This paper contributes to the literature on cryptocurrencies, portfolio management and estimation risk by comparing the performance of naïve diversification, Markowitz diversification and the advanced Black-Litterman model with VBCs that controls for estimation errors in a portfolio of...

We introduce and solve an optimal asset allocation problem under a weighted expected shortfall (WES) constraint, which contains the risk management problem under an expected shortfall constraint of Basak and Shapiro (2001) as a special case. Furthermore, we link our risk management problem under...

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in and are present also in at least thirty other papers referencing it, including the recent survey on...

This paper examines the effects of liquidity on stock and portfolio risk measures by analyzing Value at Risk (VaR). Using daily stock returns and firm market capitalization, empirical calculations confirmed that VaR has not yet succeeded to prove patterns of relation between risk and liquidity,...

We propose a new approach to portfolio optimization by separating asset return distributions into positive and negative half-spaces. The approach minimizes a newly-defined Partitioned Value-at-Risk (PVaR) risk measure by using half-space statistical information. Using simulated data, the PVaR...

The plain market-beta was a good predictor of stock returns not only during bull and ordinary markets, but also during bear markets and crashes. Thus, it was indeed a good measure of the hedge against market risk. This plain beta also predicted the subsequent down-beta (i.e., measured only on...

Return jumps on equities exhibit slowly-decaying tail behavior admitting severe downside risk; moreover, heavy-tailed jump size distributions governing these rare events pose further challenges to econometric estimation. This paper formulates a portfolio choice problem in a multi-asset...