Practical Value at Risk and Expected Shortfall Estimation for Securities Market

Proceedings of The International Conference on Research in Business, Management and Finance

Year: 2019


[Fulltext PDF]

Practical Value at Risk and Expected Shortfall Estimation for Securities Market

Yam-wing SIU



Formally, Value at risk (VaR) measures the worst expected loss over a given horizon under normal market conditions at a given confidence level (Jorion, 2007). However, there are several weaknesses of VaR. Therefore, under Basel’s latest revised market risk framework, it can be seen that Basel has shifted banks’ capital regulatory requirements from value-at-risk to an expected shortfall approach. The choice of the holding period and confidence level are relatively subjective and they may depend on regulatory requirement. Very often, daily data are used to compute VaR and ES and scale up to required time horizon with square root of time adjustment. This gives rise to two important questions when we perform VaR and ES estimations: 1) whether non-overlapping and overlapping of data windows should be used for determining VaR and ES and 2) whether the values of VaR and ES (ie. “loss”) should be interpreted as within i days or exactly on ith day.
Preliminary numerical simulation results, after matching the descriptive statistics of Standard and Poor’s 500 Index, show that, in determining the proportionality of the values of VaR and ES versus the holding period, using overlapping windows is just as fine as (if not better than) using non-overlapping windows. It is because the way we determine values of VaR in this study is simply locating -percentile in the cumulative loss distribution for exactly on ith day or maximum cumulative loss distribution for within i days respectively. There is no regression estimate of volatility.

Keywords: Basel; expected shortfall; market risk, numerical simulation; value at risk.