's preference by a power utility function leading to constant relative risk aversion. We show that the loss in expected utility is … analytical results that show how the sparsity of the constrained portfolio depends on the coefficient of relative risk aversion …>-norm for each level of relative risk aversion …

Shortfall – PSF – uses option theory to solve the problem that, under any circumstance, the risk amount is never greater than …This paper derives two new improved risk metrics LAPVaR and LAPSF. Traditional VaRDeltaNormal valuation exaggerates … the portfolio value. Risk to LIQUIDATION means every day-t, a portion of portfolio assets-i, for integer i ϵ (1, N) is …

This paper presents a methodology to analyze the Value at Risk (VaR) backtesting probability values to detect the … risk that a subportfolio is exposed to in every trading day. The paper presets statistical methods to back test the number …-values using the run test. Finally a model is presented to decompose the subportfolios' P&L risk into systematic and idiosyncratic …

This paper investigates whether multivariate crash risk is priced in the cross- section of expected stock returns …. Motivated by a theoretical asset pricing model, we capture the multivariate crash risk of a stock by a combined measure based on …. We find that stocks with a high exposure to joint crashes of the market and the momentum factor bear a risk premium which …

risk measures for portfolios with infrequently traded securities have not been explored in the literature. We propose a … methodology to calculate market risk measures based on the Kalman filter which can be used on incomplete datasets. We implement … applied to other markets with thinly traded securities. Our methodology provides reliable market risk measures in portfolios …

We merge the literature on downside return risk and liquidity risk and introduce the concept of extreme downside … same time when the market liquidity (return) is lowest. This effect is not driven by linear or downside liquidity risk or … extreme downside return risk and is mainly driven by more recent years. There is no premium for stocks whose liquidity is …

Liquidity has its systemic aspect that is frequently neglected in research and risk management applications. We build a …

The so-called risk diversification principle is analyzed, showing that its convenience depends on individual …