Following Levy and Roll [2010], we posit that the market portfolio is the efficient tangent Markowitz portfolio, i.e., it is mean-variance efficient. We then reverse engineer the expected returns and variance terms with constraints imposed by empirical data on a hierarchy of asset baskets. This...

Performance of investment managers are evaluated in comparison with benchmarks, such as financial indices. Due to the operational constraint that most professional databases do not track the change of constitution of benchmark portfolios, standard tests of performance suffer from the look-ahead...

Zipf's law states that, for most countries, the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. We show that...

We investigate the relative information content of six measures of dependence between two random variables X and Y for large or extreme events for several models of interest for financial time series. The six measures of dependence are respectively the linear correlation and Spearman's rho...

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent b close to 3. First, we show by synthetic tests performed on time series with time dependence in the volatility with both Pareto and...

The heavy-tailed distribution of firm sizes first discovered by Zipf (1949) is one of the best established empirical facts in economics. We show that it has strong implications for asset pricing. Due to the concentration of the market portfolio when the distribution of the capitalization of...

The heavy-tailed distribution of firm sizes first discovered by Zipf (1949) is one of the best established empirical facts in economics. We show that it has strong implications for asset pricing. Due to the concentration of the market portfolio when the distribution of the capitalization of...