Finance + Investing

Malkiel's Monkey: Assessing Actively Managed Fund Performance

Do U.S large-cap firms generate a greater return than our furry friend?
Malkiel's Monkey: Assessing Actively Managed Fund Performance

In 1973, a Princeton professor and economist, Burton Malkiel, published the classic bestseller "A Random Walk Down Wall Street" in which he postulated the following: "A blindfolded monkey throwing darts at a newspaper's financial pages could select a portfolio that would do just as well as one carefully selected by experts." Intrigued by this proposition, we decided to test it for ourselves using modern data and a modern approach. It was admittedly quite difficult for us to find a monkey capable of throwing darts, so we opted for a more cost-effective and safe approach to replicate the experiment; we would simulate the actions of a monkey randomly selecting stocks by creating a trading algorithm that accomplished just that. Our approach was simple - the algorithm, aptly named Malkiel’s Monkey, would randomly select 30 equities from a predefined tradeable universe of U.S equities, hold them for the year, and then sell off the positions at year-end. It would repeat this process annually for the duration of the experiment. As you might expect, it is a surprisingly difficult task to create a virtual Monkey, so our algorithm leveraged the backtesting capabilities offered by Quantopian (in particular, the Zipline API) which allowed us to assess performance on an annualized basis over a 15-year historical interval. 

For the inaugural edition of this market experiment, our analysis is contained to large-cap, U.S equities. In practice, this implies that the Monkey algorithm’s tradeable universe is restricted to those equities listed on the S&P500. The algorithm is then tasked with randomly selecting and purchasing 30 unique equities at the beginning of each year (more precisely, the first trading of the year), for a fixed 15-year back-test period. Three separate back-tests are run for the algorithm, and performance results are averaged with equal-weight. Finally, the algorithm’s performance is shown in comparison to two benchmarks; the overall market (proxied by the S&P500) and the average Asset-weighted return of all large cap funds in the United States. Returns are calculated on an annualized basis. Additionally, our algorithm’s end-of-day gross leverage is kept between 1.5 and 0.5, with average leverage in each trial hovering between 0.95 and 1.05 – this is to remove any distortionary effects on returns caused by an abundance of leverage.

Plotting Annualized Returns Over Various Intervals

Looking at our results, we are somewhat optimistic. Certainly, over the short-run large-cap funds have outperformed our Monkey on a 1-Year, 3-Year, and 5-Year intervals with returns calculated on an annualized basis. Over the 10-year and 15-year interval, the Monkey outperforms the aggregate returns of these Large-cap funds. All the while, the annualized returns of the S&P500 outperformed Large-Cap Fund averages and surpassing the Monkey’s returns over the 1-Year, 3-Year and 5-Year periods. Another important, yet absent consideration, are front-end and back-end load commissions on may of these funds which would further reduce realized returns on many of these large-cap funds. 

While our results might appear to have implications for fund management, it’s important to clarify a critical part of the way our algorithm derives returns. From a statistical standpoint, each algorithm trial (or backtest) effectively purchases a 30-stock sample of the larger S&P 500 “tradeable universe” and rebalances each year by selling the stocks and then randomly purchasing 30 more unique equities. It should be expected then, that upon completing several independent backtests over the same interval, the average return of Malkiel’s Monkey would approach the return of the S&P500, which is precisely the purpose of Malkiel’s observation; that no long-run or short-run advantage to active management funds, when observed on the aggregate. In the United States, 80.60% of funds underperformed the S&P500 over the past 5 years according to data collected by S&P Dow Jones Indices LLC. In Canada, the results are even more disappointing; 96% of funds underperformed the S&P/TSX Composite Index over the past 5-years, and only 2.94% of funds outperformed over the past three years.

Taken together, these observations lead us towards a broader debate regarding the benefits of passive and active management. More specifically, can active management funds derive abnormal returns over the market over the long run with any consistency and whether management expense fees paid to fund managers without any value being provided to unit holders in return. These issues, of course, lie beyond the scope of this column, but it should be worrying to most that any trained monkey can generate similar or superior returns compared to large-cap fund managers over the long-run.


References:

[1] SPIVA® U.S Scorecard Year-End 2019, S&P Dow Jones Indices LLC.

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