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Is active investing a zero sum game?

Dividing a cake is a zero sum game.

I have previously explained that investing in equities does not need to be a zero sum game.

Now that doesn’t mean you’re guaranteed a positive return in any one year of investing – or even over many years.

Stock markets go up and down a lot in the short-term.

But even the long term – while a much more appropriate time frame to talk about when it comes to the expected returns from shares – is unknown.

Perhaps we’ll go into some terrible 20-year economic depression, who knows? Or maybe shares will simply turn out to have been too highly rated and they’ll fall for a long time as they readjust to reality, similar to what happened in Japan.

The important point for today’s article is to understand there’s nothing inherent in investing in equities that means that for you to earn the market return, another investor must lose by the same amount.

If you’re not sure why – or if you don’t understand what ‘the market’ is, or the investing terms alpha and beta – then please read the previous article so we’re all on the same page.

Market makers

Investing in a broad stock market to achieve the same return as the index (minus costs) is not a zero sum game.

However once you try to do better than the market, it’s a different kettle of fish.

Specifically, active investing is a zero sum game.

The reason is obvious once you get it, but from experience it can take some time to do so.

First off, we talk about ‘the market’. Key to understanding why active management must be a zero sum game is understanding what the market is.

When we talk about the market, we may mean different things.

We might mean the sum total of all shares listed in all stock markets around the world.

We might even include other kinds of assets, like bonds and commodities.

More commonly we might mean a specific market – such as the UK stock market – or a further subset of that market – such as the FTSE 100 index of the top 100 largest public companies in the UK.

Let’s focus on that FTSE 100 index for a moment.

Who owns this market?

Well, pension funds, hedge funds, mutual funds, and also individuals who buy and sell stocks.

How do they own the market?

They take a stake in three different ways1:

  • Firstly, they may be passive investors who buy index funds. These funds basically own a little bit of every company in the index, in proportion to its size in the index2. If a company’s share prices rises or falls, so does the value of the fund’s holding. If companies exit or enter the index they track then they take action, but otherwise they just aim to track the market to get the market return.
  • Alternatively, the investors may have invested via actively managed funds. These are funds that own more than the index weighting of some shares and fewer of other shares. For example, the manager of a fund may believe that Tesco has better prospects than other investors seem to think, while also being less convinced about BP. In response, they buy more of Tesco than the market weighting of that company, and they own fewer or even no shares of BP.
  • Finally, the investors may directly own the shares themselves. Again, if they do so they are unlikely to own exactly the same holdings as a FTSE 100 index fund (because it would be a lot more costly and fiddly, compared to just investing via a tracker). Most likely they own a portfolio of 15-30 or so individual shares, some of which are in the FTSE 100. These investors are effectively their own active managers.

The first kind of investor is only aiming to get the market return – the beta – which is why they have invested via index funds. By definition, they track the market, and hold shares in proportion to the market’s ownership.

If some shares go up and others go down, then so will their holdings. They can do no better, but also no worse. They will get the market return (less holding costs and any tracking error).3

That leaves the non-passive investors, who may be invested in active funds or actually running the active funds, stock picking their own portfolio of shares, or maybe owning a mix of passive and active funds.

For simplicity I’ll label them all as active investors from here, as it doesn’t matter exactly how they’re actively investing for this discussion.

Note: Sometimes people will say they are not trying to beat the market when non-index investing, but rather they are trying to be defensive, or ethical, or focused on income, or one of a gazillion other variations. That’s all fair enough – whatever floats your boat – but it amounts to the same thing from the market-beating zero sum game perspective.

Actively different

So what does it mean to be an active investor?

It means your shareholdings in a particular market are different to the market’s weightings.

But the ownership of that market is comprised entirely of…

Passive investors + active investors

…so if you want to take a different position to the market, then by definition you are going to have to do so by trading with other active investors – since passive investors just hold the market, and they ain’t giving you diddly squat if it distorts their market weightings.

An example might help.

Let’s say you own the market via a tracker fund, but also you’re keener on Tesco and so you want to own more than a market-weighting of its shares.

You therefore buy shares off an otherwise identical investor who is less keen on Tesco’s prospects than you are.

You take ownership of some Tesco shares off this investor, who now owns fewer Tesco shares. In place of the Tesco shares, let’s say they increase their holding of the market.

Now let’s imagine that was the only trading any active investors did in the FTSE 100 this year. (I think that’s what they call a quiet year!)

Recap:

You own the market plus your extra Tesco shares.

The active investor you bought them off also owns the market, except she owns fewer Tesco shares.

In our hypothetical example all other investors in the world are passive investors.

So what happens next?

Well, the market delivers the market return.

So far so obvious.

However Tesco shares either return more than the market’s return, the same as the market, or less than the market.

  • All passive investors earn the market return.
  • You and the other active investor get the market return, modified by your position in Tesco.
  • If Tesco shares beat the market return then you will do better than the person who sold you the Tesco shares – and they will do worse than you.
  • If Tesco returns the same as the market, then everyone earns the same return.
  • If Tesco returns less than the market, then you’ll do worse then the person who sold you the the Tesco shares – and they will do better than you.
  • Except in the unlikely event of Tesco delivering exactly the same return as the market, one of you must do better, and the other lose by the same amount.

That is why active investing is a zero sum game.

Note this has nothing to do with the discussion of whether some active investors can or will beat the market over the long-term.

In fact, it shows it’s trivial to create a market-beating fund over any one year – just hold the index plus shares in one company in one fund, and the index and a short position (i.e. bet against) the same company in the second fund.

One of the two funds is guaranteed to beat the market that year, before costs4. But sadly, the other is guaranteed to do worse.

