volatility Drag In Investment Portfolios

To close, let’s return to the simple example posed at the beginning of the article.  We understand that most people will not be using leveraged ETFs, but they remain a quick and easy way to look at what are essentially two identical investments (1: the underlying index, and 2: the leveraged ETF) except with one of them having greater volatility.  So this begs the question, why is the long run performance not also double? The math is relatively simple: if we start with \$100, a 10% gain on Day 1 results in \$110. A 10% drop the next day then leaves us with \$99 due to the higher starting base on the second day. Double the daily performance however and we end up at \$120 on the first day and \$96 on the second, which is 3% lower than the non-doubled benchmark.

 Scenario 1 Scenario 2 Scenario 3 Scenario 4 Scenario 5 Scenario 6 Arithmetic Annual Return 10% 10% 10% 10% 10% 10% Standard Deviation 0% 10% 20% 30% 40% 50% Geometric Annual Return 10% 9.60% 8.30% 6.03% 2.58% -2.42% Starting Funds \$     100,000 \$        100,000 \$        100,000 \$        100,000 \$        100,000 \$        100,000 Ending Funds \$     259,375 \$        250,156 \$        221,935 \$        179,629 \$        129,073 \$          78,278 Total 10 Year Return 159% 150% 122% 80% 29% -22%

People will often spend inordinate amounts of time debating expense ratios and annual management charges without giving a thought to managing volatility despite the fact that any and all volatility will have a negative effect on investment returns.

 Percentage Loss Percent Rise To Breakeven 10% 11% 15% 18% 20% 25% 25% 33% 30% 43% 35% 54% 40% 67% 45% 82% 50% 100%

An investment that declines 50% must increase 100% to break even! Think about it in dollar terms: a stock that drops 50% from \$10 to \$5 (\$5/\$10 = 50%) must rise by \$5, or 100% (\$5/\$5 = 100%), just to return to the original \$10 purchase price. Many investors forget about simple mathematics and take in losses that are greater than they realize. They falsely believe that if an investment drops 20%, it will simply have to rise by that same percentage to break even. In managing volatility effectively you will often receive better returns than those who focus exclusively upon the minutiae of total expense ratios and annual growth rates.

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-The Stewardship of Wealth. Gregory Curtis. 2013. Wiley Publishing

-Variance Drain. Thomas E Messmore. The Journal of Portfolio Management Vol. 21, No. 4 1995

-The Variance Drain and Jensen’s inequality. Robert A Becker. 2012. Bloomington, Ind. : Center for Applied Economics and Policy Research