The purpose of this research is the realistic forecast of volatility in frame of a risk parity class of strategies. The custom rescaling of volatility – naïve risk parity - doesn't consider market inefficiencies which correspond to cyclical patterns like crisis and the following recovery. The...

Demonstration of the omnipresence of noise in volatilities of returns of financial instruments.Demonstration that more than 30% of SP500 securities can have percentage change in volatility of more than 10% as a result of noise filtering.In our white paper “Filtering Noise From Correlation...

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...

This paper discusses the way Value-at-Risk (VaR) measurement can be applied to oil refining, a fully liberalized industry which is largely exposed to price risk. After a description of the industry, the calculation of a single asset VaR, such for a crude oil purchase, it is introduced....

This paper considers the problem of measuring the exposure to dependence risk carried by a portfolio with an arbitrary number of two-asset derivative contracts. We develop a worst-case risk measure computed over a set of dependence scenarios within a divergence restricted region. The set of...

We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure ρ on L1. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical...

Various concepts appeared in the existing literature to evaluate the risk exposure of a financial or insurance firm/subsidiary/line of business due to the occurrence of some extreme scenarios. Many of those concepts, such as Marginal Expected Shortfall or Tail Conditional Expectation, are simply...

This article presents a simple methodology for computing Value at Risk (VaR) for a portfolio of financial instruments that is sensitive to market risk, rating change, and default risk. An integrated model for market and credit risks is developed. The Jarrow, Lando and Turnbull model (the Markov...

This paper presents a methodology to analyze the Value at Risk (VaR) backtesting probability values to detect the soundness of the VaR model, the integrity of the VaR input and output as well as providing information about the type of the risk that a subportfolio is exposed to in every trading...

Analytical portfolio risk calculations can be derived and computed in matrix form. Since the inputs are linear asset returns, the calculation outputs as percentages, eg, Portfolio Analytical VaR would be a percentage itself and not a dollar number. Marginal Contributions and Expected Shortfall...