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Here's a statement of the obvious: The opinions expressed here are those of the participants, not those of the Mutual Fund Observer. We cannot vouch for the accuracy or appropriateness of any of it, though we do encourage civility and good humor.

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In Defense of Bill Sharpe’s Arithmetic

MJG
edited May 2014 in Fund Discussions
Hi Guys,

Professor Bill Sharpe really doesn’t need a defense. Because…

Nobel Laureate Bill Sharpe generates attractive analysis like in his classic paper “The Arithmetic of Active Management”. Here is a Link to his short paper that makes a convincing case against active mutual fund management:

http://www.stanford.edu/~wfsharpe/art/active/active.htm

Professor Sharpe bases his arguments on a Conservation of Money law. Whatever the total market generates must be divided among all market participants minus leakages. The leakages are the charges extracted from investors as the cost to play.

Nowhere does Sharpe argue that active fund managers must purchase only Index stocks. His analysis addresses the global market.

Index houses like Vanguard do a marvelous job at almost precisely duplicating market return segments by holding fewer than the entire market listings. These Indices are market neutral; they merely get market performance in the segments they emulate minus a small operational cost.

The residual pot is still at the annual return level. As a cohort, active managers get to divide this pot among themselves. Some managers win even after cost adjustments, but that group must be exactly balanced by active losers who receive less than the market’s average return.

Bill Sharpe’s paper is eloquent in its simplicity and its scope. It does not claim that sub-sectors within it will not outdistance other components. It explicitly does not preclude winners or losers. The model focuses on a total active management net payout.

Individual customers may win or lose, but fund managers always win. They pay themselves first. The investor’s pot is only distributed and always diminished after the fees have been extracted.

Sharpe’s 1991 insight is precisely on-target, but unfortunately, it is largely ignored, although it is rarely disputed.

Earlier in my investing career I was a 100% active fund owner. Not now! Over time, I slowly learned. As economist Paul Samuelson said: “I hate to be wrong. But I hate more to stay wrong”. That wisdom is a good guiding rule for every investor.

Could Sharpe be wrong? I doubt it.

MFO members choose to trust Sharpe’s findings or not.

Comments

  • edited May 2014
    MJG said:


    http://www.stanford.edu/~wfsharpe/art/active/active.htm

    Nowhere does Sharpe argue that active fund managers must purchase only Index stocks. His analysis addresses the global market.

    Wrong. From his own definition at the very beginning in the linked paper.
    Of course, certain definitions of the key terms are necessary. First a market must be selected -- the stocks in the S&P 500, for example, or a set of "small" stocks. Then each investor who holds securities from the market must be classified as either active or passive.

    A passive investor always holds every security from the market, with each represented in the same manner as in the market.
    He doesn't care what the market is or how big it is as long it is a closed system as defined in his framework above. The mathematical result is valid only relative to a passive investor (you can call it an index) that holds every stock in the "defined market".

    Which means the active investor can only buy from that defined universe that is held by the passive investor

    In addition, as shown by a simple example, in the thread you are responding to, the condition " each represented by the same manner as in the market", it is valid only with an unstated interpretation - that the aggregate composition of holdings of all the participants together of the market are in proportion to the market cap. This is not true in reality, obviously.

    Appeal to authority is not good argumentation as opposed to showing a real understanding of the actual paper and addressing the actual points. Even Nobel laureates have made errors or as in this case actual theoretical results over-generalized for reality by supporters.
  • edited May 2014
    @cman I wholeheartedly agree with your math, but have a few questions:
    How closely do total market indexes track the total market. Yes, they use statistical sampling at the edges, but how much tracking error does that introduce?
    If it is small is that just because the skipped stocks have small market capitalizations and the cumulative effect of their movements relative to the whole market are unnoticeable?
    Would that then imply that small-caps are where active management makes sense, but not for mega and large caps?

    This does still assume a closed system versus cash outside of the measured equity markets, perhaps momentum is useful because it attempts to model where that closed system is being broken. Thoughts?

    (edited for clarity)
  • @jlev, just so there is no confusion about terminology, total market is the sum total of all stocks in that market of interest, total market index is an index definitiontypically composed of a small or large subset of the total market (so it is not perturbed continually by new listings and delistings) which makes no representation in the performance of this theoretical basket relative to the performance of the total market, total market index fund is an actual fund that tracks the index.

    The actual funds are reasonably good at tracking the index but the tracking differs from fund to fund. This is because it is not practically feasible (or too expensive in trading) to hold every stock in the index at the exact proportion at all times.

    This tracking seems to differ between funds on costs of trading and liquidity of the underlying equities as well as the statistical process used to track while minimizing the costs of trading and not so much on cap size except for the implication on liquidity.

    Since the indices make no representation on the performance of the index vs all the stocks in the index, it is mathematically possible for the entire universe of stocks in that category to have higher returns than the index (which usually happens with a good IPO season) or lower in bad times.

