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.

Thursday, February 2, 2017

Does passive investing undermine capitalism?

Passively managed products account for one third of U.S. mutual fund assets today—up from 20% four years ago—reflecting a net US$2 trillion shift to passive and away from management.
But questions about this trend’s sustainability, and warnings about its consequences, have arisen. Take, for instance, the note from brokerage firm Sanford C. Bernstein, entitled “The silent road to serfdom: why passive investing is worse than Marxism.” In it, analyst Inigo Fraser-Jenkins argues that active management helps the efficient allocation of capital, an important function in a free market.
For our part, we define passive investing as cap- or market-weighted indexing derived from the total market value of component holdings. All others, including alternative or smart beta, are forms of active management that require periodic rebalancing.
What consequences does the continuing movement toward passive investing suggest, and what does it mean for investors and advisors?

Valuation concerns

Passive investing does not involve analyzing individual companies, so relative and absolute valuations may be distorted, impairing the market’s ability to effectively allocate capital based on enterprise merit.
The less money available for selecting companies with better prospects, the worse off the function of price discovery that underpins the capital markets—and capitalism itself. This is the concern of Bernstein’s note, which references economist Frederich Hayek’s “The Road to Serfdom” and the complaint against “free-riding” indexers.
But consider that the annual turnover rate of active mutual fund holdings in the U.S. is 85%, according to The Motley Fool. That compares to 4.98% for the S&P 500 and 4% for the S&P/TSX Composite. So, even if passive grows to 80% of assets, the turnover from the 20% active slice would be $3 trillion—certainly enough for price discovery. More compelling than that argument is Ayn Rand’s idea of self-interest, a force that would ensure that asset mispricing wouldn’t last for long.

Diversification concerns

The investment industry’s primary risk management tool is diversification. If money flows into (or out of) all the holdings of an index at the same time, all components will move in the same direction, blunting the effectiveness of diversification against volatility.
I’d argue that risk management is most needed to protect against major declines. But when those major declines are happening, correlations tend towards 1.0, rendering diversification less effective. Advisors need better risk management tools generally, and those tools could compensate for the anti-diversification effects of passive investing en masse.


Most active managers underperform their passive benchmarks through most periods—as shown by the S&P Dow Jones SPIVA scorecard—contributing to the popularity of passive investing. But no trend goes on forever. Consider personal leverage in 1929, corporate leverage in 1987, oil stocks in the 1980s and technology stocks 2000-2001. Surely active management will have its day?
The reality is that active performance before costs equals passive performance, and this would be the case regardless of the proportion of active and passive management employed.
Passive investors would not trade and active investors would trade only with each other. Active managers in aggregate represent a cap-weighted market index.


Passive investing can create distortions in three circumstances. First, net cash flows into a passive portfolio create a cash position, leading to a performance difference from the index until the cash is invested. Second, when passive funds are forced to buy or sell, the lack of liquidity of some smaller index components may temporarily push prices higher or lower than would otherwise be the case.

Third, when the index’s composition changes, there is a period of adjustment as passive portfolios sell the removed companies and buy replacements. The cost of these changes was estimated to be 0.2% per annum in the U.S., according to Winton Capital.
After eight additions were made to the S&P TSX Composite on September 16, 2016, they were up an average of 4.2% in their first week while the index advanced only 0.4%. So, pricing distortions can follow changes to an index.
Investors need to be aware of the distortions caused by passive strategies. They allocate capital by market capitalization but can also impact individual holdings.

In a passive world, winners are investors

Motivated market players will always find market mispricing and arbitrage it away. Valuation distortions should lead to more opportunities for active managers, but the difference between the most over- and undervalued assets is an important factor in determining this. Since less-skilled investors may move to passive investing, leaving more skilled active managers to undertake price discovery, these spreads may narrow. Better long/short strategies will also close this gap.
Corporate governance may also improve as large, passive shareholders like Vanguard use their influence across all their holdings, including the smallest ones that may have escaped previous institutional scrutiny. Investors are the winners. The biggest future losers from more passive encroachment will continue to be active managers, unless they find a way to beat their passive benchmarks with more consistency or develop a value proposition using passive issue selection within active allocation strategies.
Mark Yamada is President of PÜR Investing Inc., a registered portfolio manager and software development firm. Disclosure: PÜR Investing Inc. sub-advises for, and provides risk-based model portfolios to, Horizons ETFs.

Thursday, July 5, 2012

The puck stops here: Use ETFs as a portfolio’s last line of defence

This is the third article in a series.

