1. How Should Mutual Fund Behavior and Performance React to Fund Size? The Role of Liquidity Frictions (with L. Lecesne)
A large strand of empirical finance literature has documented the effect of fund size on fund performance. A major channel conveying this link has been shown to be represented by liquidity frictions. We propose a theoretical model describing this phenomenon and apply it to the identification of mutual fund's optimal allocation decision in presence of liquidity constraints under varying assumptions about investment style and fund size. First, we devise a way to allow for asset prices and their portfolio composition deviate from the corresponding marked-to-market values in light of liquidity constraints featuring actual trading places. Next, we analyze the impact of alternative liquidity-linked sub-linear valuations on investment funds' optimal portfolio allocation based on target risk-adjusted performance measures, including Sharpe Ratio and RAROC. Last, we unveil the remarkable effect of allocation preference order inversion stemming from accounting for liquidity constraints, a property allowing us to explain the empirical phenomenon whereby increasing capital invested in low-cap funds often entails a performance decrease.
2. Market Inefficiency, Agents' Expectations, and Price Forecasting (with S. Galluccio and G. Pagliardi)
Time series forecasting is dominated by Mean Square Error (MSE) minimization, a method that is known to be optimal in a Gaussian setting. However, the vast majority of financial time series exhibits sharp deviations from a two-moment setting, including skewed and leptokurtic return distributions. Moving from partial results in the theory of signal optimization, we discover and develop a new class of estimators based on a variety of Entropy Error minimization. They involve finite dimensional as well as functional optimization problems in a suitable Frechet space. We test performance on simulated realization of stochastic processes driven by non-Gaussian noise and assess the empirical performance on high-frequency data stemming from financial markets. We show that our estimators outperform MSE schemes on a variety of target functionals and apply the methods to oil price forecasting.
3. How Firms Should Hedge Non-Tradable Risk? (with P. Guiotto)
Corporate portfolios often show joint exposure to both tradable and non-tradable revenue and cost related components on a varying extent. Given a financial endowment put forward by a firm for risk mitigation purposes, we design the best pair of tailor-made derivatives they may buy using that endowment in order to optimally mitigate the combined effect of tradable and non-tradable risk terms. One hedging instrument pays off a non-linear function of the tradable component of firm exposure, which may identified as a market price or index; the other product is a non-linear contingent claim written on any other quoted price or index exhibiting statistical dependence to the underlying non-tradable term via an arbitrary copula functions with assigned density. We derive closed-form expressions for the optimal hedging pair under minimal assumptions about the underlying model setting. In general, any solution satisfies a 2-dimensional Fredholm system of equations, whose solution is derived using the method of sequential approximation. Exponential convergence is proved in all possible non-degenerate cases.
4. Towards a General Theory of Arbitrage-Free Commodity Prices (with R. I. Brik)
Arbitrage models of commodity price arise through a variety of frameworks. We investigate the theoretical relationship between models grounded on characterization of the underlying commodity economics and those accounting for stylized facts about commodity price evolution. The mathematical structure underlying the interplay between these settings is unveiled as a sequence of increasingly complex fundamental forms, which we characterize in full detail. Five statements have been conjectured and proved using analytical tools we developed for the purpose. While analyzing implications of framework switching to model construction, extension and statistical estimation, we show a way to skip using Kalman filter for estimating models with hidden variables, a method known to leaves most of nonlinearities between forward prices and state variables unaccounted for.
Andrea Roncoroni >