Critical transitions in financial markets are shifts in prices and operational structure to a new equilibrium after reaching a tipping point. “Complexity theory” helps analysing and predicting such transitions in large systems. Quantitative indicators of a market regime change can be a slowdown in corrections to small perturbations, increased autocorrelation of prices, increased variance and skewness of prices, and a “flickering” of markets between different states. A new research paper applies complexity theory to changes in euro area fixed income markets that arose from non-conventional policy. It finds that quantitative indicators heralded critical structural shifts in unsecured money markets and high-grade bond markets.

Van den End, Jan Willem (2017), “Applying complexity theory to interest rates: Evidence of critical transitions in the euro area”, DNB Working Paper, No. 567 , September 2017.

The post ties in with SRSV’s lectures on fundamental value and non-conventional monetary policy.

The below are excerpts from the paper. Emphasis and cursive text have been added. Formulas and symbols have been paraphrased for easier reading.

Complexity theory in a nutshell

“Complexity theory…describes critical transitions in complex systems…It assumes that systems evolve as dis-equilibrium processes…Complexity theory is usually applied to analyze critical transitions in eco-systems. For instance with regard to the loss of sea-ice due to temperature changes. A complex system can suddenly shift from one equilibrium to another after a tipping point (bifurcation) where the old state become unstable.”

“[There are] two ways in which such critical transitions can emerge.

  • The first class of transitions is caused by a change in external conditions…The change…gradually erodes the resilience of the current state by which it becomes unstable… Close to a bifurcation, a small shock can drive the system across the boundary between the attraction basins and cause a critical transition to the new state. Once a bifurcation is passed, the dynamics of the system accelerate by positive feedback effects, causing a ‘runaway change’ to the new state. Those feedbacks are self-reinforcing mechanisms…a ‘tipping point’.
  • In the second class of critical transitions, the state of the system changes by itself, which in models is represented by changes in state variables. The critical transition is then caused by a perturbation of the system’s state due to a fundamental change of its character.”

Complexity theory for financial markets

“The financial system fits into the first class of complex systems, in which changes in external conditions can make the system brittle and prone to a critical transition. While the cause of the transition is the change in external conditions, the trigger of the transition is usually a small (unexpected) shock which sets the transition dynamics in motion.”

“The behavior of market participants have the propensities for irrational reactions and myopic foresight. This can result in trend-following and herding behavior, reinforced by positive feedbacks between market prices and investment positions. Such dynamics can lead to persistent deviations of market prices from equilibrium and make the system prone to shocks. At a tipping point market prices may crash in search for a new equilibrium. Such dynamics, driven by the behavior of interacting agents, are very similar to the dynamics in complex…natural systems.”

“We apply complexity theory to regime shifts in the configuration of interest rates, linking them to the increase of excess liquidity. We assume that the excess liquidity created by the central bank represents a change in external conditions which fundamentally changes market functioning.”

Quantitative indicators of critical transitions

“From the literature on complex system we take several key indicators that signal whether a system is close to a critical transition and apply them to the configuration of interest rates…

  • Critical slowing down: [This]…means that a system increasingly slows down in recovering back to equilibrium from small perturbations if the state variable approaches a tipping point…Slowing down typically starts far before a bifurcation point and that recovery rates decrease gradually to zero if the tipping point is reached. The recovery to equilibrium slows down due to the loss of resilience of the system. It implies that the system less easily can return to its existing (old) equilibrium after a shock…
  • Autocorrelation: The slowing down usually goes in tandem with an increase in autocorrelation in the pattern of system fluctuations. Because the rates of change of the system decrease, the system’s state at a given point in time becomes more and more like its past state. We measure the resulting increase in the persistence [using the first-order autocorrelation coefficient]…
  • Variance: Model analyses show that well before a critical transition the variance of the state variable increases. Due to a slowdown in the recovery of the system, the impact of shocks do not decay so that their cumulative impact increases and thereby the variance of the state variable…
  • Skewness: Before a critical bifurcation the fluctuations of the state variable tend to become increasingly asymmetric. Close to a tipping point, the rates of change are lower, implying that the state variable stays longer in the vicinity of the unstable equilibrium (closer to the new state) than in the stable equilibrium. As a result, more observations are in the tail of the distribution of the old state and so the skewness of the distribution increases…
  • Flickering: Flickering means that close to a bifurcation point the system oscillates between the old and the new state. In the unstable region there are two alternative attractors that move the system back and forth between two states. Flickering can be observed in the frequency distribution of the state variable, which before a tipping point will increasingly become a mixture of regimes. This can be measured by the bimodality of the distribution.”