Indeed, in aggregate – netting winners off against losers – active investors as a group earn the market return, just like passive investors.

They must do, since together they own the market.

What really does for investing in active funds overall is high costs.

Why active investing is worse than a zero sum game

Imagine the two fund managers who took different positions in my Tesco example charged 1% for their services.

Let’s also suppose that all that furious Tesco share trading cost them 0.5% in expenses. (Heck, it’s an expensive business in this hypothetical world of low volume trading…)

This means the total cost of their active investing is 1.5%.

In contrast, an investor in the passive fund might pay say 0.25% in annual charges.

Before taking into account these costs:

  • The passive investor earns the market return (beta)
  • The winning manager earns the market return plus their Tesco gains (beta+alpha)
  • The losing manager earns the market return, minus their Tesco loss (beta-alpha)

After costs:

  • The passive investor earns: beta minus 0.25%
  • Investors in the winning active fund earn: (beta+alpha) minus 1.5%
  • Investors in the loser earn: (beta-alpha) minus 1.5%

Schoolboy algebra tells us that combined, the active funds earn…

  • Beta minus 1.5%

… since the +alpha and -alpha cancel out.

Therefore in aggregate the passive investors beat the aggregate active investors, because of the latter’s much higher charges.

So in practice, active management is worse than a zero sum game.

The zero sum game writ large

While the example I gave above is obviously as simple as it can be, exactly the same principles hold true on the grand scale of real-world markets.

The fact is it must hold – ‘alpha’ cannot be magicked out of thin air.

The only place an active manager can go to get more or fewer shares than are held by the market is by dealing with other active investors in that market. (Because the passive investors by definition hold the market).

And then you have to subtract those higher costs.

This is summarized by Vanguard in this handy graphic:

Click the link to Vanguard in the paragraph above for full-sized image.

Click the link to Vanguard in the paragraph above for a full-sized image and PDF.

In this graph, the green vertical line above the ‘0’ on the x-axis is the return from the market.

You can see that there’s a bell curve of returns on either side of this market return.

This indicates how all the money that beats the market is offset by money that loses to the market.

Finally, there are costs, which are indicated by the gap left to the dotted line.

This has the affect of moving the bell curve of returns to the left – lowering average returns – as indicated by the curve in red.

Note that particular active funds do not necessarily deliver negative returns just because it’s a zero sum game. As a group they get the return from the market on average, before adding or subtracting alpha and costs. (They must get the market return as a group, because summed up active funds are the market, alongside passive investors).

So even though beating the market is a zero sum game, it’s not like poker, where a winner-takes-all.

The ‘beta’ delivered by the market goes to active managers as well as passive investors.

It is the ‘alpha-chasing’ part of their business that is a zero sum game.

And as shown above, it is a costly game since their higher costs mean that in aggregate, investors in active funds see lower returns than passive investors.

Is there always a winner for every loser?

Like other writers, I have often written that “for every winner there must be a loser” when it comes to active fund management’s attempts at beating the market.

This is convenient shorthand, but it is not strictly accurate.

It’s not that one active investing individual or active manager must lose for every one that wins.

It’s that the total amount of winning money (the total excess return over the market, the alpha) must be offset by the same amount of losing money.

The Vanguard article cited above puts it as follows:

The concept of a zero-sum game starts with the understanding that at any one time, the holdings of all investors in a particular market make up that market.

As a result, for every invested pound that outperforms the total market over a given period, there must by definition be another pound that underperforms.

Another way of stating this is that the asset-weighted performance of all investors, both positive and negative, will equal the overall performance of the market.

Incidentally, this is a big reason reason why many active investors poo-poo the idea of index investing.

“I’ve done fine with my funds,” they say. “I have made £12,343”.

They have no idea what the market return would have been if they’d just invested passively. And even if they did beat the market then they do not really understand that they risked losing to the market in order to do better.

I’m not saying don’t actively invest if you know what and why you’re doing it, and you also appreciate the nailed-on headwind from higher costs and the other potential downsides.

It’s a free world. Heck, I’m a stock picker myself.

But time and time again people who have a dangerously small amount of knowledge about investing – that masquerades as a deep understanding – will tell you:

“Why bother with index funds when the Something Or Other Fund did 22% last year and the market only did 12%.”

The statement might be factually correct, but there’s typically an iceberg of ignorance and misconception beneath it.

We’ve written over one million words on Monevator trying to address these misunderstandings.

We’ll keep at it!

But if for some reason you want a second opinion, you might try reading Noble prize winners French and Fama’s thoughts on the zero sum game:

Suppose we define a passive investor as anyone whose portfolio of U.S. equities is the cap-weight market portfolio.

Likewise, define an active investor as anyone whose portfolio of U.S. equities is the not the cap-weight market portfolio.

It is nevertheless true that the aggregate portfolio of active investors (with each investor’s portfolio weighted by that investor’s share of the total value of the U.S. equities held by active investors) has to be the market portfolio.

Since the aggregate portfolio of all investors (active plus passive) is the market portfolio and the aggregate for all passive investors is the market portfolio,the aggregate for all active investors must be the market portfolio.

All this is obvious. It is just the arithmetic of the fact that all U.S. equities are always held by investors.

(That is why we call it equilibrium accounting.)

In short, total actively invested money cannot beat the market because it is the market, together with neutral passive funds.

Remember that the next time someone says “Stock picking has the edge in a bear market” or similar nonsense.

It’s mathematically impossible.

Some stock pickers might have the edge. If they do better, then an equivalent amount of actively invested money will do worse.

To repeat myself, this doesn’t mean Warren Buffett isn’t Warren Buffett.

