Multi-factor Models and Factor Timing: A Dynamic Multi-factor Portfolio Approach: A Dynamic Multi-factor Portfolio Approach

Abstrakt

In the search for alpha and higher risk-adjusted returns, we have focused on two approaches popular among practitioners and academics: factor investing and macro indicators. Factor investing was made popular when Fama and French (1993) presented their famous three-factor model. Since then, all kinds of different factors have been explored and proven to provide significant alpha or describe returns not captured by the initial three-factor model. In a similar manner, different macroeconomic indicators have been documented to move together with, or have prediction power over the stock market. A relationship between some of the factor returns and the general stock market return has also been proven, but few have explored the direct relationship between the factor returns and macro indicators. We build multi-factor models consisting of seven different established factors: size, value, profitability, investment, momentum, quality and betting against beta. Using the factors, we build three different multi-factor models. The first and simplest model is an equally weighted portfolio of all the factors. The second model is a dynamic approach to Markowitz’ (1952) mean-variance model with a rolling sample window. A response to some observable macroeconomic state variables, namely the shortterm interest rate, term spread and dividend yield, is implemented following the methodology of Brandt and Santa-Clara (2006) to the third model. For the U.S. market in the period 1978 - 2017, we test whether a multi-factor portfolio in fact is better than any single-factor portfolio, and further if the timing strategies of the factor allocation improves the returns even more in terms of Sharpe ratio and market neutrality. We find that when going from a single-factor portfolio consisting of the best performing factor to the equally weighted portfolio, the Sharpe ratio increases by 23%, while the dynamic mean-variance model increases the Sharpe ratio with further 31%. Adding state variables to the dynamic approach, we achieve a Sharpe ratio of 1.64, which is a further 9% increase. This is done by fitting the model for the best combination of covariance matrix shrinkage and the length of the rolling window for both of the mean-variance models. By performing empirical analysis of the model performances, we find the improvements to be statistical significant for our in-sample data. Applying the pre-determined variables from the fitted U.S. models to our out-of-sample markets, Europe and Japan, we test whether the models are applicable to the other markets and thus work as trading strategies. We find the U.S. models to work similarly in Europe, but not in Japan. Here we find the equally weighted portfolio to be the best performing portfolio. This is because the equally weighted portfolio still benefits from the diversification, but the dynamic modelsfail to time the factor exposure. As an explanation to the failed factor timing, we argue the results are due to poor iii consistency in returns among the different factors which leaves us with no exploitable trends. The poor consistency in factor returns is documented by running a factor momentum strategy