Card counting and the stock market
- 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 |
9.48% |
$9.88 |
15.7 |
Exclude
5 worst and 5 best days |
9.75% |
$10.51 |
14.9 |
Exclude
100 worst and 100 best days |
11.96% |
$17.43 |
11.9 |
Exclude
500 worst and 500 best days |
14.98% |
$34.22 |
7.8 |
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.