The purpose of this article is to gain a concrete understanding of the perception of Value at Risk, its strengths and weaknesses, and controversies related to its use in managing risk. Two articles will be used to help with the understanding of VaR, “An Irreverent Guide to Value at Risk,” by Barry Schachter and “Subjective Value-at-Risk,” by Glyn Hoyt. These articles will give us some background by describing VaR, understanding its limits, and its developing role in risk management.
Article 1 “An Irreverent Guide to Value at Risk”
Value at Risk has been called the “new science of risk management.” Around the world, organizations are sprinting to implement the new technology.
This is a lot to ask for and it's something that cannot be delivered without compromises. VaR and Standard Deviation are both related measures of a distribution of returns. The Modern Portfolio Theory (“MPT”) tells us that the risk in a portfolio can be measured by the portfolio standard deviation, a calculation of spread in a distribution. Unfortunately, and particularly when related to hedge funds, standard deviation does not capture to total risk picture of returns. This is because most hedge funds do not have normally distributed returns.
Standard deviation, according to MPT, is the relevant information needed to construct risk limits for optimal risk management decisions. But when looking for the Holy Scale, standard deviation loses its application in MPT. When thinking about risk, managers tend to think in terms of loss of dollars, whereas standard deviation looks at volatility in terms of deviations, either above or below. This means that its expected return is not always clear. Another reason why standard deviation isn't the Holy Scale is because it assumes symmetry, everything that happens on one tail will happen to the other. But when we look at trading portfolio deviations of any amount below the expected return, they are not equal and do not happen when the deviations are above the expected return. This shows us that a different means for measuring risk is needed, and maybe the Holy Scale has been discovered in VaR.
3 Ways to Calculate VaR
VaR is evolving and should be experimented on, but when it comes to choosing the “best practice” many have come to find that there isn't one. The author titles this part of his article The Slip 'Twixt Cup and Lip, which implies that even when the outcome of an event seems certain, things can still go wrong.
VaR is typically calculated by first modeling the entire returns distribution for a position of a portfolio, then calculating the value at the percentile corresponding to the desired confidence level. There are three common methodologies for doing this: Historical Simulation, Parametric Modeling, and Monte Carlo (stochastic) simulation. These methodologies along with their advantages and disadvantages are discussed in more detail below. Parametric VaR is calculated by the following formula: mean- # of standard deviations * standard deviation. The historical simulation method consists of going back in time and applying current constraints to a time-series of historical asset returns. This return doesn't represent an actual portfolio, but rather recreates the history of a hypothetical portfolio using the current position. Instead of using past values of market factors for prediction, the stochastic simulation uses a method of financial molding in which one or more variables in the model are random. All three of these models have strengths and weaknesses.
The parametric method has the benefit of being computationally fast for linear assets, but has a problem with...