Critical transitions in euro area fixed income markets

“Excess liquidity created by the Eurosystem has led to critical transitions in the configuration of interest rates…

  • Liquidity has been supplied by unconventional monetary policy measures. In the beginning of the crisis (2007-2009) this was aimed at supporting the liquidity situation of banks and alleviating the stress in financial markets, where liquidity was rapidly drying up… In due course, the liquidity injections were further extended in terms of size and duration. This saturated the liquidity needs in the system, by which the EONIA [overnight rate] fell close to the deposit rate in July 2009…The regime change went in tandem with falling unsecured interbank transactions, indicating that the functioning of this market segment was impaired. While it is hard to disentangle to what extent the impaired market functioning relates to the crisis or to the prolonged liquidity provision by the central bank, literature also finds evidence for the latter.

  • The second critical transition is associated with the excess liquidity created by QE since 2015. This has reinforced strong demand for safe assets, short-term bonds of AAA countries in particular. The demand mainly comes from non-banks which have no access to the central bank deposit facility. For them, safe sovereign bonds are an alternative destination for their liquidity holdings. As a result, the interest rate on short-term AAA government bonds (proxy for safe asset) turned negative and fell below the deposit rate… As a consequence, particular segments of the financial markets ceased to function normally. Particularly the repo market suffered from the shortage of safe assets, which are an important asset class for collateralized lending and borrowing. The safety trap is reinforced by feedback effects, as banks tend to charge increasingly negative rates on bank deposits if excess liquidity increases. This reinforces the demand for alternative safe and liquid havens like AAA sovereign bonds and reduces bond yields even further.

“By their unconventional monetary policy measures central banks have increasingly taken over critical market functions. In first instance this concerned functions where the market failed, but gradually also functions which the market could fulfill by itself…

  • First, the Eurosystem took over maturity transformation from the market by extending long-term loans to banks and purchasing long-term. bonds…
  • Second, liquidity transformation has been taken over from the financial sector by transforming less liquid assets in central bank reserves through collateral in refinancing operations and purchases of less liquid securities.
  • Third, the Eurosystem has taken over credit risk from the market by becoming a central counterparty in money market transactions.”

“By taking over critical market functions, the Eurosystem has obtained a dominant role in allocating liquidity. This has impacted on the behavior of market participants, trading volumes and price formation and so has changed the way financial markets work.”

Market functioning so becomes endogenous on central bank measures. This can be reinforced by the perception that unconventional monetary policy is not a temporary phenomenon, but part of a new normal central banks have created an illusion of permanent liquidity by their unconventional monetary policy measures. As a consequence, phasing out such policy becomes harder the longer it is active.”

“The increased intermediary role of the Eurosystem went in tandem with a reduction of market liquidity and interbank trading. Thereby, the increased dependence on central bank liquidity may have weakened the resilience of markets, making them more prone to a (small) shock, such as an adjustment of market expectations on monetary policy. Feedback effects, following from the reactions by investors who readjust their portfolios, can exacerbate the shock effects. This may give rise to critical transitions in the system that will be reflected in shifts in interest rates, as key indicators of supply and demand conditions in financial markets.”

Applying complexity theory to euro area fixed income markets

“We test whether indicators taken from complexity theory provide signals of shifts in financial markets, interest rates in particular, caused by excess liquidity. We find that the complexity indicators…indeed flag the shift to a corridor system in the money market in 2009 and to a safety trap in the bond market in 2015 in advance.”

“A critical slowdown occurs both before the critical transition in the money market and the safe asset market.”

“The memory of the system (autocorrelation) peaks both before the critical transition in the money market and in the safe asset market.”

“The variance of the state variable is significantly high before the critical transition in the money market, but not in the safe asset market. In the money market the variance of the EONIA-deposit rate margin clearly exceeds the upper 5% interval within a horizon of 100 trading days before the critical transition (red circle in Figure 17). In contrast to that, the variance of the 3-month AAA/deposit rate margin remains far from the 5% interval.”

“Skewness and flickering of the state variables have similar patterns. Both indicators are significantly high with regard to the 3-month AAA/ deposit rate margin, signalling a critical transition in the safe asset market within a horizon of 100 trading days. Skewness and flickering also peaked before the critical transition in the money market, but they did not exceed the 5% interval there.”