How a broken machine which banks used to estimate regulatory reserves found new life in Hedge Funds

TimeLine

1980s Arrival on wall street of mathematically inclined employees, some of whom by 1987 has arrived at senior positions

1987 Stock Market Crash

Post 1987 - a dilemma: if you're honest about including so-called Black Swan event statistics into your day to day trading strategies, then these new distributions built models which no longer claimed to make money.  If you ignored them, your models prompted you to trade day by day and make money as before, until the next black swan arrived to potentially wipe you out.  These events seemed to be arriving at a frequency of once or twice per decade, they were unpredictable, unknowable and seemed to be happening faster than the usual normal distributions were predicting.

The thought emerged: allow specific market traders to continue as before but to develop a firm-wide measure to carve out extreme event spaces and add further firm-wide risk limits to those carved out extreme event spaces.  Unfortunately while still working on the base assumption of normal distribution for (log) returns.

This new focus (and new limits) specifically on tail risk coming out of each of a bank's trading markets could the be aggregated into a single all-market score.  This single score pulled together risks from all trading activity at a firm, it was hoped, in a way which would flag up, like a canary in a mine, prior to black swans.  As a prediction tool for black swans, it was always likely to fail (read Taleb for why) but it certainly could be a useful way of getting a handle on (and applying limits to) some measure of the risk taken or loss expected (measured in dollars) for a firm.  In other words, this measure, when tracked by a firm itself, every day, could provide a useful context for how much risk a firm was taking, when that increased, when it decreased, etc.

Late 1980s JP Morgan and Bankers Trust trading units were using this measure, and JP Morgan in particular pioneered the rolling up of various unit VaR numbers into a single firmwide VaR number.  Once it arrived at the level of the firm, it could be used as a measure of minimal capital adequacy.  That is to say, the firmwide dollar amount could be interpreted as the minimal amount of liquid capital a firm needed to have on hand in case that modelled-black-swan event (almost an oxymoron, actually) occurred.  Regulators were quick to pick up on this idea.  Note the flaws: tail events are unpredictable; they happen more frequently than the normal-distribution models suggest; the losses which might incur are often greater than the VaR number suggests.  

Basel I - 1988 - G10 Central Banks (plus Luxembourg) publish a set of minimal capital requirements as part of a voluntary regulatory framework.

Given the known limits of this measure, why was it accepted?  Well, it was considered a flawed step in the right direction, and given that it was a broad bank regulation, there would have been pressure to introduce a measure which was conservative - aimed at approaching theoretically perfect capital adequacy from the bottom up, gradually.  However, as Keynes, Minsky, Shiller, Taleb etc all point out, there exist mechanisms, psychological and institutional, which result in variance of animal spirits.  VaR was always going to be one of those devices which lead to a false sense of comfort so essential to the Minskyian story of incrementally greater risk being taken in a world which seemed increasingly, measurably predictable.  In this sense, Taleb is the ignored  peripheral voice shouting "Don't forget your Minsky" to which the Central Banks replied, "Lord, let me get to Minsky, but not quite yet". 

Hedge funds are thought to be more lightly regulated and more leveraged than banks, but this is not typically so (there may of course have been historical exceptions).  They are certainly more lightly regulated but are less leveraged than banks.  Banks on a weighted asset basis own much safer asset types compared to hedge funds, and both will use hedging techniques to manage their risk.  Banks are usually larger, and more systemically important, hence require more intense public scrutiny.  Of course, certain hedge funds  individually can fall into this category too and again, rightly so. Likewise, the hedge fund industry itself can be considered en masse as a systemically important area of the economy, which is why many of them have to report in quite some detail on their activities.  Thirty percent of hedge fund derivatives risk is concentrated in the top ten hedge funds (according to a January 2019 SEC report), so perhaps regulators can get good results by increasing scrutiny on those giant funds.

The problem of a consistent - temporally and across markets and jurisdictions - measure for hedge funds is a non-trivial (and unsolved) one.  Certainly AiFMD leverage is an attempt but it reflects termsheet measures, that is to say, easy to calculate and uncontroversial.  

The two places you access leverage at a hedge fund are though asset class choice, particularly in the use of derivatives, and secondly via the ongoing leverage which banks' prime brokerage units offer hedge funds.  Those two sources are, of course, related - the more asset leverage a fund takes on, the more careful its PB is likely to be in offering its own funding leverage, ceteris paribus.