Some tiny number of managers might have skill (I personally think some do) or luck, and they deliver years and years of market-beating returns.

If you have a way of finding these needles in a haystack, good luck to you.

But be sure you understand that their excess returns – their alpha – must come at the expense of the poor schmucks in active funds that are doing worse.

What if I invest actively for some other reason?

Most private investors who invest in active funds do so out of ignorance, and the rest because they want to beat the market.

However there are other reasons for investing in active funds.

For instance, you may value lower volatility in your portfolio, and for some reason you don’t want to achieve that by holding more bonds.

Or you may be trying to invest more ethically, and so you don’t want to exactly mirror the market for that reason.

These are personal choices, and if they have value to you then you can argue you’re not participating in a zero sum game.

Remember in part one I said that a zero sum game was one where everyone valued their ‘slice of cake’ equally?

Well, in this case you’re valuing certain shares for more than their market beating return potential. So arguably, you have stepped out of the mathematics of the zero sum game.

True, I think this discussion is investing’s equivalent of existential philosophy! But I mention it for completeness.

It is specifically active investing to beat the market that is a zero sum game.

Wait, I invest for dividends – who am I hurting?

I’ll also just mention this briefly, as it’s a very frequent retort from British stock pickers with their affinity for buying and holding shares for dividend income.

They’ll typically say something like:

“Sure, but I don’t get involved in all that share trading shenanigans. I’m not a gambler, I just buy and hold shares and pick up the income.

Who is losing out here when I’m not even trading?”

There are two parts to understanding why you’re still playing in a zero sum game (leaving aside the caveat just mentioned above).

Firstly, while we talk about ‘the market return’ mostly in terms of indices and share prices, we should really think of it as capital gains or losses plus dividends.

That is, we should think about the total return from the market.

If you own a bunch of high-yield shares instead of (or in addition to) the market, then by definition you own a different weighting of shares to the market.

For you to have this different weighting, some active investors somewhere else (or as discussed above, ‘some money’) must have an underweight position in the same shares.

It doesn’t matter whether you trade the shares after you take this position:

  • You get the capital gains or losses plus the dividend income every year.
  • The market gets its share of the same.
  • The ‘person’ who is underweight your shares gets less of both from those shares.

It’s still a zero sum game in terms of beating the market, although by not trading you do reduce the cost of playing it.

Again, this is not to say you should or shouldn’t invest in a portfolio of dividend paying shares.

Each to their own, and I’m rather a fan of income investing myself.

You may beat the market return over the long-term. You may do worse.

But from that perspective it’s still a zero sum game.

Similarly, people say “who cares what the market does, I am just concerned about my own finances.”

Agreed, a very healthy attitude to have towards income investing. But it doesn’t have anything to do with whether active investing is a zero sum game.

I don’t care less about the physics of fluid dynamics when I take a shower, but that doesn’t mean the laws of physics don’t apply when I lather up.

If you’re buying different shares to the index for their dividend income5, then you’re taking a position versus the market, and you’re playing in the zero sum game.

That’s not bad or good – if you know what you’re doing. It’s a calculated risk.

But as Warren Buffett has said:

“If you’ve been playing poker for half an hour and you still don’t know who the patsy is, you’re the patsy.”

Don’t be an ignorant patsy.

  1. I’m ignoring shorting here, although it’s really just a special category of temporary ownership via active investing. []
  2. So called synthetic ETFs may track an index without owning the shares, but they can be set aside for the purposes of this article. []
  3. Someone pedantic may point out in the comments that tracker funds may move prices when they are forced to buy or sell shares when they enter or leave the market. This is true, but the impact is irrelevant in the context of this discussion. []
  4. One will do so just so long as the company returns more or less than the market, as opposed to exactly the same return []
  5. Remember that you could sell some shares after they rise to generate an income instead. []

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{ 43 comments… add one }
  • 1 weenie January 22, 2015, 12:30 pm

    Gosh, probably one of the bests posts I’ve read on this website – thanks very much!

    Previously, I just couldn’t get my head around the zero sum thing – to be honest, I wasn’t even really sure what beta and alpha were, but your examples explained it all quite clearly.

    Thanks again!

  • 2 Steve January 22, 2015, 2:20 pm

    Is there room to make money out of thin air during an IPO, when you are not buying from existing active investors? TBH, my knowledge here is very thin – do companies enter tracked indexes directly following an IPO and do passive index trackers buy IPO shares?

  • 3 Cowboy January 22, 2015, 2:30 pm

    For the FTSE IPO companies usually enter at the next index quarterly review.

    Note here
    http://www.ftse.com/products/index-notices/home/getnotice/?id=338087
    there are clearly exceptions for very large offerings, but 100 and 350 trackers would usually be waiting for the update before buying

    Love the explanation btw, I know a lot more about alpha and beta now than I did and am happy I am 90% in trackers 🙂

  • 4 Mikkamakkamoo January 22, 2015, 2:51 pm

    Good article – gave my noggin a bit of a workout!

    All of the above being true, and also accepting that most people (even some active investors included) agree it is nigh on impossible to pick the next ‘star’ manager(s), one argument I sometimes hear from proponents of active investing goes something like this:

    “Whilst I agree it is almost impossible to pick the next star manager, what is possible is to NOT pick the consistently poor managers (i.e. say, bottom quartile over multiple time periods). If you can do that then you’ve made it more likely you’ll pick a consistently good performer as you’ve gotten rid of all the cr*p!.”

    I’ve always discounted this as typical active investor overconfidence, but I’m wondering now if this is just be being blinkered by my, bordering on religious, faith in the passive argument, but is there some merit to this argument?

