Ahead of RiskMinds Asia later this year, Max Wong, RBS Global Banking & Markets, shares with us his research on VaR.  Max Wong will be speaking at at RiskMinds Asia, 11-13 September at The Marina Bay Sands, Singapore.

VaR and financial crises
It is a great irony that our advancement in risk management has created a new kind of 
risk—the risk of risk measurement—the misuse of (frequentist) statistics. The credit
crisis has debunked some well-established risk models used by banks, in particular
Value-at-risk (VaR), an essential tool used for the purpose of regulatory capital and
banks’ own economic capital. In fact, the risk of using VaR models has been forewarned
by Danielsson et al. as early as 2001 in a response paper to the Basel authority.
Nonetheless, VaR has become the industry standard because of its practical simplicity
and a lack of agreeable alternatives.
VaR is the loss quantile of the P&L distribution of a portfolio, statistically
determined using data over a sample period (of multiple years) and estimated over a
specified time horizon (10 days for market risk) at a certain confidence level (for example
at 97.5% confidence level i.e. a 2.5% quantile is used). The crisis has shown that, as a
risk metric intended to measure extreme losses or tail risk, VaR is just “too little, too
late”. How far off are we?
Figure 1 shows the 97.5% VaR for the Dow Jones index; the P&L’s which
exceeded the VaRs for longs and shorts are shown as vertical bars. During the credit
crisis in 2007, the exceedences are a lot larger than VaR, in fact, very much larger than
that expected by the commonly assumed normal distribution. To get an idea if the
exceedences are realistic, consider Table 1 which shows the top-10 largest daily losses in
history. Certainly crises have occurred more often than suggested by VaR models. These
led to the popular idea of Black Swans (see Taleb (2007)), events of low probability and
high devastation located at the extreme tail of the distribution. Taleb found that such
events in financial markets are not statistically reproducible (atypical), a phenomenon he
termed extremistan. Without the element of reproducibility, Black Swans are not
amenable to statistical quantification; the usage of frequentist statistics as applied in VaR
will lead to precise but misleading (inaccurate) numbers. Because of finite sampling, a
mathematical quantile can always be determined, but the expected loss beyond this
quantile is an elusive number which may never converge under extremistan. This illusion
of precision could undermine risk management preparedness by putting risk controllers in
a comfort zone.
Secondly, VaR is always late in crisis detection—it increases sharply only after
the initial sharp selloff of a crisis. The cause, the use of a recent rolling-window in such
models means that this metric will always respond late to large market movements that
mark the onset of a regime shift. Thus, VaR is an effective analytics during “peace time”
when changes are gradual, but is useless for crisis warning. As VaR is used to determine
regulatory capital, the burden on banks will rise sharply in a crisis situation after the fact,
forcing banks to reduce positions in a falling market. Conversely, VaR is muted in a
bullish market and the benign capital requirement encourages balance sheet expansion
and the use of leverage. This phenomenon of low volatility during rallies and high
volatility during sell-downs is called the leverage effect and is well known. Figure 2
shows such an inverse relationship between the S&P and VIX indices. Thus, regulatory
risk model has the unintended effect of amplifying the boom-bust cycle; this procyclicality risk is highlighted by the Turner Review (2009). The Review calls for a
reformed capital regime which is overtly countercyclical—reserving more capital during
a boom which can later be used to cushion losses during the bust phase.
Thirdly, VaR is symmetric—it does not capture directional risks, only changes in
volatility. In Figure 1, the VaR at the base of the rally (early 2005) is the same (about
2%) as that at the peak of the market in Oct 2007. But shouldn’t the risk of a crash be
highest at the peak? This fear of crash is not only intuitive but is also reflected by the
markets. Since Bates (1991) first observed this, many studies show that the option
implied skew is highest near the top of the market just before major crashes; this is
evident in Figure 3 which shows the S&P index and its option implied skew during the
2008 crisis. But VaR could not capture this fear because statistical skewness of a
distribution does not reflect directional risk very well, due to distortion from trading
around support/ resistance levels. To understand this microstructure, consider a pegged
currency attack. Speculators who sell against the peg will bring prices down to test the
peg gradually because the currency is supported by opposing traders (and the central
bank) who bet that the peg will hold. Conversely, each time the peg holds, short covering
will likely see quick upward spikes. This causes occasional positive skewness in the
distribution even though the real directional risk is downwards. Since trading can be seen
as a battle between bulls and bears for resistances and supports, statistical skewness is
highly dependent on price levels. Figure 4 illustrates the statistical skew for the S&P
index—there is no obvious pattern near the market peak, the realized distribution is
virtually symmetric.
This leads to the fourth weakness, VaR does not distinguish between long and
short positions. In Figure 1, the VaR just before the crisis (Oct 2007) has effectively the
same values for longs and shorts. But a crash can only happen downwards! (never up). So
shouldn’t the risk be higher for longs? Likewise, at the trough of the market, shorts
should be more at risk to a (rapid) bounce, which can only happen upwards. Thus, the
present day capital regime does not penalize longs for chasing an asset bubble nor
recognize that the crash risks of opposing positions are unequal. Since the banking
system is profit maximizing and capital efficient, the rules incentivize banks to chase the
latest hot assets collectively; it is not macro-prudential.

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You can hear from Max Wong at RiskMinds Asia 2012 on September 12, in the session ‘Have We Waved Goodbye to VaR’.  To find out more about RiskMinds Asia 2012, click here to visit website.