The Wisdom of Crowds is one of the main reasons individual investors rarely outperform the index for any sustained period of time.

Michael Mauboussin, current Managing Director and Head of Global Financial Strategies at Credit Suisse, explained how this works in a 2007 paper called 'Explaining the Wisdom of Crowds' when he was employed by asset manager Legg Mason. The paper is a decade old but the proof is mathematical and thus timeless. The simple equation goes like this:

Collective error = average individual error â€“ prediction diversity.

Mr. Mauboussin conducted an experiment with his students at Columbia University where each would guess at the number of jelly beans in a large jar to see how close the average guess was to the correct number. We can use this example to illustrate the equation.

The collective error is the amount the final guess â€“ the average of all student jelly bean estimates â€“ over or underestimates the actual number of jelly beans. The average individual error is the average amount by which each student's guess missed the mark. I won't bother readers with the full mathematical explanation but prediction diversity measures how disperse or different the jelly bean guesses were.

The equation means that the size of the collective error declines as diversity increases or, the more widespread the estimates, the more accurate the final answer becomes. In the jelly bean experiment Mr. Mauboussin recounts, this led to a final estimate only off by 3.1 per cent in a jar with 1,116 jelly beans.

Applying this to asset prices it's clear why it's a mistake for individual investors to believe that market prices are wrong. The inputs to an asset price are far more numerous and varied than in Mr. Mauboussin's class, which means the final collective error gets smaller.

Just to keep things interesting, there are times like the technology bubble or bank stocks ahead of the financial crisis when the wisdom of crowds doesn't work at all. Usually, sentiment is to blame as stock price bets are widely corrupted by over-optimism.

These times are rare, however, and under normal circumstances investors should be very careful against betting against the crowd.

--Scott Barlow

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Stocks to ponder

Polaris Infrastructure Inc.
All six analysts who cover the company have buy recommendations on the stock, and the consensus target price suggests 33 per cent upside potential for the share price over the next year, writes Jennifer Dowty about this geothermal plant operator.  In addition, the company offers investors a 3.8 per cent dividend yield.

RioCan Real Estate Investment Trust.
There are plenty of minor reasons to avoid RioCan Real Estate Investment Trust right now, but there is one compelling reason to invest: RioCan's payout, unchanged in four years, is set to rise, writes David Berman. Here are the reasons why.

Enercare Inc
. This stock appeared on the negative breakouts list, showing negative price momentum, writes Jennifer Dowty. Its share price has fallen 14 per cent month-to-date, making it one of the worst performing stocks in the S&P/TSX composite index this month. The share price sharply declined after the company reported a large earnings miss. However, for longer-term investors seeking income, the recent price weakness may be creating a buying opportunity. Earlier this week, the chief financial officer was taking advantage of the price weakness and accumulating shares. The company offers investors an attractive 5 per cent yield.

Superior Plus Corp.
This stock appears on the negative breakouts list, which shows stocks with negative price momentum. The recent slide in its share price may soon provide a buying opportunity for investors, writes Jennifer Dowty. The company offers shareholders a 6 per cent dividend yield along with double-digit upside potential for its share price. The consensus target price suggests the stock price may have upside of 17 per cent.

The Rundown

Three Trump-resistant investment ideas to consider

This week's market turbulence can be pinned on waning confidence in U.S. President Donald Trump's tax-cutting and infrastructure-spending agenda, but some of the best emerging buying opportunities have nothing to do with Mr. Trump, writes David Berman. Even after Wednesday's harrowing decline, the S&P 500 was less than 2 per cent below its recent record high, which isn't exactly bargain territory. Thursday's rebound shrank that discount. He outlines the case for why these three investments can survive the "Trump trade."

Where is the loonie heading? The great debate over its direction

Which way will the loonie jump next? The market says down. Many of Bay Street's leading economists say up, writes Ian McGugan. The stark difference in opinion between investors and experts underlines a key truth about currency markets: Nobody knows anything for sure. Here are the arguments from both sides.

Virtual Reality could make these stocks the next Amazon.com

Citi's global quantitative strategy team has enjoyed resounding success in ranking the world's most promising and profitable investment themes. The list is currently topped by Video Game Growth â€“ a sector that has generated eyepoppingly strong performance, writes Scott Barlow. The promising outlook for the gaming and virtual-reality sectors makes these three stocks compelling options for investor portfolios.

