Factor taxonomy

Macroeconomic variables constitute the first set of potential risk factors that can be assumed to be rewarded by the market. They are intended to capture the state of the economy or to forecast future economic conditions. Commonly employed macroeco-nomic factors include interest rates, production growth, consumer confidence, credit spreads, steepness of the yield curve and shifts in energy prices. Macroeconomic factor models with multiple betas, where each beta relates an asset to a particular economic risk, allow fund managers to gain top-down insights into how their portfo-lios are affected by different economic scenarios. Alternatively, fundamental factor models assume that sensitivities to firm characteristics such as the price-earnings ratio (PE), leverage or size are capable of explaining the cross-section of returns.

Although it is not yet clear which systematic risks are approximated by fundamental factors, this second type of model has been very successful empirically. Employing the third type of factors, momentum models are based on the empirical finding that past return patterns may offer an indication of future returns. In contrast to those factor categories, statistically derived factors are not observable and have to be inferred from the return data using statistical factor selection procedures.

7.1.1.1 Macroeconomic factors

The possibility that macroeconomic factors may successfully predict security returns has spawned a remarkable bulk of literature that analyzes whether stock and bond returns can be predicted using macroeconomic variables. One of the best known studies is that of Chen et al. (1986). In an APT framework, the authors implement expected and unexpected inflation, industrial production, the spread between short-and long-term interest rates short-and the default premium, defined as the yield spread

between high and low rated bonds. The chosen risk factors are found to be signif-icantly priced. The predictive power of the default premium has been confirmed, among others, by Fama and French (1989) and Keim and Stambaugh (1986). The results presented by Campbell (1987) imply that excess stock returns are predicted by the state of the term structure of interest rates. A further indication of the im-portance of interest rates as well as their volatility is provided by Shanken (1990).

In an analysis of the source of predictability of monthly stock and bond returns, Ferson and Harvey (1991) look at a set of state variable proxies: the value-weighted New York Stock Exchange index return less the 1-month Treasury-bill return, per capita growth of personal consumption expenditures, unanticipated inflation, the yield spread between Baa-rated corporate bonds and a long-term government bond, the change in the slope of the yield curve, the real 1-month Treasury-bill return and the dividend yield on the S&P 500. In a later study on risk and predictability of international equity returns (Ferson and Harvey, 1993) the authors add a dollar and an oil price factor. Jones and Kaul (1996) explicitly document the impact of changes in the oil price on the stock market. In another application, Chan et al. (1998) use the growth rate of monthly industrial production, the default premium, the real interest rate defined as the difference between the return on one-month Treasury-bills and the relative change in the monthly consumer price inflation, the slope of the yield curve, the change in the monthly expected inflation and the maturity pre-mium, defined as return difference between long-term government bonds and the one-month Treasury-bill rate, as macroeconomic variables. The authors conclude that only the default and the maturity premium are significantly related to stock returns. In a work on maximized predictability in stock and bond markets in the US, Lo and MacKinlay (1997) rely on the dividend yield, the default spread, the maturity spread, the return on the S&P 500 and an interest-rate trend, calculated as the change of average yields on a long-term government bond. More recently, Lettau and Ludvigson (2001) successfully employ the log consumption-wealth ratio as a conditioning factor.

7.1.1.2 Fundamental factors

The second category of factors is related to firm-specific attributes. Various empir-ical studies have illustrated that it is possible to earn risk-adjusted returns by con-structing portfolios in accordance with fundamental factors. Basu (1977) finds the PE effect: firms with low PEs have higher sample returns and firms with high PEs have lower sample returns than can be expected in the context of a mean-variance efficient market portfolio. Banz (1981) documents the size effect with higher than expected returns for firms with a small market capitalization. Bhandari (1988) docu-ments a positive relationship between average returns and leverage. Rosenberg et al.

(1985) report the so-called value premium, where the average returns are positively related to the book-to-market equity ratio, which is defined as a company’s book

value (BV) to its market value (MV). At the beginning of the 1990s, Chan et al.

(1991) confirms the value premium also for Japanese equities. Subsequent studies, see, for example, Fama and French (1993, 1995, 1998), Lakonishok et al. (1994) and Daniel and Titman (1997), gave further confirmation of the book-to-market anomaly and tried to find different explanations for the value premium. In today’s portfolio management industry, the most important investment style is based on the value premium: a value investor invests in firms with the highest book-to-market ratios, which means investing in the relatively cheapest value companies.

Fama and French (1992, 1996) developed a more comprehensive framework. In-stead of conducting individual analyses for the various anomalies, they take the interdependencies between the different variables explicitly into account. They ana-lyze the empirical relationships between the expected return of a stock, its beta and other fundamentals such as size, book-to-market equity, leverage and earnings-price ratios. Their work is considered a milestone as they interpret the combination of different variables as a multidimensional measure for risk. The most widely used fundamental multifactor model, which dominates today’s empirical research, is the three-factor model by Fama and French (1993). It explains the cross-section of ex-pected returns by three factors: a market proxy, size and the book-to-market ratio.

Even though a solid economic theory explaining which non-diversifiable risks are proxied by size and book-to-market still has to be developed, these two factors ex-plain average returns better than the theoretically easier to justify macroeconomic factors (cf. Cochrane, 2005, 20).

7.1.1.3 Momentum and reversal

Research on momentum and reversal strategies has started with the works of DeBondt and Thaler (1985, 1987) who report price reversals over the long-term (three to five years) where stock prices overreact and eventually mean-revert. The authors demonstrate that a portfolio that is long past losers and short past long-term win-ners, yields a better performance than a portfolio constructed in the opposite way.

Jegadeesh (1990) finds that price reversals also occur over the very short term (one week to one month). Over the medium term (three to twelve months) Jegadeesh and Titman (1993, 2001) and Chan et al. (1996) document price momentum effects:

past winners continue to outperform past losers.

Long-term price reversals are consistent with the Fama-French three-factor model, because stocks that do poorly over a long time horizon build up a value premium.

By contrast, short-term reversals and price momentum cannot be explained by the Fama-French model. Some authors relate momentum profits to microstructure ex-planations such as calendar or illiquidity effects; see Cochrane (2005, 20) for an overview. However, once transaction costs are taken into account, momentum and reversal strategies, which both require frequent trading, are not exploitable as shown by Carhart (1997). Therefore, given these non-supportive arguments together with

the findings of Grundy and Martin (2001), who conclude that momentum strategies are even less attractive when applied to sectors instead of single stocks, momentum and reversal effects will not find any consideration in the following.

7.1.1.4 Statistical factors

An alternative to employ macroeconomic or fundamental variables is to derive the factors statistically. Instead of using observable real world variables, the factors are inferred from the return data by applying statistical factor selection procedures. The two primary approaches are a two-step factor analysis and principal components;

see Campbell et al. (1997, 6) for a summary. Statistical factor models yield the advantage that no external explanatory variables are required and that they provide an answer to the number of unknown factors. Moreover, one does not have to deal with problems related to multicollinearity as the statistically derived factors are usually orthogonal. However, despite their attractive in-sample features, their out-of-sample performance is usually poor (cf. Chan et al., 1998). Besides, purely statistical factors do not offer an economic interpretation. In this thesis statistically derived factors will not be considered as risk factors.