Determining the independence of various measures of financial risk

Maberley, Ed and Wilkins, Andy (2007) Determining the independence of various measures of financial risk. Australian and New Zealand Mathematics in Industry Study Group > 24th MISG [Wollongong 5/2/2007 - 9/2/2007].

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Problem Statement

There are three most common measures of financial risk, which represent a risk-reporting backbone of any Energy Company:
• Value-at-Risk (VaR) is defined to be the largest net change (not necessarily the loss) of the position or portfolio’s future value within a given confidence level.
• Profit (or Earnings)-at-Risk (PaR or EaR) – measures probable loss in Earnings due to market or volumetric movements within a given confidence level.
• PCE (Potential Credit Exposure) - risk of losses caused by a counterparty or an issuer defaulting on their payment obligations within a given confidence level. In absence of corrections due to credit ratings, very similar to the above two.
To our best knowledge, there have been no rigorous mathematical investigations into how mutually independent these measures are. It seems plausible, that the mathematical transformation might exist, which would map VaR onto EaR or PCE. If this is the case, then there would be no need in costly and time consuming redundant calculations and reporting. It will generate significant savings for Energy Companies by making their reporting framework more streamlined, transparent and risk-compliant.

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