Can you beat the market?

A small experiment on a portfolio of 15 Belgian stocks

The Brussels Stock Exchange

The question whether investors can beat the market in the long run is maybe one of the most crucial ones in the world of finance. On the one hand, active portfolio managers do believe that they can outperform the market by betting on particular sectors or stocks. On the other hand, passive portfolio managers just seek to replicate an existing index, such as the S&P 500, in order to match what they see as a “market return”. Between both, factor-investing (also called “smart beta”) portfolio managers try to track an index while adopting active portfolio allocation choices in the same time. For the Solvay Student Review, we made a little experiment that compares factor-investing strategies and passive strategies on a sample of 15 Belgian stocks from 2005 to 2015.

CAPM and beyond the CAPM: Size, Value and Momentum

According to the capital asset pricing mode introduced by William Sharpe, among others, in the years 1960s, a stock’s expected return can be expressed as a function of the excess market return over the risk-free rate. However easy to grasp and still very commonly used in practice, the CAPM has been under huge criticisms especially since the years 1990s and after the crisis of 2008 as many empirical studies demonstrated that the CAPM did not capture all determinants of a stock’s return. In 1993, Fama and French introduced a model in which a stock’s return was explained not only by a market factor but also by a size factor and a value factor. According to their empirical studies, small firms and value firms (i.e. firms with a high Book-to-market value) tended to deliver higher historical risk-adjusted returns than big firms and growth firms (i.e. firms with a low B/M value). In 1997, Carhart introduced the momentum of a stock as a fourth factor that could explain a stock’s return. Momentum, a concept that comes from physics, captures the idea that a stock that has seen its price moving up in the past might still see its price increase in the (near) future, and vice-versa. Therefore, investing in high momentum stocks (winning stocks) might be a profitable strategy to cash in on this momentum effect.

The experiment

We considered a portfolio of fifteen Belgian stocks, all coming from the Bel-20 index (except perhaps for Mobistar that left the Bel-20 in 2013) and we constructed six different portfolios, plus the cap-weighted benchmark portfolio. In order to construct the small size and big size portfolios, we ranked each stock by market capitalization every year from January 2005 to January 2015. The Small size portfolio is long all the stocks below the median of the sample’s market capitalizations, whereas the Big size portfolio is long all the stocks above the median. In order to construct the value and growth portfolios, we ranked each stock by their Book-to-market value on an annual basis. Every stock above the 70th percentile was included in the Value portfolio, whereas every stock below the 30th percentile was included in the Growth portfolio. In order to construct the Momentum portfolios, we ranked all stocks by their momentum assessed throughout the previous year and we included the top 33% of these stocks in the high MMM portfolio and the bottom 33% in the low MMM portfolio. All stocks in every portfolio were weighted in equal proportions. Finally, the cap-weighted portfolio is the benchmark portfolio that includes all 15 stocks weighted by their market capitalization (which is the stock price times the number of outstanding shares). Then, for each portfolio, we computed the annualized return and volatility (standard deviation) and the Sharpe ratio, a measure of return adjusted for risk.


The table here below displays the results of our little experiment. Interestingly, one can observe that the Small size portfolio underperformed its Big size counterparty, whereas, in contrast, the Value portfolio outperformed its Growth counterparty for this same period of time, in terms of both return and Sharpe ratio. These results thus seem to support the existence of a value premium, while casting some doubts on the small size premium with respect to our sample.


However, maybe more strikingly, one can see that the classical cap-weighted benchmark “beat” both the small size and the value portfolios. Among the factor-tilted portfolios, only the high momentum one (with a Sharpe ratio of 0.28) did slightly better than the cap-weighted benchmark (Sharpe ratio of 0.23). However, these figures do not take into account the significant transaction costs necessary to perform the high momentum portfolio allocation strategy, as a lot of stocks need to be sold or bought at every rebalancing date. After taking into account transaction costs, the cap-weighted benchmark thus seems to beat all the factor-tilted portfolios.


Does it mean that, despite all the fuss surrounding “smart beta” and “factor-tilt investing”, one should still rely on the good old market-cap weighted index? Of course, our results only apply to the past and only to the – quite narrow – sample that we choose. Nonetheless, there are several interesting insights that could be taken from this experiment. First of all, it is true that a cap-weighted portfolio will mechanically attribute more weight to a stock which price is rising (higher price means higher market cap, all else being equal), thus ending up buying high and selling low. However, if a stock price keeps rising over a long period of time, the cap-weighted portfolio will just cash in on that rise. The illustrations here above – below represent the evolution of AB-Inbev share price, one of our portfolio’s constituents, between 2005 and 2015, and its contribution to the cap-weighted portfolio. As AB-Inbev share price increased, its contribution to the market-cap portfolio became more and more important.

graph1 (1)

Secondly, this also means that the cap-weighted benchmark that we created is heavily dependent on the performance of one single stock, which makes it vulnerable to this single stock’s downturn. Moreover, our cap-weighted index looks also vulnerable to an overall market downturn in which large stocks would see their price fall by a more significant amount than small stocks, causing the index to drop more dramatically than any other ones. For 2008 only, the cap-weighted benchmark was beaten by all factor-tilt portfolios (including the “losing ones” such as the low momentum portfolio) by more than 20% on average!

graph2To conclude, this experiment fuels more questions than it actually solves. Market-cap weighted portfolios are convenient since they are cheap to operate (low transaction costs) and that they can capture positive long term price movements. Moreover, if one believes in market efficiency, they reflect the best guess at valuing stocks with all the information available. However, the overconcentration in a couple of stocks (here just one) makes them very dependent on a small number of “leading” stocks’ performance, which may reveal fatal in the case of a downturn. The battle between passive and semi-passive investments doesn’t have a winner so far.

Photo credit: Dustin Hackert,


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