  • 5 Fremantle January 22, 2015, 3:10 pm

    Avoiding dud active managers is easier due to survival bias. The active management market is awash with “lucky” managers, “unlucky” managers don’t last very long.

  • 6 Cowboy January 22, 2015, 3:15 pm

    Except you have to be able to avoid them before they go dud, and the finance industry recycles people worse than the public service

  • 7 ARGIE January 22, 2015, 4:21 pm

    A very clear and readable article, but isn’t it a bit more complicated than that?
    The message comes across that passive investors make the market return (less costs) and only active investors gain or lose compared with the market, each at the others’ expense.
    But whether you are a passive or active investor depends on how you have defined ‘the market’. Someone who only invests and holds a FTSE 100 tracker would be a passive investor, but only in relation to the the FTSE 100 market. With regard to the FTSE All Share market he would be an active investor. So, if the FTSE 100 bettered the market as a whole, the FTSE 100 investor would gain at the expense of the ‘passive’ FTSE All Share investor.
    Indeed the question has to be asked, is it possible to be a passive investor in the FTSE All Share market? Let’s assume that there are only two types of investor – those who only want to invest in FTSE 100 trackers and those who only want to invest in FTSE All Share trackers. Imagine that the FTSE 100 investors take, say, 20% of all the FTSE 100 available shares. Then the FTSE All Share investors cannot buy the correct market weighting of FTSE 100 companies shares (because 20% of them have been bought up by the FTSE 100 investors) and therefore end up being reluctant ‘active’ investors in relation to the All Share market, who will lose out to, or gain from, the FTSE 100 investors depending on whether the FTSE 100 does better or worse than the All Share market.
    Needless to say it becomes even more complicated when looking at the world as a whole! Potential Global Equity tracker investors can’t be true passive investors because there will be insufficient UK stocks available to build a properly weighted share holding as a result of all those pesky UK investors who only want to hold UK shares!

  • 8 The Investor January 22, 2015, 7:01 pm

    @weenie — Thanks!

    @steve — Before the company enters the index — pre-IPO — it’s not in the index. It is in a different ‘market’. See my reply to Argie below. Companies of course do eventually enter an index (and there are potential inefficiencies that hedge funds and others try to exploit around such movements) but (a) it’s an esoteric subset and (b) I think the “market” in this case would be defined as “index+IPOs that are going to be part of market”. I’m just writing off the cuff though, it’s doubtless a bit more nuanced. 🙂

    @Cowboy — Cheers!

    @Mikkamakkamoo — Thanks! In terms of your question, remember this article is not about *how* to invest or whether to be active or not (although I agree the inference is pretty obvious for most people!) It’s just saying active investing to beat the market is a zero sum game.

    With that said, I’d question whether avoiding the very worst fund managers is really such a big achievement? What’s the point? It’s almost as if tracker funds don’t exist to give you the market return (minus trivial costs). But they do. So why bother?

    As @Freemantle says, I think ironically, losing funds are closed down all the time. Always remember that active fund management group literature pretty much *never* highlights aggregate returns including all the funds closed/merged/and so on. We’re not talking about a minority of funds here, either. From memory I have a hunch most funds that ever existed have been closed down or merged! (That might be an exaggeration though, so please don’t quote me!) The point is, it’s many thousands.

    Why bother? What is the point, for the average person? None I can see.

    @Argie — Thanks, glad you found it readable. What you’re talking about is not whether active investing is a zero sum game (I appreciate you’re not claiming you are, but this is what the article is about). You’re talking about, I guess, asset allocation to try to achieve optimal / superior returns.

    Of course if you hold only the better performing markets all the time, then you’ll see higher returns then if you held some poor performing ones.

    This is really semantics, and about ‘what is a market’.

    For instance, to your point about comparing one market with effectively a subset of another, this has been a criticism of Neil Woodford’s track record over the years, when compared to the FTSE All-Share say. Woodford has tended to hold a significant minority of US/European stocks, and also some small caps or even unlisted stocks.

    His investors don’t care as long as he makes money you could argue (though they should think about risk) but it matters if his marketing team at Invesco then said “Look how Neil has beaten the FTSE All-Share”, when some of that outperformance has come from holding a different market.

    People in the industry can get very het up about all this. 😉

    I think you’re also implying a wider question: Can a skillful investor do better by holding the better markets, and even if they hold them via passives are they really passive investors when they make that choice?

    To the second point, I don’t think it matters. It’s just words. Passive funds are the cheapest way to get the market return. It’s not a religion. 🙂

    In terms of skillful market selection and so forth, well again this will get nerdy. 🙂 To compare Manager A’s purported skillful market selection with Manager B’s, you’d have to define the market as “All those markets that A and B (and however many other active managers are involved) can choose from.”

    The managers who do better at choosing the best subset of markets from the master set will do so at the expense of those who do worse. Everyone else is a passive investor — alpha cannot be magicked out of thin air.

    I’ll repeat again this isn’t really a tirade against active investing, except in as much as I think 95% of the marketing is misleading and I don’t think the average investor needs it or needs to pay up for it. It’s more about pointing out *why* the marketing is so misleading.

    An active fund management company can properly say “Miss Whizzybang is a wonderful stock picker, here’s her record, put your money with her” and from the point of view of this article that may be a correct statement. (There are other reasons why you might ignore the advert, such as that outperformance seldom lasts).

    What I’m saying is nonsense is when they or their promoters in the press say something like “Trackers are all very well but active management shows its value over the long-haul / in a bear market / in a volatile market / in a stock pickers market”.

    It’s nonsense because for every £1 that does better from active investing, a £1 of actively invested money must do worse. As above. 🙂

  • 9 Uncertain January 22, 2015, 9:48 pm

    Another nicely written piece
    But can I post an alternative suggestion, that is that active market participants add value, but that that value is most cheaply and efficiently captured by index investing.