Portfolio managers can learn from hockey. Previously, we’ve discussed balanced and aggressive attacks for neutral and positive markets, and the neutral-zone trap as to defense defend against a potentially hostile markets. This month, we address the “chip and chase” and the last line of defence, goaltending.

Low-volatility chip and chase

Playing the puck deep into the opponent’s end and quickly pursuing it involves risk. Giving up control may award your opponent with possession. Some risk is mitigated by the fact that it happens positioning so deep in the opponents’ end. A low-volatility market is perfect for taking such risks. But you need good speed and solid fore-checking.

Gordie Howe and Bobby Hull rarely employed this approach; Jagr, Malkin, and Crosby use it infrequently. However, the Canuck’s line of Alex Burrows and the Sedin brothers [DASH] who don’t mind banging bodies in the corners [DASH] are extremely effective in frustrating and wearing down opponents with their “cycle”-type offence.

The “cycle” approach is like identifying uncorrelated asset classes [DASH] some will do well, while others won’t. Equities, commodities and bonds are three good examples (see, “Equities, commodities, bonds,” this page). Someone should always be open for a shot or a pass.

Yet asset correlations aren’t static. The relationship between stocks, bonds and commodities will change over time and must be watched carefully, particularly when volatility is high or rising. Other aspects of the chip and chase are similar to the 2-1-2 structure described in the first article of this series (see, “ETF tips from the rink,”

Last line of defence

Recent market volatility has shown that cash or short-term fixed-income instruments are occasionally the only safe havens. Diversification simply fails to control risk during periods of high volatility. In a low-interest-rate environment, this is an even more painful realization. If investing time horizons are long [DASH] 10 years or more [DASH] trying to rebalance to a fixed mix may pay off. For some individual investors, however, there is no guarantee asset-class returns will approach the long-term averages that underpin their financial plans in time to skate them back on side. Sometimes, we must rely on that last line of defence [DASH] goaltending.

Goaltending has evolved, as have the choices in short-term fixed-income offerings. Today, most goalies use the “butterfly” technique. They spend lots of time on their knees with legs splayed outwards to maximize ice-level net coverage. Glove, blocker and stick skills deflect everything else, making superior mobility and quickness important. Glenn Hall and Tony Esposito were early proponents. One risk is the so-called “five hole” between the legs. Like credit or liquidity risk for a bond fund, this is not normally a concern, but occasionally causes gnashing of a coach’s teeth.

So how should we deal with money-market funds in low-interest-rate environments? Forget about them. iShares Premium Money Market ETF (CMR) has an MER of 0.27%, compared to major banks’ money-market mutual-fund MERs of about 0.55%, a bargain if your client has $25,000 or more to park.

However, it is difficult to justify with annual returns of around 1.0%. Like a vulnerable goaltender on the blocker side (the Leafs’ Jonas Gustavsson) or on the glove side (James Reimer or Ben Scrivens), low net-of-fee returns from money-market funds suggest looking elsewhere for protection and yield income.

Marty Brodeur, Tim Thomas and Dominik Hasek have successfully used hybrid goaltending styles. Likewise, other ETF vehicles can be used effectively as money market substitutes but with more risk. Short-term fixed-income ETFs are the obvious first choice, but short-term laddered-fixed-income government and corporate ETFs, and short-target-maturity ETFs, give advisors even more flexibility (see “ETF vehicles,” this page).

In low-volatility environments, diversification helps most. Consider equities, commodities and bonds. When volatility increases, stronger defence may be needed. Short-term fixed-income choices, other than money-market, are available to enhance yield; but watch out as costs become more important considerations. AER

Table 1

HED: Equities, commodities, bonds

Broad-based equities
Broad-based commodities
Broad-based Canadian bonds
iShares MSCI World (XWD)
iShares Broad Commodity (CBR)
Vanguard Canadian Aggregate Bond ( VAB)
Vanguard MSCI US Broad Market (VUS)

iShares DEX Universe (XBB)
iShares S&P/TSX Capped Comp. (XIC)

BMO Aggregate Bond (ZAG)

Table 2
HED: ETF vehicles

Short-term fixed income
Mgt. Expenses
Vanguard Canadian Short-Term Bond
BMO Short term Federal Bond
iShares DEX Short-Term Bond
iShares DEX Short-Term Corporate
BMO Short Provincial Bond
BMO Short Corporate Bond

Short-term laddered
Mgt. Expenses
iShares 1-to-5 yr Laddered Government
Powershares 1-to-5 yr Laddered Investment Grade Corporate 
iShares 1-to-5 yr Laddered Corporate

Short-term target maturity
Mgt. Expenses
BMO 2013 Corporate Bond Target Maturity
RBC 2013 Target Corporate Bond
RBC 2014 Target Corporate Bond

The neutral-zone trap: Positioning  ETFs to counteract volatile markets 
This is the second in a series. Next month: the chip and chase for rotational markets and goaltending styles for the last line of defense. 

