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Volatility is the canonical measure of financial risk, a role largely inherited from Modern Portfolio Theory. Yet, its universality rests on restrictive efficiency assumptions that render volatility, at best, an incomplete proxy for true…
In this paper we assume a multivariate risk model has been developed for a portfolio and its capital derived as a homogeneous risk measure. The Euler (or gradient) principle, then, states that the capital to be allocated to each component…
In this paper we consider a generalization of the Markowitz's Mean-Variance model under linear transaction costs and cardinality constraints. The cardinality constraints are used to limit the number of assets in the optimal portfolio. The…
Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that is generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first…
The mean and variance of portfolio returns are the standard quantities to measure the expected return and risk of a portfolio. Efficient portfolios that provide optimal trade-offs between mean and variance warrant consideration. To express…
We study the feasibility and noise sensitivity of portfolio optimization under some downside risk measures (Value-at-Risk, Expected Shortfall, and semivariance) when they are estimated by fitting a parametric distribution on a finite sample…
We extend and test empirically the multifractal model of asset returns based on a multiplicative cascade of volatilities from large to small time scales. The multifractal description of asset fluctuations is generalized into a multivariate…
We introduce new mathematical methods to study the optimal portfolio size of investment portfolios over time, considering investors with varying skill levels. First, we explore the benefit of portfolio diversification on an annual basis for…
We build the time series of optimal realized portfolio weights from high-frequency data and we suggest a novel Dynamic Conditional Weights (DCW) model for their dynamics. DCW is benchmarked against popular model-based and model-free…
The instability of historical risk factor correlations renders their use in estimating portfolio risk extremely questionable. In periods of market stress correlations of risk factors have a tendency to quickly go well beyond estimated…
Machine learning (ML) methods have been successfully employed in identifying variables that can predict the equity premium of individual stocks. In this paper, we investigate if ML can also be helpful in selecting variables relevant for…
In portfolio risk minimization, the inverse covariance matrix of returns is often unknown and has to be estimated in practice. This inverse covariance matrix also prescribes the hedge trades in which a stock is hedged by all the other…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
We derive new results related to the portfolio choice problem for power and logarithmic utilities. Assuming that the portfolio returns follow an approximate log-normal distribution, the closed-form expressions of the optimal portfolio…
This paper considers the mean-reverting portfolio design problem arising from statistical arbitrage in the financial markets. The problem is formulated by optimizing a criterion characterizing the mean-reversion strength of the portfolio…
This study presents an ANWSER model (asset network systemic risk model) to quantify the risk of financial contagion which manifests itself in a financial crisis. The transmission of financial distress is governed by a heterogeneous bank…
We introduce a new set of consistent measures of risks, in terms of the semi-invariants of pdf's, such that the centered moments and the cumulants of the portfolio distribution of returns that put more emphasis on the tail the…
In the market place, diversification reduces risk and provides protection against extreme events by ensuring that one is not overly exposed to individual occurrences. We argue that diversification is best measured by characteristics of the…
In order to properly manage risk, practitioners must understand the aggregate risks they are exposed to. Additionally, to properly price policies and calculate bonuses the relative riskiness of individual business units must be well…
Classical portfolio optimization methods typically determine an optimal capital allocation through the implicit, yet critical, assumption of statistical time-invariance. Such models are inadequate for real-world markets as they employ…