Even mutual fund guru Gordon Pape thinks ETFs are usually the best option

If you can't beat them, join them, writes mutual fund guru Gordon Pape, noting that a number of mutual fund companies have launched exchange-traded fund (ETF) products in the past few years as ETFs gain in popularity. Now, he's looks at why investors are turning to ETFs and whether three of the most popular ETFs stack up as an investment compared to similar mutual funds.

How dividends came to dominate our investment portfolios

After housing, the hottest thing in personal finance is dividend stocks, writes Rob Carrick. Even as interest rates remain stuck near historical lows, the amount of investment income received by Canadians has surged in recent years. You can thank dividends for that. More and more, they're the go-to vehicle for retirees and others who want investment income. He outlines what key factors you need to know about dividend stocks.

A lesson from the stock plunge: Bonds are essential in a portfolio

Investors disagree on many things, but these days there seems to be at least one consensus: Everyone hates bonds, writes portfolio manager Dan Bortolotti. Here's his argument about why you need to have bonds in your portfolio.

Does your adviser have your back on cutting investment fees?

A standard investment industry putdown of robo-advisers is that they lack the human touch, writes Rob Carrick. But if human advisers care so much about their clients, why aren't they doing more to reduce the fees that clients pay to own the investments in their portfolio? There's good reason to ask this question after the robo-adviser Nest Wealth announced last week that it has updated the list of exchange-traded funds it uses for client portfolios in a way that will reduce fees by an average 28 per cent.

Market bets against Home Capital have just plunged. Here's why

The huge short position in Home Capital Group Inc., which peaked at more than 50 per cent of shares outstanding at the end of April, has been cut roughly in half over the past few weeks, according to data and analytics research firm IHS Markit Inc. Yet, it may not signal any higher degree of confidence in the beleaguered company's future, writes Larry MacDonald.

Let's stop bashing active management

"Active Managers Trail Benchmarks in 2016" proclaims a recent article in Investment Executive. Even more worrisome is the fact that according to a story in The Wall Street Journal, about 82 per cent of all active U.S. funds trailed their benchmarks over the past 15 years. The numbers are similar in Canada, as well. No wonder the number of ETFs listed on the Toronto Stock Exchange has more than doubled since 2011. Why is it almost impossible for reported numbers to show that active managers beat benchmarks? But beyond that, what may make it actually difficult for active managers to outperform benchmarks? George Athanassakos explains.

Others:

A defensive stock with a bullish 'golden cross'

Holland Bloorview Investor Challenge: How three fund managers fared in the first quarter

The week's most oversold and overbought stocks on the TSX

Number Crunchers

These 15 dividend stocks surface in our search for value in Canada's oil patch

These 17 leisure companies show strong price momentum

Seven financial dividend stocks with limited mortgage exposure

Question:
I'm 71 and I will be taking RRIF payments this year. My TFSA is maxed out. I've started investing outside my registered plans. What are the most tax-effective investments?

There is a wide range of tax-effective securities from which to choose including REITs, limited partnerships, preferred shares, and Canadian dividend-paying common stocks. Some mutual fund companies also offer tax-effective funds, such as the Nexgen line from Natixis Global Asset Management.

While all these securities are tax effective, some are more so than others. Eligible dividends (those paid by large companies) are the best bet if your total income is relatively low. Because of the way the dividend tax credit is calculated, the effective rate for someone with an income of under \$45,000 is under 10 per cent in most provinces.

--Gordon Pape

Do you have a question for Globe Investor? Send it our way via this form. Questions and answers will be edited for length.

What's up in the days ahead

This weekend is the final instalment of Rob Carrick's ETF Buyer's Guide, with a closer look at global dividend funds. Next week, David Milstead will look at the investment case for Cenovus. Ever since the company announced its transformational deal to buy \$17.7-billion worth of oil-sands assets from ConocoPhillips, the company's stockholders have headed for the exits. But that could be opening up an interesting opportunity for long-term investors.

Click here to see the Globe Investor earnings and economic news calendar.

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Compiled by Gillian Livingston

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