Value-at-risk (VaR) models, which were blamed by many for the financial crisis, continue to play a central role in understanding risks in investment portfolios. As much as regulators deny it, VaR is hard-wired into the global financial system.
VaR provides investors with an estimate of the worst expected loss that might occur within a specified time period. The number is expressed at a certain confidence level – for example, a five-day 99% VaR of $100 million means that in one out of 100 days a portfolio could lose more than $100 million over a five-day period.
Risk managers who rely on VaR have in recent weeks been keen observers of the Japanese bond market, where an exceptional rise in volatility has raised concern that some banks might breach VaR limits and be forced to dump JGBs, leading to the possibility of a pro-cyclical rout.
That view is largely predicated on a perception of VaRs role before and during the credit crisis, when it was alleged distorted VaR models allowed certain firms to take on more leverage than they could handle.
The reason is that the VaR measure has an Achilles heel, which is that while it is good at measuring the chances of a loss over a certain amount, it offers no indication of what those losses might be.
In not being able to quantify tail losses, an investor might know their chance of losing more than $100 million, but not how much more. Some say that failure in the model was directly connected to the accumulation of leverage before the financial crisis.
“Because VaR does not take account of tail losses, there is an argument to say that firms leading up to the financial crisis were able to hold much less capital against their trading book and so take much more leverage, and fund this in the short-term wholesale markets,” says Amir Khwaja, CEO at London-based Clarus Financial Technology.
“Once the crisis hit and short-term wholesale funding dried up, some firms simply did not have enough capital to meet the liquidity crunch. One could argue that VaR was culpable in this failure.”
Another issue with VaR highlighted by the financial crisis was limits in its range of application. The formula is usually expressed in terms of a number of days, usually to a maximum of 10. However, when losses stretch over weeks and months, as they did during the crisis, VaR has no answer.
In addition, the model works well for liquid markets in which positions can be unwound quickly but does not provide for illiquid securities for which prices might not be available.
Despite the seemingly fundamental damage to its reputation, VaR has not gone away. Instead, industry participants have looked to address its weaknesses, largely by introducing measures of tail risk to the simulation.
“VaR remains useful and is employed across the industry for many purposes, from risk management to margin calculations and regulatory capital,” says London-based consultant Bill Hodgson. “It’s still widely used and over recent years people have improved and adapted their specific implementations to reflect regulatory requirements and market feedback.”
Banks have looked to mitigate holes in the model in two ways – through the concepts of expected shortfall and worst-case loss, both of which aim to give risk managers an idea of the scale of potential losses should the VaR model be breached.
In simple terms, expected shortfall is the average of all scenarios beyond VaR, while worst-case loss is the biggest-loss scenario, and both are commonly used by banks and others alongside internally designed models of stress-testing.
Regulators have aimed to achieve the same result through the concept of stressed VaR, which requires banks to simulate VaR scenarios using periods of extreme market volatility to calculate capital against market losses in the trading book.
Whether or not these additional measures work is a moot point. The most egregious recent example of that not being the case were the losses accumulated by JPMorgan Chase trader Bruno Iksil, known as the London Whale. Iksil lost more than $2 billion in 2012 after the formula used to calculate his VaR was changed, US SEC chairman Mary Schapiro told a congressional panel last May.
JPMorgan has not provided details of the specific changes to Iksil’s VaR model, which cut the reported risk by half, but industry sources say it was focused on how the risks within Iksil’s portfolio were measured.
“From what I understand, the VaR model did not capture basis risk,” says a senior quant based in New York. “The model which produced the higher number decomposed the portfolio into single names whereas the model which produced the lower number did not do that decomposition.”
While the details have yet to be divulged, the Iksil case highlights that while VaR models can be improved, they can also be tweaked to suit individual purposes, suggesting a key parameter remains the human element.
“A good model is all about good governance,” says the senior quant. “There is always a certain amount of discretion over how you manage risks and if banks want to do that then there is nothing the model can do about it.”