Let’s suppose you walked into a casino and bet 100 dollars on some game; the following are all of the possible outcomes, along with their respective probabilities :

1. 80%: You walk away with nothing
2. 19%: 200 dollars gain
3. 1%: 2000 dollars gain

Now, suppose you have gambled so often that you have encountered all three of the above scenarios (the more likely ones, of course, happening more frequently than the rarer ones). During the next party you attend, you’d like to pick one experience to share, in order to impress your friends. Which of the following are you more likely to say?

“Once, I won 2000 dollars with only a 100 dollar chip.”

“I have won 200 dollars a couple times.”

“I have gambled 134 times in the past two years and lost 5600 dollars in total.”

The extreme winning case would be no doubt be the best story to impress, regardless of how incomplete (misleading, even) it is.

We might not be surrounded by heavy gamblers, but you have probably come across some of these “success stories” from friends, relatives, and coworkers here and there. They go like this:

“I made \$1,000 just in September on the market”

“I had a \$4,000 gain in one day, betting on this specific shipping company”

Frankly speaking, these stories are quite dangerous, since they construct extremely biased images of the stock market. The stock market is a great place to compound wealth, but it shows no mercy to irrational speculators with overnight get-rich-quick schemes as agendas. There are two major problems with these success stories: first, the consistency of the return and second, the risk taken.

## Consistency of the Return

Next time, when you hear your cousin say, “I made 3K on two stocks in just two months”, before thinking that it implies he makes \$3,000 every two months consistently (an impressive 18k a year!), ask this question: “What is your annual return since you started to invest?” Expect to see reluctance and hear a not-so-impressive figure.

Indeed, it is not uncommon to be in the negatives, if he is honest. An even better question to ask is: “What is your annual return after the transaction fees?” I’m confident to bet that it will be less than investing in a passive market tracking ETF. Or, one might ask, “What is your annual return relative to the index?” Investors who can do no better than the market index should simply give up and buy the index, rather than spend time attempting to speculate.

Indeed, almost by definition, a great investor is one whose returns are better than that of the entire market overall. The market return is by definition the weighted average return of all of the relevant stocks; so, if some investors made superior returns, it means some investors must have made worse returns, since all investors’ returns have to add up to the market average. With the presence of the transaction fees (\$5-10 per trade, typically, with major brokerages in Canada), active traders’ returns on average will be worse than the market index.

But then, why do we still hear so many success stories? The answer most likely lies within our nature: it is human nature to exaggerate the positive events happening to us, and to omit the negative ones. (Particularly when the exaggerator has a vested interest in their half-truths, such as investment firms advertising for your money).

Sometimes these massive gains you’ve heard of are absolutely genuine and well-deserved. But, more often than not, they can be explained by mere statistics (luck) alone, and when put in a greater context may seem much less impressive.

Consider the following statistical experiment: repeatedly flip one coin three times and another coin ten times, and measure the outcomes.

Statistically, an “extreme outcome” (i.e. all heads or all tails) is far more likely to occur in the first case than in the second (i.e. it is less likely to have ten tails in a row than three tails). In other words, when looking at smaller sample sizes, you are more likely to have extreme results. If “heads” represents better performance than the market average, and “tails” represents worse performance, it implies that if you trade three times a year, you are more likely to see extreme cases (say, all good returns) than placing trades 30 times a year.

Unusually high or low returns can often be explained by low sample sizes, but as investors, the key is consistent returns over time, not extreme outcomes here and there. Only by seeing repeated and continual gains, averaged over a long period so that the variability is “smoothed out”, can one see the true abilities of an investor. Therefore, an “I made 3k just in two months” type of story might not mean as much as you’d think, from a statistical perspective.

## Risk Taken

Some investments inherently have higher risks than others. Such investments are typically either smaller companies, or companies in particular fields, such as new technology, pharmaceuticals, or commodity related businesses. They could be great investments alone or fit well in a portfolio; however, they are often much more volatile than average stocks. As such, it is much more common with these stocks that extreme success or loss stories happen.

People love to share success stories (and hide the embarrassing ones), and thus the audience is inevitably encouraged to take excessive risks, hoping to copy these stories, which often end up with huge disappointments (ask those who invested in technology stocks in 2000). But these disappointment stories don’t get nearly as well disseminated as the success stories. If a friend tells me how much he has lost in a regretful investment, I would admire his or her honesty and humbleness.

Back to investment, it is only meaningful to compare return when the risk levels are comparable. It doesn’t mean much when an aggressive investor received 30% return, while a conservative investor made only 7% of return in the same period of time. Why is that? Because when the market downturn arrives, the same aggressive investor could report a -30% return, while the conservative investor will see only a slight dip in her portfolio. Professional active portfolio managers commonly have their performance measured in metrics called information ratios and Sharpe ratios, not simple return figures.

A famous Chinese saying goes, “don’t expect to have dry shoes when you walk near a river all the time”. In this context, it means one should not be surprised by negative events when taking risks over long time periods.

Volatile stocks can be great investments, but only if the investor is fully aware of the turbulence ahead and financially prepared to absorb any adverse shocks. Playing with fire is not always a bad thing (figuratively speaking), but only if you can afford to lose that shirt to the fire.

Just like many other aspects of life, there is no shortcut in the stock market. Huge potential gain comes with an equal amount of risk. If you were to sample a number of successful investors, they are no doubt characterized by their ability to exercise independent judgment, patience, and self-discipline.

So, the next time you hear about these massive gain stories, you now know the questions to ask before being impressed.