Proposed new capital standards for large banks (Basel Endgame) include some fundamental changes in measuring market risk. The new standards would replace the current value-at-risk (VaR) approach with the expected shortfall approach. The market risk proposal is exceptionally complex, and I don’t intend to get into the gory details. Instead, I’ll focus on broad conceptual differences between the two approaches and the rationale for making the change.
The Notice of Proposed Rulemaking (NPR) for the Basel Endgame includes sections on components of capital, credit risk, operational risk, securitization risk, credit valuation risk, as well as market risk. The market risk section runs 212 eye-glazing pages. That includes both Standardized and model-based approaches, plus various fallback and add-on components to account for various gaps and limitations to the risk measures. Those details are important, but understanding the rationale behind the move to expected shortfall is a necessary starting point.
Scope of the Proposal
Current capital rules as well as the Basel Endgame proposal view “market risk” narrowly. The rules address the market risk of trading portfolios and not interest rate risk of the banking book (IRRBB), at least not directly. The Basel Endgame would require a wider range of firms to recognize unrealized losses on available-for-sale (AFS) securities. These securities became underwater due to interest rate risk, but the unrealized loss is more akin to a loan loss reserve than holding a risky asset. Even with the limited applicability, the AFS component may be a bigger deal for many firms. For example, the market risk capital charge for Charles Schwab was about $47 million ($477 million RWA) as of September 30, 2023. The capital adjustment due to unrealized AFS losses would be $8.9 billion. The firm’s unrealized losses on held-to-maturity securities are even larger, at $19.4 billion.
A Federal Reserve Staff Memo accompanying the NPR states that, Capital requirements for trading activities are estimated to increase substantially, more than doubling for some firms.” That sounds like a lot, but with a few notable exceptions, the base is quite small. The table below compares risk weighted assets under the Market Risk Rule to total RWA under the Standardized Approach for the ten largest bank holding companies (BHCs).
The market risk component represents more than 10% of capital only at Goldman Sachs and Morgan Stanley, where trading is their central business. Market risk represents around 5% of total RWA at financial supermarkets like JPMC, B of A, and Citi. Large traditional banks, like US Bank and PNC are below 1%. The Staff Memo is not specific on the characteristics of the “some firms” that might see a doubling of the market risk capital requirement. That would be a big deal for Goldman Sachs but not so much for PNC.
VaR and Expected Shortfall
Value-at-risk (VaR) has been around at least since the 1990s and is the key measure to calculate risk-based capital requirements for market risk. There are various ways to calculate VaR but the easiest way to think about it is as the 95th or 99th percentile trading loss. Let’s say you have four years of data with 250 trading days a year or 1,000 total observations. The 95% VaR would be the 50th worst trading day. The 99% VaR would be the 10th worst trading day.
VaR can provide a good indicator of the general volatility of trading activity but doesn’t tell you much about extremes. After all, nothing bad happens in Russian roulette 83% of the time. It’s the other 17% you must worry about. Bank supervisors care about extremes.
Expected shortfall addresses this issue by taking all the bad outcomes into account. It looks at losses at a certain percentile threshold and everything worse. The Basel endgame sets that threshold at 97.5% confidence. Let’s take a simplified and stylized example. Consider, say, the fifteen worst trading losses by a bank over the past two years (500 trading days).
A 99% VaR would be the fifth worst trading day, or $200. The expected shortfall (ES) would be an average of the 12 worst trading days and part of the thirteenth.[1] That equals $322. VaR ignores the outliers, but those outliers are incorporated into the expected shortfall calculation. Falling outside of the VaR threshold doesn’t mean the loss is that rare. If the VaR model works as specified, that will happen two or three times a year. If trading gains and losses were normally distributed, the 97.5% expected shortfall would be roughly equivalent to a 99% VaR. Often, they aren’t.
Why Do Regulators Care About Extremes?
Traders and even risk managers tend to focus on what they see as plausible rather than the worst-case scenario. Regulators tend to take a different view. While a profitable banking industry is in the regulators’ best interest, avoiding catastrophic losses that could cause a bank to fail is more important. Bear in mind that capital requirements are calibrated to a 99.9% confidence level, “on average once in a thousand years.” Regulators established this high standard, in part, to take measurement error into account, but capital standards are designed to cover extreme, unexpected losses.
Expected shortfall models must incorporate stress periods. The NPR specifies that internal models need to go back to at least 2007. But you really can’t really project a once-in-a-thousand-year event with less than 20 years of data. You’d pick up the Global Financial Crisis, but not every market shock since the days of Canute the Great. No South Sea Bubble, Tulipomania, 1929 crash, nor even 1970s stagflation. Expected Shortfall picks up extreme losses, but only those in comparatively recent memory. The 2007-2009 period also was terrible for the markets overall, but not necessarily for every asset class. The NPR addresses this issue by establishing stress periods not only at the enterprise level but also for individual trading desks. More problematic will be newer financial products where there’s not much data to work with.
Backtesting
There are all sorts of processes and statistical tests to evaluate models. But how do you know whether the models actually work? One way of answering that question is through backtesting, also known as outcomes analysis. Backtesting compares a model’s forecasts to actual results. Did the model work in the real world? VaR is pretty well suited to backtesting. Compare your VaR to daily “clean” P&L. If, over the past 250 trading days, your daily loss exceeds your 99% VaR, one, two or three times, the VaR model is working as intended. Four times could still be considered noise. However, five or more breaks suggests the VaR model is underestimating risk and there’s a capital penalty under the Market Risk Rule.
Backtesting works less well for stress testing or for tail risk. In this case, the model is only making a conditional prediction – what happens under a specific, adverse scenario. That scenario is supposed to be unlikely. The same goes for expected shortfall – extreme P&L days that drive the measure’s difference from VaR rarely happen. The NPR preserves the backtesting requirement with some modest refinements. The key point is that backtests will continue to be based on a firm’s VaR model. Weaknesses in a firm’s VaR model may make supervisors less confident of a firm’s expected shortfall estimates, but it’s unclear whether you can infer much about expected shortfall modeling merely because its VaR modeling has a good track record. The backtesting may capture how frequently daily P&L exceeds the 97.5% and 99% thresholds, but not by how much.
Will it Work?
Expected shortfall makes more conceptual sense than VaR as a measure of tail risk. How the new approach will work be in practice is more debatable. The NPR includes a supervisory approval process for expected shortfall models and better practices usually emerge from such a review. Regulators also expect a bank to “integrate its internal models used for calculating the expected shortfall-based measure for market risk into its daily risk management process.” Using expected shortfall in day-to-day risk management can provide a clearer view of that technique’s strengths and limitations well before it gets hardwired into capital requirements. Unfortunately, banks often respond to a proposed new regulatory requirement, especially one that’s costly to implement, by stalling and hoping it goes away. FRTB proposals go back to 2012. Will banks soon add expected shortfall to their suite of risk measures? I suspect most will still go with stall and hope.
[1] A 97.5% confidence over 500 trading days equates to 12.5, so I’m only partially weighing the 13th worst loss.