Editorial Open Access

Deviation Measures

Abstract

Variance reduction, or standard error reductions, is a well-known element of classic portfolio management. Standard deviation, on the other hand, has been criticised since it fails to account for the phenomena of "fat tails" in cost probabilities and penalises highs and lows alike. Value-at-risk, or VaR, is a more prevalent tool in practical scenarios than confidence interval. However, due of mathematical flaws (lack of curve and homogeneity, as well as appropriate continuity), and its incapacity to adapt to the size of prospective losses underneath the limit it finds, it has also been problematic. Conditional valueat-risk, CVaR (also called as difference and tail-VaR in some settings), a similar concept, has proven to be superior in several regards and hence more appropriate for the optimizing of financial planning decisions. A theory linking these diverse strategies and enabling their impacts to be evaluated is vital for solid financial strategy. It pioneered the concept of a cohesive risk measure, showing that VaR lacked cohesiveness. Despite the fact that there was a lot of motivation, "coherency" hasn't really taken hold in the application community. The axiom, which deals with made by adding a fixed to the output of a financial random variable, has been one stumbling block. Despite its explanations, many people were questioning that premise. It's possible that this difficulty stems from a misunderstanding of the term "loss." Loss denotes a negative consequence, although many practitioners interpret it to mean a shortfall in comparison to expectations. This is exacerbated by the fact that, in most applications, VaR and CVaR are used to evaluate such shortfalls rather than pure loss.

Karrie Williams