Ludovic Cales

Portfolio Symmetry and Momentum

This paper presents a theorical framework to model the evolution of a portfolio whose weights vary over time. Such a portfolio is called a dynamic portfolio. In a first step, considering a given investment policy, we define the set of the investable portfolios. Then, considering portfolio vicinity in terms of turnover, we represent the investment policy as a graph. It permits us to model the evolution of a dynamic portfolio as a stochastic process in the set of the investable portfolios. Our first model for the evolution of a dynamic portfolio is a random walk on the graph corresponding to the investment policy chosen. Next, using graph theory and quantum probability, we compute the probabilities for a dynamic portfolio to be in the different regions of the graph. The resulting distribution is called spectral distribution. It depends on the geometrical properties of the graph and thus in those of the investment policy. The framework is next applied to an investment policy similar to the Jeegadeesh and Titmans momentum strategy [JT1993]. We define the optimal dynamic portfolio as the sequence of portfolios, from the set of the investable portfolios, which gives the best returns over a respective sequence of time periods. Under the assumption that the optimal dynamic portfolio follows a random walk, we can compute its spectral distribution. We found then that the strategy symmetry is a source of momentum.

Long-Term Portfolio Management with a Structural Macroeconomic Model

The aim of this paper is to investigate long-term portfolio management in a fully structural macro- financial framework. First, we estimate a Dynamic Stochastic General Equilibrium (DSGE) model that describes the dynamic of the US economy and financial markets. In addition to the typical macro-economic variables, the model includes fi nancial variables such as rm market values, dividend payments, and long-term government bond returns. The model provides us with long-term forecasts of key variables, which are used for the dynamic asset allocation of long-horizon investors. We show that the DSGE model outperforms an unrestricted VAR model in long-term portfolio allocation.

Cross-Sectional Analysis Through Rank-Based Dynamic Portfolios

The aim of this paper is to study the cross-sectional effects present in the market using a new framework based on graph theory. Within this framework, we represent the evolution of a dynamic portfolio, i.e. a portfolio whose weights vary over time, as a rank-based factorial model where the predictive ability of each cross-sectional factor is described by a variable. Practically, this modeling permits us to measure the marginal and joint effects of different cross-section factors on a given dynamic portfolio. Associated to a regime switching model, we are able to identify phases during which the cross-sectional effects are present in the market.