Regulators don't ask hedge funds to report VaR for capital adequacy reasons, but hedge funds do calculate it nonetheless.  Why?  Well, it has become known in the industry - banks are aware of it of course, and PB units after all have to feed in their contribution of VaR to the overall bank position, after all.  Investors know about it also.  But VaR is not used by hedge funds to judge how much capital must be set aside to cover tail events.  They usually have instead, in their risk policy, specific liquidity buffer requirements expressed as a fraction of their current AUM.  They also have ongoing negotiations with PBs on an almost deal by deal basis and feel the pain via increased funding costs for particularly burdensome trades (due to their size or their asset leverage or their perceived capital-at-risk).  For those reasons too it would be of interest for regulators.

VaR is still useful in hedge funds, and risk policies often express a limit as a a fraction of AUM.  For example, the firm might state that it aims to manage risk in a way which keeps capital usually below a VaR limit of 1% of AUM.  This can be tracked over time to give a useful measure of risk taking.  It will indirectly guide the capital allocation function in setting risk capital to traders.

However, precisely the same risks of complacency apply here - VaR doesn't predict anything, and being regularly under the stated level should give an investor only a passing feeling of comfort that tail risks are being managed better.

Operationally, calculating a firm's VaR is a labour intensive process - who's looking after the effects of all those illiquid and private assets as they're fed into the VaR machine?  Who is modelling and managing all the correlations and volatilities?  If you're using historical implementations of VaR, how are convertibles behaving as you roll back the corporate events?  Who handles the effect of unusual splits on options?  How do you model M&A deal risk?  SPACs?  Etc Etc.

1997 VaR found a further role as the quantitative measure of choice for making public statements about the degree of firms' derivative usage, following an SEC 

Basel II, 1999, which now just now (2020) mostly implemented, solidifies VaR as the preferred measure of market risk.  It identifies and places an onus on related institutions to quantify and incorporate three components of risk in their capital adequacy calculations, namely market, credit and operational risk.  These three numeric inputs feed into a  minimum capital calculation, the threshold of which is set by regulators.  VaR is the preferred market risk measure; there are more procedural and varied options for the other two, based on how large and complex the organisation is.

For advanced (in-house) credit measures, the firm makes an estimate, for each of its significant creditor risks, the probability of default, the loss given default, and the expected exposure at default.  For advanced operational risk  measures, you take as a starting point all your business line gross incomes and multiply them by a scaling factor to estimate the risk to each business line).

Conditional VaR, also known as expected shortfall or tail loss, provides a more accurate estimate (and larger) of the expected loss than plain VaR.  The following article spells that out nicely.   The essential point is worth quoting:

A risk measure can be characterised by the weights it assigns to quantiles of the loss distribution. VAR gives a 100% weighting to the Xth quantile and zero to other quantiles. Expected shortfall gives equal weight to all quantiles greater than the Xth quantile and zero weight to all quantiles below the Xth quantile. We can define what is known as a spectral risk measure by making other assumptions about the weights assigned to quantiles.

However even here the hedge fund faces the same problem of feeding a potentially large VaR engine with many recalcitrant asset types in order to produce a meaningful output.  Given that, hedge funds sometimes try to measure firm risk via a collection of scenario models, together with specific hand crafted 'worst case' analyses of major risks/trades.  These worst case analyses, however, sometimes don't have correlations burned into them, hence aren't so useful as firm measures of risk in the same way that VaR can be, but they can be used to manage trading and investors also find them interesting when aggregated chronologically as measures of concentration through time.

Basel III - November 2010 (post the 2008 financial crisis) but implementation extended to Jan 2022.

Its goal was more work to be done on capital requirements and to bring down leverage.  Broadly there were three limits here - again capital adequacy set as a fraction of risk weighted assets, a non-risk weighted leverage ratio based on tier 1 capital and total balance sheet exposure and finally a liquidity requirement whereby the firm has to prove it can cover with liquid assets 30 days of expected outflows.  Capital adequacy and leverage are both very closely related, and I think of the leverage addition as a way of further tracking derivative exposure.  Hence capital adequacy and leverage are both size measures and liquidity is a flow measure.  Of course, liquidity also affects risk, and hence the risk weighted capital numbers, so in a way all three cohere.

From this it becomes clear just how clearly a modern risk manager is a child of the Basel accords, and those in turn are children of that time when for the first time trained statisticians and mathematicians faced the aftermath of the unpredictable turn in business cycles.

Generally Basel says to relevant institutions: (1) you must calculate these items; (2) you must allow us to make sure you're doing it right by showing us what you did, and (3) you must periodically tell the market what those numbers are too.  These are the so-called three pillars of the accord.  Step 1 is done in Risk and Compliance departments in the firm, Step 2 is largely covered by the regulatory reporting that hedge funds have to perform, and step 3 appears in marketing documentation such as offering memoranda and investor newsletters and Opera.

