PORTFOLIO

"Optimal Portfolios with Random Environments, Frictions and Incentives"

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 Obiettivo del progetto (Objective)

'This project focuses on a class of portfolio choice problems arising in Mathematical Finance. These problems share a common relevance for financial applications, and lead to novel mathematical questions, mainly in the area of Stochastic Processes. Research is proposed on dynamic portfolio choice with: (i) Random Environments; (ii) Trading Frictions; and (iii) Incentive Fees. Random environments encompass those asset pricing models in which interest rates, risk premia, and covariances may depend on state variables. These model are important because recent empirical investigations show that variables such as the dividend yield, or earnings/price ratios drive expected returns, paving the way to multifactor models. Transaction costs lead to similar technical questions, although for conceptually different reasons. State variables arise in these models implicitly, through the notion of shadow prices. This partial isomorphism between market frictions and random environments suggests that transaction costs have an hidden potential as tools for explaining pricing anomalies. Incentive fees, traditionally neglected as minor imperfections, are now actively studied for their role in shaping the behavior of intermediaries. For example, high-water mark contracts, now prevalent in the hedge-fund industry, have ambiguous effects on fund managers. Understanding these effects is crucial for evaluating the potential consequences of regulation. In summary, the proposed problems share a common relevance, and similar technical features, which require novel mathematical tools. This project aims at developing these tools, and at bringing to life their implications.'

Introduzione (Teaser)

Better understanding of advanced probability theory may help improve how financial markets operate. A series of findings and publications on the topic is set to achieve this aim.

Descrizione progetto (Article)

Mathematical finance, which takes observed market prices as input, represents an important field of applied mathematics that supports financial markets. For mathematical finance to succeed, however, it requires advanced probability theory where a stochastic or random process tracks the evolution of a system of random values.

Against this backdrop, the EU-funded project 'Optimal portfolios with random environments, frictions and incentives' (PORTFOLIO) explored a specific class of challenges in choice of portfolios that arise in mathematical finance. Specifically, it looked at how a common relevance across these problems can be relevant for applications, bringing forth new mathematical questions in the area of stochastic processes.

To achieve its aims, the project team investigated dynamic portfolio choice with random environments, outlining a way to derive optimal portfolios and risk premiums. It proved static fund separation theorems for investors with a long-term horizon and constant relative risk aversion, and with stochastic investment opportunities. The team also proved three kinds of portfolio turnpikes, in addition to examining consumption in incomplete markets.

The second part of the project looked at different trading frictions, such as asset pricing under transaction costs, and the dynamics between transaction costs, trading volume and liquidity premium. Topics also included high risk aversion, endogenous spreads and dynamic trading volume.

Lastly, the project studied incentive fees, particularly performance maximisation of actively managed funds, as well as incentives of hedge fund fees and high-water marks. It also explored topics such as robust portfolios and weak incentives in long-run investments, in addition to hedge and mutual funds' fees and the separation of private investments.

Several publications and/or papers have been published on these separate topics, with more publications on the way. These analyses and investigations are expected to yield novel mathematical tools that will refine the study of financial markets and ultimately help improve how they operate.