    The stock market is ultimately there to find prices so that capital can be allocated efficiently to the most productive places. If someone somewhere along the line is not making intelligent decisions about the price capital will become inefficiently allocated and the overall returns of the stock market will fall.
    Individually each active investor may make some foolish decisions colectively the passive investor is dependant on them.

  • 10 grey gym sock January 22, 2015, 11:34 pm

    fama is a nobel-prize winner, but french isn’t. that’s the only error i can find in this article 🙂

    Uncertain: the stock market does have a real role in allocating capital; but that is a very small part of what it does. deciding whether to put new money into companies is about allocating capital: that includes both rights issues, and IPOs – if the money raised goes into the company. trading shares with other investors on the secondary market isn’t directly about alloating capital; nor even are IPOs, if the money raised is just used to buy out existing shareholders. sometimes, secondary trading may have an indirect affect on capital allocation decisions; e.g. perhaps a share price falls because investors think a company isn’t returning enough of its capital to its shareholders (via dividends and buy-backs), and the price recovers when the company’s management does what the shareholders want. whether to accept a takeover bid can also be a real decision about allocating capital. overall, i think you have a small number of decisions about capital allocation, swamped by an ocean of non-productive trading activity.

    the trouble is that the total cost of active management is far too high for the small amount of useful capital allocation decisions being made. charges are generally proportionate to the level of activity, most of which is non-productive – or zero-sum, in the terms of the article.

  • 11 PP January 23, 2015, 9:25 am

    Great Article. You mention the aggregate active funds earn beta minus 1.5%, should that not be beta minus 3%?

  • 12 The Investor January 23, 2015, 3:03 pm

    @Uncertain — An interesting way of looking at it. 🙂 It doesn’t change the maths from the POV of as private investor, of course, but there’s no doubt price discovery is an important role played by active investors. I think there’s also no doubt that the investing community (i.e. the public) massively overpay for it, too. I’ve seen estimates that 25% as much money actively invested would be sufficient… right down to a few who say just a handful of active investors would do the trick! (Extreme view I think!)

    @grey gym sock — What’s a Nobel prize between friends, especially one in economics… 😉 Thanks for your thoughts.

    @PP — Cheers. No, not 3%, it’s 1.5% tithed away from the returns of all active investors, winners and losers alike. (Same way as you and I may pay 40% income tax each, rather than together paying 80% income tax. 🙂 )

  • 13 Fremantle January 23, 2015, 4:42 pm

    @Uncertain

    I agree with grey gym sock.

    The Stock Market is not there to efficiently provide capital to productive industry, but to provide liquidity to existing stockholders.

  • 14 ermine January 23, 2015, 5:31 pm

    Nicely argued, and internally consistent. You haven’t exactly specified the boundary conditions – after all the market is probably more like VWRLD than VFTSE but given that, it’s fair enough.

  • 15 R Lee January 23, 2015, 10:32 pm

    Speakin as an instinctive indexer, I think this argument overstated. This is clearly a straw man fallacy:

    “What I’m saying is nonsense is when they or their promoters in the press say something like “Trackers are all very well but active management shows its value over the long-haul / in a bear market / in a volatile market / in a stock pickers market”.

    It’s nonsense because for every £1 that does better from active investing, a £1 of actively invested money must do worse. As above.”

    Because the argument you should be addressing is that active management gives *good* active management the chance to outperform, etc. etc. just as it gives bad management the chance to underperform. The “zero sum game” argument only bites on someone insane who aspires to own the totality of the actively-managed market.

    Indexing probably makes sense, because crapness is more common than excellence and because bad outcomes are bad to a greater extent than good outcomes are good. But there is
    a significant opportunity cost in giving up the chance to outperform the index to an extent which pays for the extra costs involved, and it is over-evangelical to pretend otherwise.

  • 16 The Investor January 23, 2015, 11:03 pm

    @R Lee — Thanks for the comment, but I don’t buy it, or take the criticism as valid. 🙂

    Firstly, I go out of my way in the article to say several times that I am not saying some active managers don’t/won’t beat the market, or that you shouldn’t try. That is hardly the definition of ‘over-evangelical’.

    Secondly, the active fund industry constantly uses the ‘straw man’ that I have supposedly got stuck into here in its marketing. Many ‘semi clued-up’ investors believe it. (Where clueless — in the non-pejorative sense of the word — investors think “of course” smart people can beat a computer that holds everything because it seems like common sense, and ‘semi clued-up’ investors are those that half understand the case for indexing, but read around just enough to think they ought to try to do better, without understanding the maths/risks/downside.)

    Thirdly, evidence from all developed world markets show a majority of funds fail to beat their markets over any time period beyond a few years. (Here’s a summary of some UK data). Some studies have come up with figures close to 1%.

    Given that, I have absolutely no interest in the argument that I “should” be addressing, as you put it. I say in the article it’s easy to create a winning fund by indexing and owning one stock, and indexing and shorting in another.

    That’s a more important takeaway for most people. The fund management industry is built on getting a few years of lucky returns, marketing it as skill, and harvesting an income.

    Fear not, readers of this article are entirely free to get back to trawling through the endless promotional material, puff pieces in the press, fund manager interviews, and whatever else they want to read to hear from the other side should they choose to… 🙂

  • 17 R Lee January 23, 2015, 11:49 pm

    I still think you are skewing it when you suggest that only a tiny number of managers beat the market – on your own incontrovertible argument the number of winners can’t be tinier then the number of losers. I am not really arguing here – I am an index investor after all – but the opportunity cost of indexing is significantly greater than nil.

