Thursday, July 29, 2021


Card counting and the stock market

Previously, we compared the stock market with a casino to see which investment strategies offered the best odds. We observed that:

  • all active investment strategies outperform sometimes;
  • identifying outperformers ahead of time is almost impossible; and
  • in the long run, selecting any strategy’s index at low cost is a good bet.

As evidence of the first point, low volatility ETFs in Canada outperformed other available strategies over the three- and five-year periods ending Oct. 31, 2017. Yet risk-based strategies generally outperformed most frequently in the Cass School of Business’s 10-million monkey survey, which looked at performance from 1968 to 2011 for 10 million randomly constructed U.S. equity indices.

This month we study how investors, like gamblers, can use odds to their advantage. For instance, in blackjack, which has house odds of less than 1%, professionals often create an edge through card counting.

Counting on the past

By keeping a running count of high and low cards played, the card counter assesses whether remaining cards in the deck have more high-count cards (10s through aces, which advantage the player) or low-count cards (two through six, which favour the dealer). The strategy works because casino rules require the dealer to draw on certain hands, and because odds depend on the decks of cards rather than chance.

When the remaining deck still contains more high cards on balance, the player is favoured not only because the chance of hitting 20 or 21 is higher, but because the chance the dealer will go over 21 is also elevated. In August 2014, Evan Horowitz wrote in the Boston Globe that disciplined card counting could improve a player’s odds by 0.5% or more.

Professional gamblers, like professional investors, diversify their bets. Making many small bets improves the chances of capturing a small edge. How does this apply to stocks? Consider that the S&P/TSX Composite advanced 18 of 27 calendar years between 1990 and 2016; the worst year saw -35.0% performance (2008), while the best year was +30.7% (2009). Making small annual bets (1% of bankroll) would have limited exposure to big declines and maximized exposure to the 66.7% up-market edge. Passive investing benefits from this principle.

Let’s apply the idea to daily returns.

Recall that in card counting, the cards played impact the cards remaining. Historical stock returns tell us little about future returns (the monthly autocorrelation is about 0.04%) but past volatility tells us quite a bit about future volatility (the monthly autocorrelation is 0.6%).

Table 1 shows the annualized return, growth of $1 and risk (standard deviation) of the S&P/TSX Composite Index from May 23, 1992, through Oct. 30, 2017, a period for which Australian data was available for comparison.

Table 1: Canadian performance, 1992 to 2017

Annualized return

Growth of $1

Standard deviation

S&P/TSX Composite Index




Exclude 5 worst and 5 best days




Exclude 100 worst and 100 best days




Exclude 500 worst and 500 best days




Source: TMX Group

Canada is skewed

Removing the worst and best days increases the portfolio’s annualized return. Excluding the worst and best 100 days boosts the return to 11.96%, while eliminating the 500 worst and 500 best days would have provided a 14.98% annualized return—a staggering 5.5% advantage over the index return of 9.48%. Is this an anomaly?

We examined the impact of eliminating worst and best days from Canadian, U.S. and Australian stock indexes from May 31, 1992, to Oct. 30, 2017. Portfolios from all markets are negatively skewed, and all would have benefited from eliminating the worst and best days. Canada and the U.S. would have benefited from eliminating up to about 500 worst and 500 best days, and for Australia, it’s about 442. The Canadian market’s skew (-0.51), however, stands out compared with that of Australia (-0.33) or the U.S. (-0.07).

Gamblers would try to exploit this return distribution by removing highs and lows. For their part, investors try to identify characteristics that will outperform over time like value, small cap and low volatility. But in stock markets, like casinos, winners come only at the expense of losers. Professional gamblers use card counting to determine whether odds favour them; similarly, exploiting a stock market’s negative skew may stack the deck for investors. As we’ve seen, standard deviation falls and returns increase when highs and lows are eliminated. Next month we will explore how much of this advantage we can capture by controlling risk as measured by standard deviation.