Exploiting Anomalies in the Risk-Return Relationship

Exploiting anomalies in the risk-return relationship

A study on momentum, the volatility-effect and the January-effect

ABSTRACT

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Table of Contents

1 Introduction        

2 Literature review        

2.1 Momentum        

2.2 Volatility Effect        

2.3 January Effect        

3 Data description        

4 Methodology        

4.1 Momentum        

4.2 Volatility Effect        

4.3 January Effect        

4.4 Regressions        

5 Results        

5.1 Momentum Results        

5.2 Volatility Effect Results        

5.3 Excess Return        

5.4 Transaction costs        

5.5 January Effect Result        

5.6 Asset Pricing Models        

6 Conclusion        

7 Bibliography        

8 Appendix        

1 Introduction

Many different investment strategies with different approaches have been described in the existing literature on anomalies. Most of them focus on the effectiveness of the particular strategies, as they are considered to provide higher risk-adjusted returns. We find three types of anomalies interesting in particular: momentum, the volatility-effect and the January-effect. Their interesting implications for asset pricing theory and the efficient market hypothesis will be discussed in this paper. A lot of research has been done on the matter. By focusing on a European setting, by only including the 100 largest European stocks in our data sample, we want to add to the existing literature on the matter.

We are interested in finding positive alphas in each of the three anomalies. Our research question focuses on whether the excess returns from momentum, the volatility-effect and the January-effect can be seen in a European setting. We will test for excess returns that result from the three strategies with respect to the CAPM and the 3-, 4- and 5-factor models.

We find that profits from pursuing a momentum strategy exist for combinations of 6(F)x6(H) and 6(F)x1(L)x6(H) at the 5% significance level, and for 9(F)x1(L)x3(H) at the 10% significance level. Overall, the momentum strategy generates an annualized return of 10% on average and we conclude that 6(F)x1(L)x6(H) is the most successful combination to exploit momentum. Regarding the volatility-effect and the January-effect, we don’t find any significant results. This may be due to our sample of European stocks, one has to remember that this research focuses on the European stock market.

This paper will proceed as follows. First, we will discuss the existing literature on the topics in section 2. This will provide the knowledge and the foundation on which we can build our research. In section 3, we provide a brief description of the data that has been used. Section 4 explains our methodology on momentum, the volatility-effect and the January-effect. The regressions that were used are also analyzed more thorough full. In section 5, we present our results on the matter. Section 6 concludes.

2 Literature review

2.1 Momentum

From the efficient market hypotheses it is known that future stock prices are not predictable, and that trading strategies that continue to outperform the market do not exist.  But a lot of financial literatures from the 70’s report that to a certain extent, future stock prices are predictable when looking at past returns. Jegadeesh and Titman (1993) published the first paper that reported the medium term momentum effect in stock prices. They documented in their paper that over a 3 to 12 month period past winners continue to outperform past losers by 1% a month.

The following formula displays the momentum effect according to Jegadeesh and Titman:

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This means that stocks () that have higher (lower) than the average cross-sectional returns () in one period also have higher (lower) than average returns in the following period (). [pic 4][pic 5][pic 6]

Momentum strategies are mostly about looking at trends in the past. The most famous and commonly used strategy is price momentum; this trading strategy involves investing based on the previous period’s stock prices. The most commonly used method for the construction of this factor is the following:  first the stocks are ranked based on their profitability of the past 3 to 12 months (the formation period is usually 3, 6, 9 or 12 months). After that the ranked stocks are divided into 10 deciles.  The portfolio containing the stocks with the highest past returns is called the winner portfolio, whereas the portfolio containing the stocks with the lowest past returns is called the loser portfolio (Sondergaard, 2010).

After the publication of Jegadeesh and Titman researchers all over the world started looking for the momentum effect in different formation periods and in different markets. Rouwenhorst found significant result for the momentum strategy in European market (1998) and in Emerging stock markets (1999). In 1998, Conrad and Kaul followed the same method and strategy as JT (Jegadeesh and Titman), with the same holding period and the same formation period. They also found that the momentum effect is very significant. So this research confirmed the result by JT. Many practitioners and researchers argued that the momentum strategy isn’t profitable, because short selling and the small positions that are needed in these strategies would entail too high transaction costs. But like JT, Korajczyk and Sadka (2004) also found that even after the inclusion of risk and transaction costs the momentum strategy is still profitable.

In recent years very different explanations are given to the momentum effect. In general there are two camps on what really causes the momentum effect. The first group argues that momentum has a risk based explanation and that the return is a compensation for the risk.  The other group argues that the explanation lies in the way investors think and behave. Hong and Stein (1999) for instance think that there are two kinds of investors, namely news watchers and momentum traders. News watchers will trade on new fundamental information, which triggers the momentum traders. Both kinds of investors drive up the price until the stock is overpriced and reverses back to its fundamental value. Other behavioural economists like Kahneman and Tversky argue that there is a disposition effect. This means investors don’t treat stock gains and losses the same way; they feel much more pain from a percentage loss than they feel joy from the same percentage gain. So when there is a profit, investors will sell faster. While when there is a loss investors hold on to their losing stocks. While there are explanations from different areas of finance, there is still no-one entirely clear explanation on what causes momentum.