    And so, the larger the number of stocks outside the index in that category, the greater the opportunity for active managers to over or underperform over the index by picking the stocks outside the index. But that is only one of the tools available to the manager. They can weight the index stocks differently based on fundamentals or technicals and overperform in theory.

    Small cap managers may have some advantages from lower liquidity, larger number of funds coming in and exiting (to arbitrage those), etc. Same reasons may apply to EM stocks as well.
  • Hi Cman,

    Thank you for replying.

    You are absolutely correct that I erroneously concluded that the Sharpe paper said “Nowhere does Sharpe argue that active fund managers must purchase only Index stocks.” He made no such assertion.

    When I wrote that line I was thinking of the global aspects of his analysis; hence I immediately followed with “His analysis addresses the global market.”. I should have said “My interpretation addresses the global market.”

    As you, and many others point out, it depends on where boundaries are drawn. I draw the boundaries with regard to this specific topic around the entire equity marketplace. Neither passive or active investors can be perfectly assigned to each category. Today, even Vanguard’s S&P 500 Index fund does not precisely duplicate its benchmark. At last count, it held 504 positions.

    My extremely simple position is best represented by my conservation of returns argument. Any costs and fees are leakage from an individual investors rewards. The cut of the equity annual return’s pie is reduced by the cost drainage.

    The integrated excess profits from successful active fund managers, who do exist, are swamped by the integrated below market returns from unsuccessful active managers. The differential is the moneys that active managers and other Wall Street entities expropriate.

    That is a summary of the main theme of my post. I choose to draw my conservation circle around all large and small cap holdings.

    I am still experiencing difficulties posting and have shortened my comments to secure access.

    Best Wishes.
  • edited May 2014
    @cman Thank you for the insight on the vagaries of how total market index funds operate, I've been meaning to look into it. My bigger question though was in regards to how much things like good IPO seasons or "bad times" can cause active managers as a group to out or under perform the indexers in question as a whole.

    Individual active managers can always outperform in the ways you've cited above and elsewhere. One major logical fallacy that seems to pervade these zero sum arguments of active versus passive management questions is the question of whether the passive investors are holding the same set of assets that the group of active managers are. Though I am apparently copying @MJG a bit in his response, I'm not convinced that the aggregate of cost drainage versus uncovered opportunities is negative.

    The similar example I am looking at is the Total Market of investable US stocks and comparing passive investors in Total Market Index Funds to those in actively managed funds as the person in MJG's link is attempting to. How large is the opportunity space for aggregate outperformance of these active managers versus passively invested managers? In a closed system, their math is perfectly correct and on average, indexing should beat active management. What I'm trying to figure out is how much is the closed system broken in practice? how much space is there for active managers in aggregate to find additional performance that would not be captured by indexers?

    As you've mentioned IPO's should be one such source and stocks not contained by indexes, or weighted in the index funds below their marketcap %'s should be another. Choosing to go outside the investable universe by holding cash would be another, but for the sake of the example let's assume people are sticking to US stocks and $'s, a big universe.
  • Ok.

    I am just pointing out that Bill Sharpe's paper cannot be used to claim anything about active investors relative to passive/index investing in practice as so frequently done by indexologists. It would require not only that the passive fund that is supposedly the better alternative hold every asset in the global markets but also that it hold the assets in the same proportion to the aggregate (which changes from day do day). So it is not even a question of approximating. The theoretical framework is too restrictive to have ANY applicability in practice.

    The other alternative is to establish this empirically as people have attempted to do. But, I have pointed out the problems with those indexology argument as well.

    Have no problem with a postulate as you have regarding active vs passive. As long as one doesn't inappropriately use theory or empirical studies to attempt to claim "proof", however often it is repeated as such.

    My view is that such a debate is moot and irrelevant. In a practical sense, active trading is necessary for price discovery which the passive investing depends on as well. This activity exists only because on the aggregate, there is economic incentive to do so, otherwise it would lead to quick extinction and along with it any validity behind a market. So there is no point in deifying one and demonizing the other. It is much more fruitful to figure out how one can benefit for themselves in the system that exists given the choices.

    Index funds are great at capturing the full upside of the market consistently. But they really suck in down markets. If you assume that there are more up periods than down periods or one has a longer horizon where that assumption can be held, index funds are the way to go. Index hugging active managers are a waste of time and money.

    However, as that investing period becomes shorter, and the ability to wait out a down market decreases, one needs risk management and active fund managers do this very well or at least enough to reliably pick those that do. Whether they beat the index every year is the wrong question for that.

    If shortfall risk didn't exist, then one can do their own risk management by allocation to cash and indices but the problem here is that a shortfall risk is reality for most people, so you need a strategy that is adaptive to market conditions. Sitting out a bull market because of age risks shortfall. This is where active managers can play a role.

    But the debates are usually about stock picking skills and silly and irrelevant for the most part.
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