Back to the 80s? An Analysis of Value and Size Strategies in the STOXX Europe 600

Cover - Value and size anomalies

The purpose of this article is to analyse the performance in the European markets – during the last five years – of two strategies that refer to two well-known market anomalies: the value and the size anomalies. Before looking at the results of our research, we will briefly discuss the theory behind them.

A Definition of Financial Anomaly

A financial anomaly is a cross-sectional and time series pattern in portfolio returns that is not predicted by a central model. In the present analysis, the model is represented by the famous CAPM. The CAPM theory, introduced independently by W. Sharpe and other economists in the 60s, develops the work of Markowitz on capital allocation and portfolio theory. It aims to predict the expected return of an investment strategy, based on the expected returns of the market and on the sensitivity of the returns of this strategy to the returns of the market. Briefly, the model assumes that all investors are rational, that is that they prefer the highest possible return for each level of risk. This assumption, together with other minor hypothesis, implies that the market is efficient, because investors either buy or sell securities until their return is the “correct” one. Like in the Markowitz’s model, risk is expressed as the standard deviation of the returns of the strategy. However, since investors can diversify their investment, the part of risk that is rewarded with higher (expected) returns is just the one that cannot be diversified away. This part is reflected by the market Beta, that represents the part of the movement of the stock linked to the movement of the market. The final formula of the CAPM is, finally, as follows:

Empirical studies, however, have found several examples of anomalies, meaning, again, returns of fixed, predetermined investment strategies not explained by the CAPM. This may be due to two reasons: either that the CAPM does not hold – for instance because there are factors other than the market that explain the returns of a strategy – or else that the CAPM does hold, but the assumption that the market is efficient is simply too strong. This second explanation is for sure valid for some anomalies, since these have naturally disappeared once someone revealed them, simply because investors started to exploit them. Today, we will just go through two anomalies: the value and the size anomalies. These are at the basis, for instance, of the so-called Fama and French three-factor model.

General Overview of Value and Size Anomalies

The value anomaly is probably the oldest to have been investigated in financial markets. It is known since the ‘40s, but has been formally tested only during ‘70s and ‘80s. The key variable is the Book-To-Market ratio, that is, the inverse of the P/BV ratio. According to several analysis, high BtM stocks (“Value stocks”) usually outperform low BtM stocks (“Growth stocks”), even though periods when this tendency is reversed exist. One simple explanation for this anomaly is that value stocks are basically “cheaper” from an accounting standpoint. Another more sophisticated explanation links this ratio to the riskiness of the stock – since usually companies under distress fall into this category – and thus the excess return simply points to the fact that the Beta of the CAPM fails to “highlight” this specific risk. Finally, there exists a behavioural explanation: investors are sometimes fascinated by “glamour” stocks, and tend to overpay for them, thus reducing their future returns (think for instance at the prices of tech companies during the tech bubble).

The size anomaly, instead, has been first analysed in 1981 by Banz, according to whom “small” companies, in terms of market capitalization, systematically outperformed “big” companies. Again, some explanations have been proposed. For instance, some say that this indicator is once more a source of risk: small companies tend to be more volatile than large companies, and the beta may not be a perfect indicator of this risk. Another possible explanation is that stock prices’ growth is linked to the economic growth of the company, and that since for a small company is easier to grow faster, the same may be true for its shares. However, it must be said that the size effect has since them almost disappeared.

Empirical Tests

As hinted at the beginning of this article, our purpose is to test whether these two anomalies have shown up in the European financial markets during the last five years. In order to do so, we used the STOXX Europe 600 index, which contains 600 stocks of small, mid and large companies across 17 countries in the European region. This index is thus a good choice in terms of diversification across geographical markets, capitalization (which is required to compute the size strategy) and business sectors. Its major drawback is that it includes stocks traded in different currencies, and thus some adjustments have to be made, in particular with respect to the market capitalization. The following paragraph explains how we practically performed the tests for the two anomalies.


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