Gerardo Ferrara, Maria Flora and Roberto Renò
Financial markets process orders faster now than ever before. However, they remain prone to occasional dysfunction where prices move away from fundamentals. One important type of market fragility is flash events. Identifying such events is crucial to understanding them and their effects. This post displays the results from a new methodology to identify these, but also longer lasting V-shaped events, as we show here with an application to three sovereign bond markets.
Detecting when markets are inefficient
One challenge that the financial system has to face is the fragility of financial markets. By “fragility” we mean the dysfunction whereby market prices are away from fundamentals (that is, the market is “inefficient” in the Fama sense) for a sustained period of time. The growth of electronic and automated trading has the advantage of improving market liquidity, but it also has given rise to an increase in the number of “flash crash” episodes. Quoting the definition of the Bank of England (Financial Stability Report (2019)), these are “large and rapid changes in the price of an asset that do not coincide with — or in some cases substantially overshoot — changes in economic fundamentals”. Several such episodes have occurred across many asset classes, including liquid Government bonds, foreign exchange (FX) spot transactions and equities.
There could be implications for the real economy if a flash episode in a market becomes longer lasting. But how can we tell when market prices are far from fundamentals? Chart 1 shows the price of the 10-year future on three bonds (UK Gilt, Italian BTP and German Bund, all rescaled to start at 100) during the spread of the coronavirus pandemic at the start of the year. The three markets appear far from fundamentals during March 2020, especially the Italian one. To assess the presence of market distress during this month, we use the V-statistics proposed in Flora and Renò (2020), which is specifically designed to test for significant V-shapes in prices.
Chart 1: Prices (rescaled) of 10-year bond futures
Sources: Bloomberg and authors’ calculations.
The idea of this new approach is to use drift as a measure of distress instead of the usual volatility or jumps. Christensen, Oomen and Renò (2018) (henceforth COR) introduced the econometric foundation of this idea and Bellia et al (2020) provide an application to flash crashes. Intuitively, the “drift” can be considered the mean of the short-term returns, while “volatility” (and jumps) can be considered as their standard deviation. The main assumption is that the drift is small in functioning markets. This is the reason why financial econometrics has largely ignored the drift component of returns; the drift term is negligible with respect to the variance in the short term. However, COR show that this relation reverses often in financial markets. In fact, during flash crashes the drift term dominates. Here comes the new idea: the drift term can dominate the volatility if the drift becomes extremely large; and that is exactly what the COR test can detect. COR also show that when drift dominates volatility, absence of the arbitrage principle is violated. When the drift also changes sign (from negative to positive, or vice versa), which is what happens during a V-shaped price pattern, it is also a clear signal of market inefficiency, as discussed in Flora and Renò (2020).
Importantly, detecting abnormal drift, and the relative strength of drift with respect to variance, is relatively easy. Using price data, the estimated drift is divided by the estimated volatility to give a ratio that we can use to calculate the V-statistic. In particular, at each point in time the V-statistic is the product of this ratio just before and just after the current observation. Large negative values of the V-statistics detect anomalies in the data, implying that the price overshot and is returning to fundamentals. Large positive values of the V-statistics signal the presence of a sustained trend. Large volatility, due to either continuous movements or jumps, instead is not in contradiction with efficient markets, as explained in Flora and Renò (2020), and thus techniques based on volatility only are less effective in detecting distressed conditions. Confidence bands for the V-statistics can be built using the modified Bessel function of the second kind of order zero, a distribution that is just the product of two independent standard normal variates, or using bootstrap techniques.
In this post, we apply the V-statistics to the daily bond futures data displayed in Chart 1. Chart 2 shows the V-statistics for the three markets. The 99% asymptotic confidence bands are crossed in March for all of them. Broadly speaking, the V-statistic captures the different phases of what happened in March. First, a flight-to-quality while uncertainty about the virus was spreading. At this point, the V-statistic picks up an abnormal rally in prices (especially in German bund futures). Second, the ‘dash for cash’ when investors sold government bonds to get cash and there was disruption in government bond markets. This is when the V-statistic is particularly high, especially for gilt futures. The more negative value of the V-statistics for the Gilt is explained by the faster recovery in prices. Finally, towards the end of March central bank policy action calmed government bond markets.
Chart 2: The V-statistics of Flora and Reno (2020)
Sources: Bloomberg and authors’ calculations.
Of course, flash crashes or longer lasting V-shaped events could also affect markets other than Government bonds with negative externalities for the economy. For example, Duffie (2010) also highlighted V-shaped price patterns, ranging several days, for secondary equity issuances, US Treasury and corporate bond issuances, and even ranging few months for mutual funds experiencing large redemptions.
This post illustrates a new methodology to detect distressed markets. This methodology could be extremely useful for monitoring financial markets or, alternatively, for detecting (ex-post) periods of market distress which the authorities can investigate. We show that the V-statistics recently proposed by Flora and Renò (2020) can be extremely useful for this purpose.
Gerardo Ferrara works in the Bank’s Capital Markets Division, Maria Flora and Roberto Renò work at the University of Verona.
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