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Value-at-risk (VAR)
Risk Quantum
Bank of America saw tail trading risk blow up last year, as the gap between lower- and higher-confidence value-at-risk measures widened to the highest in at least 10 years.
Over the year, one-day VAR averaged $129 million when measured at a 99% confidence level, but only $40 million under a 95% interval – the widest gap, in absolute terms, since 2013, when the bank first disclosed comparable measures.
In proportional terms, the higher-confidence figure was 223% higher than the lower-confidence one, up from 194% in 2021 but still well below 2020’s record 266% divergence.
Compared with 2021, the gap between the two averages widened the most within covered positions, the core trading portfolio, going from $27 million to $41 million. The distance was widest within credit risk – $28 million under 95% VAR, $71 million at 99% confidence – though the gap was down compared with 2021.
‘Less liquid’ exposures and fair-value loans exhibited the biggest gulf, in proportional terms, across the two VAR measures, with higher-confidence values 443% and 264% higher, respectively.
VAR measures the potential loss due to adverse market movements over a defined time horizon to a specified confidence level. The figures used in the article related to losses over a one-day horizon.
The confidence level indicates how often losses will not be contained within the estimated VAR. For a 95% confidence level, losses should exceed VAR just 5% of the time, or one day every 20 trading days. At a 99% interval, this should fall to just two to three exceptions per year.
Bank of America was among the first major dealers to disclose management VAR at higher and lower confidence intervals. Most banks still report VAR measures under one confidence level only.
The gap between VAR measurements at different confidence levels can be used as an indicator of tail risk, that is, the occurrences that sit in the ‘left tail’ of the probability distribution curve.
Regulators impose a 99% confidence interval on regulatory VAR, but with the VAR model used for internal risk management, the choice of confidence level and time horizon is up to the bank.
Management VAR also differs from regulatory VAR in that it may cover a smaller or wider perimeter. In Bank of America’s case, management VAR encompasses both the trading perimeter – covered positions and less liquid exposures – and positions outside the trading book but still marked-to-market, namely fair value loans and associated hedges.
Not all banks disclose VAR across confidence intervals, so it is hard to say whether tail risk has risen across the sector, or at the US’s second-largest bank alone.
There are signs it was not just particular to Bank of America. At HSBC, which began disclosing parallel measures two years ago, the distance between VAR averages rose from $13.1 million in 2021 to $17.5 million last year. And when Nomura switched from a 99% confidence level to 95% in the first quarter of 2022, average VAR for the quarter dropped by almost half.
A widening of the gap between VAR figures at 95% and 99% confidence levels indicates a greater risk of extreme losses. In other words, a fatter tail means that if things do go wrong, the bank will be hurt so much more than was the case before.
On each day in Q3 2022 – the most recent period for which quarter-specific data is available – Bank of America had a 1% chance to see expected losses totalling roughly triple the estimated maximum under the 95% confidence level. Over 66 days – the number of workdays for that quarter, national holidays notwithstanding – the probability of this happening at least once becomes 48%.
Those are hardly reassuring odds – but in Bank of America’s case, odds that managers are aware of. On the other hand, a bank with a similar trading portfolio, but which relies solely on the 95% VAR figure for risk management, might be at risk of being damagingly blindsided should markets jerk too violently.
Readers of Risk Quantum now have access to some of the datasets that sit behind our stories – not just the segment of data that is the focus for the story, but the full time series, for the full population of covered firms. Readers can choose the institutions they want to look at, the metrics they are interested in, and download the data in CSV format to run their own comparisons and build their own charts. Risk and capital managers told us it would be helpful for internal reporting and benchmarking, but we figured many of our readers might get something out of it.
Currently, the available data covers more than 70 banks and over 100 risk and capital metrics, but we’ll be adding more throughout the year. The Risk Quantum database can be found here. The full list of data points currently available can be found here.
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