  • 18 The Investor January 24, 2015, 12:01 am

    @R Lee — Fair enough, it’s all worth discussing, but I still don’t agree. 🙂

    You say “the opportunity cost of indexing is significantly greater than nil” but I think that’s because you’re not risk-adjusting that opportunity cost. Given that the risk of doing worse than indexing is extremely high (as shown by all those studies) I suspect the opportunity cost is very low for the average investor, if not negative.

    Only a tiny number of managers beat the market because they charge so much for their services. I’m not sure if you’re a regular reader here or not (very happy to have you stop by either way! 🙂 ) but we’ve been through all this stuff many times in the archives.

    If active managers charged the same as passive (some very few Vanguard funds in the US have started to offer this, for example) then it would be more about risk of diverging from the market. All the fund literature that talks about ‘stock pickers doing better in downturns’ and so on would still be guff, but it would be better than the worse than a zero sum game we have today.

    Thanks again for sharing your thoughts.

  • 19 oldie January 25, 2015, 12:53 pm

    Hi
    thanks for readable and understandable article.

    Is there a feedback effect whereby active investors go into a particular sector which drives up the price. The passives have to follow by definition. At a later stage the situation reverses. Haven’t the actives created some advantage over the passives?
    thanks

  • 20 The Investor January 25, 2015, 3:31 pm

    @oldie — They have made the market more volatile, but there’s no extra return going to the active *in aggregate*. Remember, in aggregate the actives get the market return too (before costs).

    Particular active funds that bought in before the sector ran up in value and then skillfully/luckily swapped out of that sector at the top and into shares/sectors that didn’t fall as much *would* do better than passives who just went up and came back down. But that ‘alpha’ would be at the expense not of passives but of the *active* who sold them cheaper shares before the run up, and who then bought their expensive shares off them before the bust.

    The “alpha” created by the winning actives comes from the *negative* alpha of the losing active funds. The two net off against each other to zero.

    Obviously the aim of an active fund is to be (/claim to be) the guys who buy low and sell high, rather than their patsy active rivals. And then to repeat the feat for years or decades. The vast majority don’t succeed.

  • 21 Jeff January 26, 2015, 12:42 am

    Considering all investors, outperforming the market is unlikely. However it is possible either with good investment strategies or with good methods for selecting outstanding fund managers (or preferably investment trust managers).

    Also, if the proportion of money in passive indexing funds increases, then the prospect of a well managed fund outperforming increases.

    Currently, 1.25% of my portfolio is in index funds. The remainder is in either self selected stocks or mostly with Investment Trust mangers who have shown they probably know what they are doing on a long teem basis. Ideally I would decrease the proportion in index funds.

  • 22 Tom January 26, 2015, 11:40 am

    Interesting article, and I agree that on average active funds lose money, however it is possible to pick the outperforming fund managers as there are several consistent ones.

    You are also assuming everyone is an investor for the same reason. However in reality there are market participants that aren’t trading for fundamental reasons of because of a fundamental view of a company, for example:

    A company completing a buyback of its own stock
    The BoJ asking the Japanese pension scheme to purchase stocks
    An entrepreneur/CEO selling shares because otherwise he can’t use his millions of stock options to buy a house
    A day trading who has seen a hammer reversal pattern and believes the share will go up for the next hour
    Not to forget the classic passive fund manager buying a share because it’s got more expensive!
    Employees purchasing stock in a company SAYE scheme

    So I agree that active investing is zero sum on aggregate however, none of these market participants are trading based on a fundamental view on the share price and company’s value. There will be plenty more like these out there so the philosophy behind active management is that by always keeping a long term mindset they can trade with the non-profit seeking traders.
    Remember there are plenty of Indices that have gone sideways of downwards over many years, so passive investing does not guarantee accumulation either (CAC 40, Nikkei 225)

  • 23 Peter March 1, 2015, 10:39 pm

    Great site, and I’ve had far too many late nights reading through recent posts, and starting to browse the archive!

    Having been investing for 5 years (hello SIPP) and only just heard of passive investing through some US coworkers, I’m still trying to get my head around the zero-sum game. On a macro level it is; on a micro-level of one particular investor (i.e. me) I’m not so sure. It could be zero-sum, it could be negative or it could be positive, depending on the funds I picked.

    What I wanted to ask for input on was the ‘excessive charges’ for actively managed funds. I was curious about this – if I work on the assumption that an actively managed fund picked on extensive research *may* perform better than the index – by how much would it have to perform better to get the same return.

    I put together a spreadsheet to try it out: https://docs.google.com/spreadsheets/d/1OWaxjHJ4lsWGS6tig0KnESeZDfd0d8iDVz2D4wsZaoU/edit?usp=sharing using two Europe ex UK funds I was comparing this evening. If I think the active fund is going to out-perform the index fund by ~1% it looks worth it.

    Are there any flaws in this logic? First time I’ve tried to do compound values in a spreadsheet, let alone model something financial 🙂

  • 24 The Investor March 2, 2015, 10:52 am

    @Peter — A zero sum game approach to a market of many investors by definition can’t be applied to one investor. That’s not a zero sum game! 🙂

    If you are asking “is it possible for a single investor to beat the market” the answer is definitely yes, especially over the short term. We have abundant evidence that’s true. We also have abundant evidence that (a) most don’t and (b) (more controversial) most who do beat the market through luck, or taking on more risk.

    That’s why passive investing makes sense for most. The odds are terrible, and even worse when compounded by high charges. (For active fund management to be worthwhile, it has to at least deliver excess returns (alpha) ahead of its excess costs (fees and trading costs) compared to passive funds. The high cost drag is the biggest problem for active fund managers. They keep up with the market on a returns basis (because, as explained above, they *are* the market.)

