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Sunday October 21st 2018

Stock Index Funds vs. Monkeys

Monkey stock picker beats index.
All Photos courtesy Standard Sports Photos

Over the past couple of decades, index investing has become a popular investing style. The general idea is that, instead of trying to pick individual stocks that will beat the market, why not just own the entire market? Fifty years ago this was not feasible. But in 1976, John Bogle started the first index fund, Vanguard 500 Index Fund (VFINX), making it possible for small investors to own all 500 or so stocks in the Standard & Poor’s 500 Stock Index.

Index investing became popular, in part, thanks to books like A Random Walk Down Wall Street, by Princeton economist Burton Malkiel. First published in 1973, Malkiel’s book popularized the idea of the stock market as a random walk,  the efficient markets hypothesis and that it was nigh impossible to beat the market by picking stocks or market timing.

The S&P 500 is a market-cap weighted index, which means that each stock is weighted in proportion to it’s market capitalization. This raises the question: is the best way of forming an index?

Monkey stock picker beats index.

Alternative Index-Construction Methods
A recent paper from Cass Consulting, part of Cass Business School in London, has received a lot of interest lately. Their paper,  An evaluation of alternative equity indices. Part 1: Heuristic and optimised weighting schemes, compared the traditional cap-weighted index with eight alternate index-constructon methods. Five of the methods were heuristic-based and three were optimization-based.

Table 1 summarizes the results. The best and worst are color-coded. See the paper for the exact index-construction methods and detailed results.

Table 1. Comparison of 9 Index-Construction Methods
(1969 - 2011)
Index
Weighting Method
Return Std Dev Sharpe Max
Drawdown
0. Market Cap 9.4 15.3 0.32 -48.5
1. Equal weight 11.0 17.2 0.39 -50.2
2. Diversity weight 10.0 15.7 0.35 -48.8
3. Inverse Volatility 11.4 14.6 0.45 -45.7
4. Equal risk contribution 11.3 15.6 0.43 -47.5
5. Risk clustering weight 9.8 16.7 0.33 -48.9
6. Minimum variance 10.8 11.2 0.50 -32.5
7. Maximum diversification 10.4 13.9 0.40 -41.1
8. Risk Efficient 11.5 15.9 0.43 -56.0

Observe that the traditional Market-Cap weighting was worst by two of the four measures. All of the alternate index-construction methods had higher return and better Sharpe Ratio than the traditional Market-Cap weighting. The Risk-Efficient Method had the highest return.

The Minimum Variance Portfolio MVP Index Method was the best by 3 of 4 measures. It is not surprising that it had lowest volatility. But MVP also had the smallest Max Drawdown, and the highest Sharpe Ratio, which measures risk-adjusted return. Yay, Minimum Variance Portfolio! Risk-adverse investors would prefer the Minimum Variance Index over all of the other indexes.

Monkey stock picker beats index.

Almost All Ten Million Monkeys Are Winners
The researchers took it a step further. To see if the results were simple due to chance, they simulated 10 million monkey portfolio with randomly selected weights. The distribution of the terminal values of wealth are plotted in Figure 5 on page 24 of the paper.

The results are shocking. Not just the average monkey, but nearly all of the monkey portfolios outperformed the market-cap weighted index. An investor with absolutely zero knowledge of business or the stock market could randomly pick weights and would have beaten a market-cap index.

In Figure 5 of the paper, the equal weighted index performed about the same as the average monkey. If you think about this a little, it make perfect sense. The average monkey portfolio would be about equal weight.

Turning attention to Figure 5 on page 25, the distribution of Sharpe ratios, again the market-cap weighted index was worse than nearly all 10 million monkey portfolios. Equal-weight, once again, closely matches the monkey average.

But the champion, by Sharpe ratio, is the Minimum Variance Portfolio. MVP beat out of the other portfolio-construction methods, and all of the money portfolios.

In the next article, I’ll look at creating a stock portfolio similar to the MVP using ETFs.

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