# Active Management Exposed

I read a few articles recently that promoted the view that active management is superior to passive management. “Why settle on mediocrity?” suggested the article. Another article suggested that markets aren’t completely efficient and can be exploited by active managers and this led to their conclusion that active management is superior.

Both the mediocrity claim and the efficient market claim can be true and still passive management can be superior to active management.

An index fund will never be the top performer in any given year. This is as true as the average mark on a test can never be the highest mark if there is any variability around the average. The fact that index investing can never be the best over a given year led the author to label passive / index investing as mediocre. But as years pass the passive strategy outperforms more and more active strategies. The S&P 500 index outperformed 57% of large-cap US funds for the 12-month period ending June 30, 2017. Ok, somewhat mediocre. This changes as the time horizon expands. For the 15-year period ending June 30, 2017, the S&P 500 outperformed 93% of large-cap US funds. An A+ is anything but mediocre.

Efficient markets are not necessary for passive management to be a top performer over the long-term. Simply understand that investing is a positive sum game. We get better at what we do over time and generations. But, although investing is positive sum game, it is a zero-sum game around the market return. Any outperformance above the market return necessitates underperformance below the market return. This is pre-cost. Cost makes it worse. This is regardless of whether markets are efficient or not.

Back to the poker analogy to explain the positive sum game but zero-sum game around the market return.

10 folks sit down with $10,000 each and play poker for one year. Everyone understands that there will be winners and losers and any amount won is offset by losses. There is $100,000 on the table always. This is a zero-sum game.

After year 1 they get tired of dealing and hire a dealer who charges 2% per year. At the end of year there will be $98,000 at the table and $2,000 in the dealer’s pocket. This is a negative sum game. All could have less than their original $10,000. But, it is a zero-sum game after the dealer’s charge of 2%. All could hold $9,800 each at the end of the year. There will be winners and losers around $9,800 but money won and lost offset.

After 10 years of playing there will be $18,293 in the dealer’s pocket and $81,707 available for the players. At the end of year 10 each player could hold $8,171. Any player holding more than $8,171 necessitates at least one player holding less than $8,171. This is a negative sum game but a zero-sum game around the “annual return” of negative 2% per year. To hold more than the original $10,000 at the end of year 10 requires exemplary skill and/or great luck. Cost matters greatly over the long-term.

Now we introduce a magical poker game. It is magical because at the end of each year poker chips magically replenish by 7%. At the end of the year every player’s chip stack grows by 7% and then diminishes by the dealers 2% charge. At the end of year 1 there is $105,000 worth of chips on the table and $2,000 in the dealer’s pocket. There is $110,250 on the table at the end of year 2 and so on. This is a positive sum game. All could hold more than their original $10,000. But, it is a zero-sum game around magical replenishment rate of 7% less the dealer charge of 2%. All could grow their poker chips by 5% per year. It is a zero-sum game around the after-cost replenishment rate and if some grow their poker chips by more than 5%, others will offset this with slower or negative growth.

Let’s pretend these folks play for a long time. At the end of 10 years there is 162,889 on the table and $25,156 in the dealer’s pocket. After 20 years there is $265,330 on the table and $66,132 in the dealer’s pocket. After 40 years there is $703,999 on the table and $241,600 in the dealer’s pocket.

If they played without a dealer there would be $1,497,446. on the table in 40 years. Chips grew to $703,999 with a 5% after-cost growth rate but would’ve grown to $1,497,446 at a 7% growth rate. That is a big difference. Let’s analyse this. The difference is $793,447. The dealer cost explains $241,600. The balance is explained by the extracted dealer cost is not growing at 7% per year. Poker chips magically growing at 7% are growing 40% faster than chips magically growing at 5%. A 2% fee sounds small but is extracted from the already small 7% growth rate. Cost matters!

Let’s get back to the game. Five out of the 10 participants have figured things out quite well. They understand that the magical replenishment rate is special. They don’t want to gamble. They talk to the dealer and ask to be dealt out. The dealer says to sit at the table and not gamble costs .15%. After all, the dealer is doing no work for them. The remaining five sit and gamble and continue to be charged the 2% fee. The five non-gamblers chips grow annually at 7% - .15% = 6.85%. The five gamblers compete for chips growing at 7% - 2% = 5%. The five gamblers are participating in a zero-sum game around the 5% after-cost replenishment rate. The five non-gamblers are receiving a certain 6.85% growth of chips as a group and individually.

After 1 year each non-gambler each holds $10,685. The gamblers are competing for $52,500 (5 x $10,000 x1.05). All five could’ve grown their chips to $10,500. If one or more grow their chips to more than $10,500, at least one holds less than $10,500.

After year 10 of the special game, each non-gambler holds $19,672. The gamblers are competing for a pool of $85,517. All gamblers could grow their chips to $17,103. Any gamblers above necessitate at least one gambler below.

After year 40, each non-gambler holds $141,573. This is their original investment of $10,000 growing at 6.85% per year for 40 years. The gamblers are competing for a pool of $351,999. This is the original pool of the 5 gamblers of $50,000 growing at 5% per year for 40 years. All five could grow their chips to $70,400. If one or more of the 5 grow their chips to a greater amount, it is certain that at least one holds less than $70,400. Or, in other words, they are competing in a positive-sum game but a zero-sum game around the after-cost growth rate of 5%. All 5 gamblers could’ve grown their chips by 5% per year. But if one or more grow their chips by more than 5% per year, at least one grows their chips by less than 5% per year. A gambler who is extremely lucky and/or skillful may outperform the non-gambler, but it is a heavy task. They must more than double the zero-sum game level of chips.

The results from the 40-year period illustrate the long-term consequence of cost. Each year 2% of the chips are extracted from the gamblers pool. In year 1 the 5 gamblers had $1,000 extracted. That is $1,000 not growing at 5% per year for 40 years. By year 40, they are short the $1,000 plus the $6,074 of lost growth. The non-gamblers had $75 extracted from the combined pool in year 1. $75 growing at 6.85% per year for 40 years results in $987 of lost growth at year 40. This explains the lost growth from year 1 dealer cost only. The longer the time horizon the greater the effect of lost growth. Lost growth from dealer cost in year 39 is negligible. Cost matters!

**Would you rather be the gambler or the non-gambler?** I think it is obvious that arithmetic is on the side of the non-gambler.

How does this relate to investing?

The players represent all participants investing in financial markets. The $10,000 represents their initial investment. The dealer cost represents cost when investing through a financial advisor or planner. The cost to sit at the table and not gamble represents the cost of a do-it-yourself financial advisor utilizing passively managed, low-cost, broad-market ETFs. The magical replenishment rate represents the long-term average annual return (7% is a low-ball). The non-gamblers represent passive market participants. The gamblers represent active market participants or those investing through a financial advisor.

So why is the vast majority of savings managed actively? Because those who work in the industry need and deserve to be paid. They are doing work. However, it is difficult to justify the work they are doing. And, the magical replenishment rate, or the market return rate, solves problems. Many pick up their financial statement and are pleased to see their savings grow even though they likely underperformed the market return by at least their cost factor. Even with a high cost factor, they likely outperformed the pure safety of a GIC. There is no entry on the financial statement that indicates what savings would be worth with no or a low cost factor. The market return allows high cost active management to continue without much questioning.

All active managers want your business and explain how they will outperform. Unfortunately, it is impossible for all to outperform. The market delivers finite gains over the long-term. The finite gains are shared unequally between all participants and more join the list of the underperformers as time passes.

The long-term reward to BYOFA is substantial.

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