But really, on the assumption that tail events (and business cycles generally) are unknowable, regulators are in an impossible position here.  All they can do is make sure the risks don't grow in the normal course of events, which is definitely something.  They cannot now, or ever, I feel, see or predict a black swan in any of this data.  Lastly, expected loss is even more tenuous than VaR.  If so much doubt exists about our ability to measure even VaR at the 99th percentile, imagine how less certain we ought to be about the whole fat tail from 99 out to 100.  So how can expected loss be in any sense more accurate when it more fully resides in the unknowable region of black swan possibility?

Those of a statistical bent will immediately recognise the structural similarity between a one-sided hypothesis test and the VaR calculation.  And with that connection it becomes clear that what the originators intended was to carve away the space of unknowability, looking very much from the perspective of 'business as usual' market conditions.  It is very much a statement of how the normal world might apply and perhaps even deliberately said not very much about what might transpire beyond that threshold of normal market conditions.  Think of how it is usually expressed: "an amount of loss you aren't likely to exceed over your horizon window, given your certainty parameter".

Two of Taleb's as yet unmentioned criticisms of VaR are that it wasn't born out of trading experience, rather it was born out of quant applied statistics.  This isn't necessarily a bad thing.  And second, that traders could exploit its weakness by burying enormous risks in the final 1%.  This is why a modern hedge fund has literally thousands of relevant risk controls in place to practically mitigate this weakness.  However his point on its generation of black-swan complacency was already well made at a broader level by Minsky and others.   Perhaps my favourite quote about VaR is from Einhorn, who compared it to an airbag which works beautifully under all circumstances except during crashes.

These are both unfair, since all it takes is for the industry to realise its weakness, and the complacency argument goes away.  Hedge funds have thousands of risk controls.  Banks too.  They are not complacent as a rule, though, according to Minsky, we all vary in time in our level of complacency, which I would agree with.  Paired with other controls, and in the context of the proper level of scepticism, and with its other uses to track firm-wide consumption of risk over time, it is in fact practically useful.

Second order benefits include: you won't get good VaR until your volatilities, correlations and prices are good, so it is a fantastic tool to be able to spot modelling or booking anomalies.  Secondly you can throw it into reverse and imply out a firm-wide volatility also, and compare that to the realised volatility of observed firm-wide returns.  When also calculated at the trader and strategy level, you can put numbers on the diversification contribution each trader or trading style makes.  So-called marginal VaR recovers the prized concept of sub-additivity.  And of course conditional VaR (expected loss) makes pretence of a peak inside the black swan zone.

To summarise the Minsky point from a risk management perspective: most models are calibrated on historical data, usually recent historical data (perhaps even exponentially weighted).  When your calibration history looks euphoric, your models tell you everything is gonna be alright, which in aggregate grows confidence, which leads to growth in a feedback loop which could be described as positive-then-very-negative, when the surprise event happens, and none of your recent-history calibrated models saw it coming.  If you know this weakness and build that into your models, then your day to day returns will be so below your competitors in normal market conditions that chances are good you'll go out of business, eaten by competition before the next black swan hits.


As an interesting footnote, the Wiki page for  Dennis Weatherstone states:

JPMorgan invented value-at-risk (VaR) as a tool for measuring exposure to trading losses. The tool emerged in the wake of the 1987 stock market crash when Sir Dennis Weatherstone, JPMorgan's British-born chairman, asked his division chiefs to put together a briefing to answer the question: "How much can we lose on our trading portfolio by tomorrow's close?"

VaR of course didn't quite answer this, it answered the question: with 99% confidence, how much are we sure not to lose more than by tomorrow's close assuming the recent past is kind of like today?  Wheatherstone's question is partly answered by the  related conditional VaR, or expected loss calculation.  The question is beautifully simple to ask and devilishly hard to answer.

Less interesting footnote:  the team lead at JP Morgan for VaR creation, development and implementation was Till Guldimann, who was Swiss, and born in Basel, so VaR is simply coming home. 

VaR lead to the spin out of of RiskMetrics, the risk consultancy.A great legacy with VaR at banks was gaming the system - stuffing risk into the tail.  It is simultaneously the most you could lose 99% of the time and the least you could lose 1% of the time.  That's a fantastic definition.  If you have a lot of historical data, deal in liquid assets and have the resources to man the coal room, VaR is useful.

Another way to use VaR: imagine you're running a hedge fund and you have an AUM.  Imagine also that you have a handle on the fraction of a loss you'd need to make before you realise and your investors realise it is game over.  Armed with these two numbers, you can then gradually increase the correlations between assets currently held until you reach a VaR result equal to that teminal loss.   You now know what your death correlation is and can track it.  Separately you can do the same for volatilities, giving you a death volatility.  When you can adjust in a historically meaningful way the covariance matrix such that you achieve a predicted terminal loss, this is in fact how VaR is calculated.