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Of elephants and mice - the untold story behind the rise of index trackers and the demise of active funds

Raphael Fiorentino
9th April 2019 - 5 min read

Elephant and mouse

The success of index trackers over the past few years has been nothing short of stupendous. They charge incredibly low fees and hardly any active fund manager has come close to beating them. Many retail investors have found religion in “going passive” and even wonder how actively managed funds can still exist. And if it is that hard for smart full-time professionals to beat a stupid passive fund, what does it say about your chances of being a half-decent steward of your self-invested pension money?

Turns out your chances rise with every passing day, whether to pick the right fund manager or the right stocks to invest in. Consider a game involving two elephants and two mice. You must pick the one animal that you believe will gain the most in percent of its weight over one year. In order to win the bet, you need to beat the gain realised by a weighted index of the ecosystem. The index is calculated using 50% of the weight of each elephant and 0% of the weight of each mouse. After a year, one of the elephants and one of the mice each gained 10% while the other two animals lost 10%. And so half of the population gained weight and half lost weight. The weighted index remains unchanged because one elephant gained what the other elephant lost (the performance of the mice is irrelevant to the index since they represent 0% of it). Without any skill at picking elephants and mice, you have 50% chance of picking the right elephant or mouse to realise a 10% gain over the index, and 50% chance of realising a 10% loss. Your expected return, purely based on luck, is therefore 0% = 50% x 10% + 50% x -10%. Without some animal-picking skill to tilt the odds in your favour, you won’t get richer no matter how long you play the game. And if you are asked to pay 2% upfront to take part, then you’ll need at least a 60% probability of picking the right animal to get to an expected return of 0% = 60% x (10% - 2%) + 40% x (-10% -2%). In other words, you need skill to increase your win probability from 50% to at least 60%, that is, an increase of 20% over the initial 50%. Anything short of this and you’re better off siding with the index.

The game can get a lot easier when both mice gain weight, or a lot tougher if only one of the elephants gains weight. In the first instance, your probability of picking a winner and beating the index by sheer luck rises to 75%. In the second instance, the probability drops to 25% and so your skill must be able to contribute at least another 25% (+100%), or 35% (+140%) if you pay 2% upfront.

The 2% upfront fee becomes an even thornier issue if the weight difference between gainers and losers is +/-5% instead of +/-10%, as it now takes over 70% win probability to make the game worthwhile, with 70% x (5% - 2%) + 30% x (-5% -2%) = 0% expected return.

Back to the world of equities, when outperformance is heavily tilted in favour of a few large (elephant) stocks, the market lacks breadth. And when the difference in performance between outperformers and underperformers is small, the market lacks dispersion. As illustrated with our elephants and mice index, breadth and dispersion set the stage for how impossibly hard or how ridiculously easy it could be for fund managers to beat their index over a given period.

The table below illustrates how the minimum level of skill required for funds managers (f) and self-investors (g) change as market breadth moves from normal (a) to wide (b) to narrow (c), as well as when stock return dispersion is high (d) versus low (e).

Bottomline: the narrower the breadth and the lower the dispersion, the more skill you need to compensate for the poor odds of beating the index.


The prevailing conditions of the past few years have been as ideal for passive strategies as they have been a terrible headwind for active funds, 2018 being a case in point and 2017 an exception (for instance in Europe, 45% breadth and 8% dispersion in 2018 vs. 51% breadth and 16% dispersion in 2017). Easy monetary policy and market liquidity dominated by index buyers are amongst the many factors thought to be responsible for this exceptional stretch of narrow market breadth and low stock return dispersion. When, not if, the pendulum swings the other way (ie. “reversion to the mean”), active stock picking will be back to the fore, and probably more so than after the mid 90’s, the only period in the last 40 years bearing similarities with the current one and the only other time when “going passive” was (with the benefit of hindsight) a no-brainer.

The bar for fund managers was always set high (due to their high fees) but it’s been rising even more over the past decade (increasing regulatory burden, decreasing informational edge, asset redemptions). And as the graph below shows, fund managers need substantial skill to justify their fees whatever the market breadth conditions. Not so for self-investors who now have comprehensive and competitive access to global equity markets, and for whom lack of skill can be largely compensated by digital means. As for fund managers, their challenge is to make better use of technology to boost their knowledge productivity, that is, their capacity to acquire and distil better insights faster for sustained quality investment decisions.


Butterwire is an AI equity analyst developed as a web app to contribute the 10%- 20% “extra luck” that a well-trained machine can contribute to active management performance. Its rationale: if you take a step back from the recent market conditions and apply "normal" assumptions (for breadth, dispersion, transaction costs, etc.), then the little bit of edge contributed by the machine is enough to make an investor better off most of the time by a material amount (see table below).


Butterwire's internal model combines data from various investment lenses (fundamentals, quants, macro, technical) to distil actionable knowledge on individual stocks, portfolios, and markets. Its ergonomic interface was built to ensure that a maximum amount of insights can be absorbed in the minimum of time. And its engine was designed to be infinitely scalable and versatile, meaning that it can be taught to adopt all the specifics of a fund, from a stock universe beyond the 5,000 global stocks already covered by it, to special features like the integration of proprietary stock data/metrics, the analysis of non-traditional risk factors, etc. In other words, whatever data-intensive task that can be delegated to it in order to free a fund management team’s time and brain-space and boost the fund’s knowledge productivity.

In its simplified non-customised form, Butterwire can also be very useful to many self-investors, and indeed sufficiently so to make active investing worthwhile in most market conditions (ie. market breadth above 45% per above graph). For instance, the app’s portfolio construction assistant makes it quite easy to build a portfolio of individual stocks from scratch or to upload an existing one and improve its return/risk prospect. Even for those not keen on becoming part-time managers of their own funds, the portfolio assistant can provide unique “bottom-up” insights on the portfolio of an active fund whose units you might be considering buying, so you no longer have to solely rely on promotions from fund supermarkets and backward-looking statements.