An optimal portfolio with the highest possible Sharpe ratio plays an important role for capital allocation and performance evaluation. This paper introduces a simple algorithm for finding the Sharpe-optimal portfolio without solving a non-linear problem. The results are tested on S&P 100...

Many practitioners annualize VaR just like the standard deviation. We show that this approach is incorrect, and a more sophisticated formula should be used for deriving a periodic VaR from parameters of the daily returns distribution. Another problem addressed here is the distribution of daily...

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk...

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk...

The metalog distributions represent a convenient way to approach many practical application. Their distinctive feature is simple closed-form expressions for quantile functions. This paper contributes to further development of the metalog distributions by deriving the closed-form expressions for...

Conditional Value-at-Risk (CVaR) represents a significant improvement over the Value-at-Risk (VaR) in the area of risk measurement, as it catches the risk beyond the VaR threshold. CVaR is also theoretically more solid, being a coherent risk measure, which enables building more robust risk...

Some researchers have recently criticized using the normal distribution for modeling stock returns. While it's true that the normal distribution is inappropriate and leads to the extreme outliers, known as the Black Swans problem, other elliptical distributions allow addressing this issue. The...