    I don’t think you do, but if just in case you mean “is all investing a zero sum game, even for a micro investor” the answer is no. You can invest with the expectation of returns for all investors, before costs:

    http://monevator.com/is-investing-a-zero-sum-game/

  • 25 Peter March 2, 2015, 12:22 pm

    @The Investor: Many thanks for your reply, it clarifies a lot I was misunderstanding about the ‘zero-sum’ nature – I thought you were saying “investing a zero sum game, even for a micro investor” 🙂

    Completely agree with your (a) and mostly with (b), though not sure the risk is much greater than passive equity investing (I may crash and burn harder, but in a stock market crash everyone will too). Still trying to get my head around bonds, but my reading is now isn’t a good time to put money into them for a ‘safer’ investment.

    Where I do think we disagree is the “compounded by high charges”, which if my spreadsheet is right shows the difference isn’t that much. You’ll be worse off if your actively-managed fund with a 1% fee performs the same as a passive fund with a 0.1% fee, but it’s not as significant as I feel people are making out.

    Great discussion 🙂

  • 26 The Investor March 2, 2015, 12:31 pm

    @Peter — If your active fund does better than the market sufficiently well to outpace its fees, then fine. But most don’t! If you’re saying the 0.9% difference is not material for identical returns, though, I really don’t agree.

    Also, additionally, please remember active funds have fees beyond the annual charge.

    See this article for one worked example: http://monevator.com/cost-of-active-fund-management/

    Regarding risk, it means something slightly different in financial terms. For instance, small caps are well known for delivering superior returns, but they are more volatile (i.e. they go up and down more than large caps). This makes them riskier in financial terms.

    So an active fund could beat the FTSE All-Share buy holding, for example, 50% of a FTSE All-Share tracker, and 50% in a small cap fund.

    Over the long term the active fund would likely do better (ignoring fees) but it would also be riskier (i.e the price would go up and down more, and to higher highs and lower lows). There’s a bit more to it than that (you can adjust for risk etc) but that’s the gist, and I’m at work.

    These videos might help: http://monevator.com/tag/investing-cost-video-series/

  • 27 Maynard Periwinkle March 12, 2015, 8:06 pm

    I did enjoy the article – so thank you!

    However, I feel the “zero sum game” concept is a little over-simplified … It’s an elegant idea – but built on a bit of a misconception

    No funds actually return what they appear to return … When we look at any fund’s performance, it only shows us a time-weighted return … What the fund actually returns to investors (as you probably well know) is a dollar-weighted return … And the two tend to be quite different

    The average S&P 500 tracker’s dollar-weighted return is about 100bps lower than its time-weighted return, while with active funds it tends to be even worse … And this is down to investor behaviour: we’re more likely to invest when a fund’s expensive, etc

    While there are all sorts of behavioural inefficiencies among stock-pickers (not to mention institutional investors), the way we buy and sell funds is in itself a source of significant inefficiency

    Tapping this alone, there would be room for every active fund in the universe to outperform its index on a time-weighted basis … Whether this translated into a better dollar-weighted return would be – obviously – another story

    A market subtext, no less …

  • 28 The Investor March 13, 2015, 10:33 am

    @Maynard — Well I’d quibble slightly with your comments about time versus money-weighted returns, in that I think the time-weighted return does show how a fund performed, especially an index fund which is less likely to be distorted by growing/falling AuM than a fast-growing/outperforming active fund. But that’s perhaps a matter of opinion, and of course you’re quite right about investor behaviour. (I just think that’s the investors’ ‘fault’, not the funds. 🙂 )

    It’s too early in the morning for me to think deeply about your claim that the ‘behaviour gap’ you’re describing is free alpha for active funds, but my gut feeling is it’s not at all — for an active fund to benefit it still has to do so at the expense of a opposite out-of-position active fund (/amount of money). But possibly this is captured in your penultimate paragraph and we don’t really disagree.

  • 29 Hughie Jessel August 20, 2015, 9:50 am

    I am here to contest the notion that active investing is a zero sum game. In the case of e.g. the S&P 500, the index is free-float adjusted, so active investors who’s stakes are excluded from the free float can beat the market in aggregate. Granted, only a small portion of active investors do this, but in theory the majority of them could, meaning in aggregate they could conceivably beat all passive investors

  • 30 The Investor August 20, 2015, 10:33 am

    @Hughie — Interesting to think about (and I haven’t yet, so not immediately sure if I agree) but of very little practical relevance here to be honest. Really it’s changing the question. When people talk about active versus passive investing, there’s not a third option where you can suddenly (and cost-less-ly) get meaningful restricted stock in public listed companies. Once you start looking for weird anomalies like that I’m sure there are many out there. 🙂

  • 31 Hughie Jessel August 20, 2015, 10:52 am

    Let me make it more general for you then.
    Any company that is not 100% free float (e.g. Google and Wells Fargo) is by definition under-invested by passive investors (assuming most passive investors follow a free-float benchmark), therefore passive investing is not a zero sum game (vs. a benchmark). One can therefore conclude the same for active investing. Restricted stock is not the only thing that would render equity excluded from the free float…. any stake that allows some level of control may be excluded. There may indeed be practical use here, for example investing in an activist fund, where shares can end up being so tightly held that passive investors simply cannot get hold of enough shares. This is by no means a regular occurrence, but I am only contesting the theory of active investing being a zero sum game.

  • 32 The Investor August 20, 2015, 12:20 pm

    @Hughie — I don’t think you’re right. The price of the non-free floating shares are set by the free-floating shares, where the zero sum game rules apply.

