Our research finds that randomly selected equally weighted equity portfolios have outperformed market-capitalisation-weighted portfolios globally and in various regions over the past 15 years. These results – and structural features of market-capitalisation-weighted indices – call the supposed efficiency of these commonly used benchmarks into question.
In October 2011, David Harding, Winton’s CEO and founder, published Winton’s research into the efficiency of market-capitalisation-weighted portfolios . The main result was that randomly chosen, equally weighted portfolios had outperformed the S&P 500 from 1965 through to 2011.
A monkey throwing one hundred darts at a list of stocks in the index would likely have outperformed the traditional benchmark. Such a result throws the efficiency of market-capitalisation-weighted portfolios into doubt.
One explanation might be that the randomly chosen portfolios outperform because they take on higher risk, which conforms to the Capital Asset Pricing Model (CAPM). But the evidence suggests otherwise: the randomly chosen portfolios also achieve higher Sharpe ratios.
We attempt a similar experiment on a global scale to see if the result is US-specific – or if the monkey wins globally.
In an approach similar to the original research, each year, we randomly selected 20% of the average number of stocks for each region in the MSCI World to obtain our portfolios.
We carried out this sampling process 1,000 times to obtain 1,000 randomly generated portfolios. The performance of the random portfolios was then compared to the regional indices that make up the MSCI World Index.
In Figure 1, we summarise the results for each of the four regional indices – MSCI USA, MSCI Europe, MSCI Japan and MSCI Pacific ex. Japan – as well as the global MSCI World. The green line is the performance of each market-capitalisation-weighted index, the grey lines are the randomly generated portfolios, and the blue line is the average performance of the randomly generated portfolios.
The result seems to hold globally: for all the regional portfolios and the MSCI World itself, the random portfolios outperformed the index without taking on significantly more risk.
Figure 1: Performance of market-capitalisation-weighted indices versus randomly generated portfolios
The Sharpe ratio – or the ratio of expected return minus the risk-free rate, to the volatility of return – is a widely used measure of portfolio efficiency. In table 1, we show this ratio along with the returns for the random portfolios and the market-capitalisation-weighted indices.
Table 1: Sharpe ratio and return comparison
According to CAPM, investors should hold the market portfolio because it is the optimal portfolio of risky assets. Table 1 contradicts this – over the past 25 years, monkey-generated portfolios have outperformed their market-capitalisation-weighted counterparts in both absolute and risk-adjusted returns, and in every region of the MSCI World Index.
This is not the only reason to doubt that market-capitalisation-weighted portfolios are the optimal risky asset portfolio. Figure 2 shows the cumulative percentage of market capitalisation accounted for by a given percentage of stocks in each regional index. The stocks are ordered by size, so the largest stock is added first and the smallest stock is added last.
Figure 2: Stock concentration by regional index
The main takeaway here is that a relatively small number of stocks account for a large proportion of the total market capitalisation of each index. For example, in the MSCI Europe Index, the largest 20% of constituents account for roughly 60% of overall market capitalisation. Similar results hold for the other regional indices.
Another way to gauge concentration is the Gini coefficient, which measures the extent that the overall weight distribution is dominated by large weights on a few stocks. For an equally weighted index, the Gini coefficient is 0. This figure will range between 0 and 1 for other weightings, with higher values indicating greater concentration.
Table 2 shows the Gini coefficient for various MSCI indices and the S&P 500. As one might expect from the market-capitalisation distributions charts, these indices are very concentrated.
Table 2: Gini coefficients for MSCI indices
To hold an equally weighted portfolio in the CAPM framework is to introduce a substantial “size exposure” relative to the market-capitalisation-weighted benchmark. But if CAPM does not hold, then there may be no reason to hold the market-capitalisation-weighted portfolio. Instead, one might reach the conclusion that this weighting methodology has a substantial “size exposure” itself given its concentration.
Of course, the total holdings of equities must equal the total amount of equity outstanding in aggregate, but different investors may well opt from different, less-concentrated weighting schemes.
A second issue with CAPM theory is it implies that all investors should hold the same market-capitalisation-weighted global index as their equity allocation, regardless of where they live in.
The reality is very different. Table 3 shows the percentage of market capitalisation of each country in the index and the amount of that market held in domestic equity portfolios for selected countries . According to global CAPM these numbers should be the same .
Table 3: Home bias in equity portfolios
Only a subset of major markets from the working paper is included, but shows how investors hold more of their domestic market in their portfolios than they should according to CAPM. A large number of papers have attempted to reconcile this “home equity bias” with CAPM, but this has been a fruitless task so far, given the extent of the deviations from the theoretically implied portfolio proportions.
The monkey is global. There are good reasons unrelated to the dart-throwing prowess of the monkey to doubt that market-capitalisation-weighted portfolios possess the theoretical properties of risk efficiency and optimality. In contrast, it seems that when the monkey is finished throwing darts, it throws a dagger right through the heart of CAPM.
 D. Harding, Some new ideas in financial mathematics, Pensions and Investments, October 2011.
 Reproduced with permission from Sercu and Vanpee (Home Bias in International Equity Portfolios: A Review, Leuven School of Business and Economics Working Paper, 2007). This table is a little dated but the numbers do not change drastically from year to year.
 Here we have assumed that purchasing power parity (PPP) is correct and so an investor bears little foreign currency risk.
This article contains simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity and cannot completely account for the impact of financial risk in actual trading. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results and all of which can adversely affect actual trading results. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any investment will or is likely to achieve profits or losses similar to those being shown.
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