3 June 2019

Utrecht Complexity Research: Are capital markets mad?

Coen Teulings

Complex systems can be found as a driving force behind many of the events we encounter in day-to-day life, and play an important role in the social challenges. Coen Teulings provides some food for thought on complexity in his research. Teulings is a Distinguished Professor at Utrecht University, and his research is based at the Faculty of Law, Economics and Governance.

The financial crisis has shocked the public’s confidence in financial markets, which are thought to be irrational and subject to unpredictable mood swings and herd behaviour. Periods of tranquillity, as between 2004 and 2006 when stock prices remained relatively stable, alternate with periods with wide swings in stock market indices, as in the Fall of 2008 after the Lehman Brothers bankruptcy. Complexity theory and agent-based modelling offer useful tools for analysing this herd behaviour.

Economic theory is currently presented with a conundrum. On the one hand, rationality is at the heart of most theories of economics. On the other hand, it has proven difficult to explain the observed levels of high volatility in equity prices in a consistent general equilibrium model. The volatility is much lower for the present value of the dividend stream than for the prices of the corresponding equity, while both should be equal. Robert Shiller earned the Nobel Prize in Economics in 2013 for pointing out this problem.


In my research I aim to find a resolution to this puzzle. The key is the volatility of the dividend stream. This volatility is itself volatile over time. Since investors are risk-averse, a high volatility of the dividend stream makes equity a less attractive asset. There is a trade-off between the riskiness of an asset and its return: only a high return can convince investors to hold a risky asset. During high-risk episodes, the expected return on equity must also be high. This can only be true if the price of equity is below its attractor, so that investors can expect this price to rise in the near future. As a consequence, when the news of an upward shock in the volatility of dividends arrives, stock prices fall immediately as to enable a higher expected future return. The volatility of the second moment of stock prices therefore contributes to the volatility of their first moment. My research question focusses on the extent to which this mechanism can explain the puzzle.

Two types of models

This mechanism can be modelled by a system of stochastic differential equation. Like many other systems in economics, this system exhibits saddle point stability: when a shock to the system arrives, asset prices immediately adjust to return the system immediately to the unique path along which the system will subsequently move to its saddle-point-equilibrium. These sudden swings in asset prices offer an explanation for their volatility, in that they determine how shocks to the volatility of dividends are transmitted immediately to asset prices. These mechanisms lead to fat tails, in particular since news on volatility does not arrive at a constant rate, but comes in tidal waves, very similar to the prediction agent-based models. There is a thin line between both types of models (understandably, since they try to explain the same phenomena). One of the research questions is therefore whether one can sensibly discriminate empirically between the two models.

Taking risks early in life

The answer to these questions has an enormous relevance to society, in particular for the organisation of pension funds. If this theory of asset price volatility is correct, people should take large investment risks early in their life cycle. Since swings in volatility are known to be temporary – sooner or later, the uncertainty will be resolved – equity prices revert to their attractor value. For elderly people this might come too late, after they passed away. Hence, elderly should limit their exposure to stock market risks. Youngsters still have a long future ahead and can therefore assume a lot of risk. In fact, pension funds should invest in equity on behalf of future generations for optimal risk sharing. This matters enormously for social welfare. A proper distribution the investment risk over the life-cycle of participants increases lifetime welfare by 10% of gross domestic product by providing a much trade-off between risk and return.