  • 33 Hughie Jessel August 20, 2015, 1:24 pm

    I think I might be right!
    Let me illustrate by way of example. Let’s say that the market is represented by 1 passive investor with $3 to invest and 1 active investor with $5 to invest. The investable universe is made up of 2 companies, each initially worth $4 but one company only has 50% of free float, while the other is fully floating. The passive investor owns $2 in the free floating company and $1 in the less liquid company. The active investor owns $2 of the free floating company and $3 in the less liquid company. The shares of the less liquid company go up more than the other. Active investor wins. This could equally be the case if there were multiple active investors, all invested in the shares that were not freely floating. There is no need for half of the active investors to take the other side of the trade – they can all beat the passive investors.

  • 34 The Investor August 20, 2015, 1:51 pm

    @Hughie — I’m busy with something at the moment, but might be able to give this some more thought at the weekend. (I’m not a market academic and don’t discount the possibility you’re right, but you’re not convincing me — and to be honest if you did I’d want to appeal to someone who researches this for a day job before declaring defeat).

    However at the moment my gut tells me you’re just making up an arbitrary situation that doesn’t really tell us anything.

    For instance, in your thought experiment example, with your two $4 companies, there’s $2 of free float of the less liquid $4 company. Yet somehow your active investor owns $3 of stock in it. (i.e. $2 of non-free floating stock, because we know the passive investor owns $1). I am presuming you are declaring the ‘insiders’ of the 50% free float company to be active investors. But they’re not, they’re entrepreneurs — or something else if they got this share another way. Say they bought it off market participants and that float was withdrawn from the market for some reason to lock it up. (Perhaps the company acquired the shares and put them in Treasury). Whatever the case, you’d have to go further back into chain of ownership.

    I’m sure it’s true, as I said earlier, that there are plenty of outlying cases where the non-zero rules don’t apply (such as private equity, say) but that’s because I think they’re not in the active/passive game, they are doing something else. As I understand the discussion, anyway.

  • 35 Hughie Jessel August 20, 2015, 5:09 pm

    Meh….. semantics
    Either way, the zero-sum-game theory should not be focused on market cap but instead of ultimate economic value, i.e. the cash flows to shareholders into perpetuity, which I would argue is not a zero sum game….. but I am also too busy to go into more detail!

  • 36 The Investor August 20, 2015, 6:17 pm

    @Hughie — It’s not semantics. Your theory was wrong. Thanks for taking the time though.

  • 37 The Investor August 20, 2015, 6:20 pm

    p.s. To your second point, *investing* is indeed *not* a zero sum game. See:

    http://monevator.com/is-investing-a-zero-sum-game/

  • 38 Hughie Jessel August 20, 2015, 6:25 pm

    How bizarrely contradictory of you. You previously stated my theory was correct, although attempted to diminish it as “not practical”, which is an irrelevant argument for a theory. Now you are saying it’s wrong. Make up your mind. As for my second point, it should be perfectly obvious that I am referring to active investing.

  • 39 The Investor August 20, 2015, 6:59 pm

    No I didn’t. To quote I said:

    “I don’t think you’re right.”

    and later:

    “However at the moment my gut tells me you’re just making up an arbitrary situation that doesn’t really tell us anything.”

    Happily, readers can look at the above comments and make their own minds up.

    It’s important to me to state that I believe you’re wrong. That’s not to score points with a stranger, but so that readers of my blog are not confused by the points you’ve raised, which are misleading/confused, in my view, and don’t prove the zero sum theory wrong at all.

    I think this conversation has run its course.

  • 40 The Investor August 20, 2015, 7:01 pm

    As for my second point, it should be perfectly obvious that I am referring to active investing.

    You said:

    Either way, the zero-sum-game theory should not be focused on market cap but instead of ultimate economic value, i.e. the cash flows to shareholders into perpetuity,

    That was why I referred you to the second article.

  • 41 NS September 9, 2015, 5:18 pm

    Hi – found your article on Google and really enjoyed it. I agree with the zero-sum concept to active management in theory, but you need a wide definition of active management. I’ve had colleagues argue that it is the case within a sector – i.e. UK Equity funds, but that ignore all the other buyers of such stocks, such as Global Equity funds, Hedge funds, retail investors etc.

    However – no one really talks about share buy backs. Here you have the company entering the market to buy up their own stock, with no attempt to “outperform”, just prop up their share price. What are your thoughts on buy-backs as part of the zero sum theory?

  • 42 DonF June 11, 2016, 10:10 am

    @TI: Thanks for keeping up the good work. Don’t you ever get tired of it…? 😉
    Great article as always, by the way. Crystal clear. Not sure why anyone would disagree with it, it’s just (simplest) math. Perhaps because they’ve got something to gain from it…

  • 43 Punit Jain April 17, 2017, 7:43 am

    I agree with this article. However, I have a different perspective. I also speak in the context of the Indian stock market. Lets think of investing as a meritocracy. So well known good companies attract more funds, and well known bad companies lose investors. The GCBC divide can be in the Index stocks, as well as non index stocks. It can be in actively managed funds and in the rest. At a stock market level, say Indian stock markets, it may be a zero sum game. But why not look at multiple stock markets – many investors are free to exit one and enter the other. Even other asset classes like gold, oil, commodities, etc. can be entered and exited fairly freely. So if the Indian stock markets are seen as attractive, the assets may exit others to enter here, and the index will do well here, and the non index may also perform better or worse. My point here is that active management that is very good at picking GCs and ignoring BCs, may be able to attract funds from many other asset classes and outperform the market much better than previously imagined. Regards, Punit Jain

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