In the previous issue, we discussed the need for a balanced and aggressive attack during neutral and positive markets. This month, we examine the neutral-zone trap for protecting against a potentially hostile market.
Setting the trap
When the opposition controls the puck in its own end, the neutral-zone trap can be used to counteract the rush before it develops into a major threat. In recent years, capital markets have appeared unpredictable for extended periods. They seem to react to one crisis after another, while dominating investors by keeping them off balance. Current events, rather than longer-term disciplines, seem to be most important.
Both Jacques Lemaire (Devils and Wild) and Guy Carbonneau (Canadiens) have leveraged the trap effectively to thwart attacks. Randy Carlyle, too, used it to coach Anaheim to the 2007 Stanley Cup (Leaf fans can dream on!). It was so effective that the NHL moved to strictly enforce obstruction rules, while allowing the two-line pass to make the trap less useful (see “Two-line passes,” this page).
Meant to disrupt momentum, players space themselves in the neutral zone in a 1-2-2 formation with one fore-checker looking to take advantage of a turnover. In a portfolio, this checker can be an aggressive equity fund like a small-cap or an emerging-markets fund that will respond quickly if the market trend suddenly turns positive (see “Fore-checker: aggressive small cap and emerging markets,” this page).
Two forwards block any attack lanes along the boards forcing the play toward the centre. These players must be ready to strike if they create a turnover. Broadly-based equity positions would serve this two-way function well, perhaps one domestic like XIC or VCE and one global/international like XWD, VEF or ZIN. (See “Forward: Canadian Equity,” and “Forward: global/international equity,” this page).
The two players on defence delay attackers while their forwards reposition to defend if no turnover can be forced. In a portfolio, these positions will depend on the risk tolerance of the investor. In a low-interest-rate environment, some return potential is important, but defence is the primary objective. High-yield or convertible bonds are risky, but offer better upside. Pairing with a defensive offset, like a short term/duration or laddered ETF, would provide the right mix of defence with offensive potential.  (See “Defence: high yield and convertible bonds,” and “Defence: short-term or laddered bonds,” this page).
Mounting a defence in the face of a powerful market onslaught can be a challenge. When volatility picks up, there are few tactics [DASH] other than cash or high-quality short-term bonds [DASH] that can preserve capital. Whether or not you have a sense about the kind of market threats ahead, ETFs can be useful players in positioning you correctly to defend and attack. AER

Thanks again to Dr. Jim Sugiyama, hockey savant, for his input.   

NOTE TO ART: This will likely be two pages

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HED: Two-line passes

HED: Fore-checker: aggressive small cap and emerging market funds

Exchange traded fund
Mgt. Expenses
iShares Russell 2000 Index Fund (CAD hedged)
Vanguard MSCI Emerging Markets Index
iShares S&P/TSX SmallCap Index Fund
BMO Emerging Markets Equity Index
Claymore BRIC ETF
Claymore Broad Emerging Markets ETF
iShares MSCI Emerging Markets

HED: Forward: Canadian Equity (broad lowest cost)
Exchange traded fund
Mgt. Expenses
Horizons BetaPro S&P/TSX60 Index (swap)
Vanguard MSCI Canada Index
BMO Dow Jones Titans 60 Index
iShares S&P/TSX 60 Index
iShares S&P/TSX Capped Composite Index

HED: Forward: Global/International equity
Exchange traded fund
Mgt. Expenses
Vanguard MSCI EAFE Index (CAD hedged)
iShares MSCI World Index
BMO International Equity Hedged to CAD Index

HED: Defence: High yield and convertible bonds
Exchange traded fund
Mgt. Expenses
Claymore Advantaged Convertible Bond
iShares DEX HYBrid Bond Index
Claymore Advantaged High Yield Bond
iShares U.S. High Yield Index
XTF Canadian Convertible Liquid Universe
Powershares Fundamental High Yield Corporate Bond
BMO High Yield Corporate bond

HED: Defence: Short term or laddered bonds
Exchange traded fund
Mgt. Expenses
Claymore 1-5 year Laddered Government Bond
BMO Short Federal Bond Index
iShares DEX Short Term Corporate Universe + Maple
Powershares 1-5 year laddered Inv. Grade Corp. Bond
iShares DEX Short Term Bond Index
Claymore 1-5 Year Laddered Corporate Bond
BMO 2013 Corporate Bond Target Maturity
RBC Target 2013 Corporate Bond
BMO Short Term Bond