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“Skewness” means that at any given time, the index is going to be affected by a tiny number of stocks that are delivering outsized gains. This positive skew makes life difficult for active managers.

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John Reese is chief executive officer of Validea.com and Validea Capital, the manager of an actively managed ETF. Globe Investor has a distribution agreement with Validea.ca, a premium Canadian stock screen service.

The odds of winning a coin flip beat the chances of hand-picking a winning portfolio of stocks. This effect has been well documented over the last year as active fund managers failed to beat broad market benchmarks such as the Standard & Poor's 500.

J.B. Heaton, a lawyer and PhD in financial economics, has written recently about a phenomenon called "skewness" that helps explain why stock pickers can't get an edge. His work builds on previous academic research on the subject from as far back as 20 years ago.

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"Skewness" means that at any given time, the index is going to be affected by a tiny number of stocks that are delivering outsized gains. This positive skew makes life difficult for active managers. Out of the thousands of possible stock combinations, there is only a small likelihood that they will be holding the same winning stocks.

In a 2015 paper, Dr. Heaton, along with N.G. Polson and J.H. Witte explained it using a hypothetical index of five securities, four returning 10 per cent and one returning 50 per cent. In this scenario, the active managers chose portfolios of one or two stocks and equally weighted each investment. There were 15 possible one- or two-security portfolios. Of the 15, 10 would return 10 per cent, because they wouldn't hold the best-performing stock. So, two-thirds of the portfolios would deliver lower returns than the index.

The academics concluded that the higher cost of active management isn't fees, but the very act of stock selection. This is a powerful concept for investors, who have been pulling billions of dollars out of actively managed funds and pouring money into funds that track market indexes. But even here, there are other factors at play that investors need to consider.

The typical mainstream indexes weight their holdings according to market capitalization. When index funds were being developed decades ago, they took on this same characteristic. It was less work to weight by market cap because the portfolios didn't have to constantly be adjusted to stay in line with the index they were tracking.

Weighting by market cap emphasizes stocks of big companies over small ones and tend to favour markets that are driven by momentum.

You would think "skewness" would favour a market-cap weighted index, but what's interesting is that an equally weighted index of S&P 500 stocks has beaten the market-cap weighted S&P 500 index for the past 12 years.

As it sounds, an equal-weight portfolio holds stocks in equal amounts, regardless of market cap. It is necessarily going to hold stocks of smaller, less liquid companies. It is a strategy that benefits when small- and mid-cap stocks are in favour. SPDR S&P 500 ETF Trust, an exchange-traded fund tracking the S&P 500, lagged the performance of the iShares Russell 2000 ETF, which tracks the eponymous small-cap index.

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A recent paper by the smart-beta firm Research Affiliates says equal-weight indexes have two clear advantages. They outperform market-cap weighted indexes and are easy to understand. But they have higher turnover because they need to be constantly rebalanced and they buy and sell lower liquidity stocks.

Equal weighting and market-cap weighting both have the problem of buying overpriced stocks and selling undervalued ones. Equal-weight funds could have higher costs because they have far higher turnover to keep the portfolio balanced.

The firm argues that fundamental-weighted indexes are a better bet. Rather than emphasizing market cap, this strategy looks at book value, dividends and other characteristics of the underlying stocks. It tends to favour value stocks, which are cheap relative to their peers. The downside is that they could lag the market when value stocks aren't in vogue.

Obviously, they are familiar with the idea. Research Affiliates uses quantitative factors like market volatility to take the emphasis off of market cap. Nearly $130-billion (U.S.) of assets track the firm's smart-beta indexes, including its fundamental index, the FTSE RAFI US 100, which it says follows contrarian investing principles. The idea behind the fundamental strategy is to sell stocks that have gained and buy those that have fallen.

Fundamental investing is a hallmark of many of the gurus that our models track. Warren Buffett and Peter Lynch made careers out of identifying hidden gems in undervalued stocks and zigging when other investors were zagging.

But investors need to consider the pros and cons of each strategy. If simplicity is the goal, the market-cap weighted index may be the best option. If you believe small- and mid-cap stocks are poised to gain, an equal-weight index may be for you. If believe fundamentals and valuations matter over time, you can choose one that tracks a fundamental index.

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I think the key is not to get "skewed" by chasing or overreacting to recent performance or failing victim to sky-high fees. The ingredient for success is to find an approach you identify with and can stick to for the long haul and do it at a reasonable cost. If you can do that, you'll be ahead of most investors.

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