[Back to main page]

My research blogs


How to best create structure in more than 1500 stocks

Why does a child play with a toy car, while most grown-ups fancy a real car instead? Obvious as this may seem, most academics play around with financial models involving a handful of asset prices (or more recently "large" dimensions up to 100), whereas real asset managers have to manage asset portfolios with more than a 1,000 asset prices. Are academics like children, and is it maybe time they grow up and study financial phenomena at the scale that is empirically more relevant?

Like driving a real car is much more challenging than driving a toy car, so is coping with realistically large numbers of assets. In our paper Estimation Risk and Shrinkage in Vast-Dimensional Fundamental Factor Models we study one of the challenges: how to cope with the large number of parameters in models with a large number of assets. In particular, we study a number of recently suggested techniques (called linear and non-linear shrinkage) and their adequacy for solving this challenge. We do so not in the standard academic toy setting, but in a setting of models that are typically used in the financial industry. Such models are called fundamental factor models. We find that such fundamental factor models are already a strong benchmark: academic shrinkage techniques add little to the fundamental factor model performance in the settings we study. In addition, we find for our vast dimensional setting that shrinkage techniques need to be adapted: some of the tuning constants needed to make the techniques work, can no longer be put at their theoretically optimal plug-in values, but need to be readjusted to the new context in order to generate (modest) gains in performance.

Download the paper as Tinbergen Institute working paper version.


The strong persistence in (realized) dependence for stock prices can help for forecasting at longer horizons

Stock prices typically move together. For instance, two stock prices can be affected similarly by common news about the industry they are in, or about the local or global economy. Different methods have been proposed to describe this time variation. A recent method that appears to work well in many settings exploits stock price variations within the day: for instance, every minute, or even more frequent. At such high frequencies, the dependence between stock price movements is typically very persistent: the dependence structure found on one day has quite a long lasting relation to the dependence structure on future days.

In our paper Fractional Integration and Fat Tails for Realized Covariance Kernels, which has been accepted by the Journal of Financial Econometrics, Anne Opschoor and Andre Lucas (me) address the question whether this strong persistence can actually be exploited for longer term forecasting. The short answer is: yes. Even though the information underlying the measurements of dependence is on a minute-by-minute frequency, the resulting measurements can be helpful at horizons as long as up to one month. The tools needed for this have to account for many of the features of stock prices and stock price dependence, such as erratic big price movements (fat tails), changing market nervosity and uncertainty (time-varying volatility), and the strong persistence due to the high-frequency underlying measurements. All of these tool features are needed, but at different periods in time. Whereas accounting for changing market nervosity is always important, correctly accounting for erratic big price movements is particularly relevant during crises, and accounting for strong persistence is important during calmer episodes. Previous methods did not account for all of these features simultaneously in a coherent way.

Download the paper published version in the Journal of Financial Econometrics or see the Tinbergen Institute working paper version.


Making good peer groups for banks when the world moves fast:
a marriage of financial econometrics and machine learning

How to identify the apple, the orange, and the banana if the juggler tosses everything around at high speed. Or differently, how to identify which groups of banks and other financial institutions are alike in a situation where new regulation kicks in fast, fintech companies are rapidly changing the scene, and central banks are implementing non-standard policies and keep interest rates uncommonly low for uncanningly long.

In our paper Bank Business Models at Zero Interest Rates, which has been accepted in the Journal of Business and Economic Statistics, Andre Lucas (me), Julia Schaumburg, and Bernd Schwaab investigate how to come up with groups of peer banks in such a volatile environment. Identifying peer groups is extremely important for regulators to create a level playing field. Similar banks should be charged similar capital buffers to safeguard the financial system and to retain fair competition at the same time.

We devise a new technique inspired by the machine learning literature (clustering) combined with ideas from the financial econometrics literature (score models). Think of it as allowing the moving center of the fruits of the juggler (the apple, orange and banana) being described by one statistical model, and the size of the fruits being determined by another model.

The model is put to work on a sample of 208 European banks, observed over the period 2008-2015, so including the aftermath of the financial crisis and all of the European sovereign debt crisis. Six peer groups of banks are identified. These groups are partly overlapping and partly different from classifications by ECB experts. The findings can thus be used as a complement for policy makers to compare bank profitability, riskiness, and buffer requirements. For example, leverage (as a measure of riskiness) and share of net interest rate income (as a measure of profitability) evolve quite differently for some groups of banks than for others, particularly during the low interest rate environment. A follow-up of this paper is Do negative interest rates make banks less safe?.

Download the papers published version in the Journal of Business and Economic Statistics or see the Tinbergen Institute working paper version or the ECB working paper version.


Treat outliers for risk models with due care!

Risk managers, pension funds, asset managers and banks nowadays use advanced models to assess the risk of investment portfolios. Much scientific progress has been made over the past decade to develop new techniques to measure the risk of such portfolios. In recent years scientists and professionals have started to use so-called high-frequency data to measure the risk. High-frequency data are frequent measurements of for instance stock prices or exchange rates. You can think of measurements every minute, every second, or in some cases even every millisecond. Such measurements often result in more accurate risk assessments than traditional daily measurements.

An important issue, however, is how to deal with so-called outliers in high-frequency data. An outlier is an anomalous measurement in the data. Think of a temporary crash in markets due to a faulty algorithm, a typo by a trader, or any other reason. Such anomalous events occur more often than you would think. For instance, in May 2010 there was a famous flash-crash than unsettled the main U.S. financial markets. Within the time span of 36 minutes, the Dow Jones index droped by 9%(!!) and subsequently recovered. Such big swings within the day result in enormous swings in risk measures and incorrect risk forecasts for subsequent days.

Anne Opschoor, Andre Lucas (me), Pawel Janus, and Dick van Dijk have developed a new technique to deal with such anomalous observations in high-frequency data. Our paper New HEAVY Models for Fat-Tailed Realized Covariances and Returns has been accepted in the Journal of Business and Economic Statistics. The core novelty of our approach is that anomalous event do not automatically inflate risk forecasts as in traditional models. Instead, the model trades off whether the increased risk is due to a true increase in risk, or to an incidental, anomalous event. We use statistical techniques calibrated on financial data to properly make this trade-off.

We test the model on a long time series of 30 U.S. stocks over the period 2000-2014. During that period, we have seen big events like the financial crisis of 2008, but also peak events like the May 2010 flash-crash. Using the new techniques, risk forecasts are significantly better than with the most recent competing methods. Moreover, our method is relatively straightforward to implement, which should increase its potential impact.

Download the papers published version in the Journal of Business and Economic Statistics or see the Tinbergen Institute working paper version.


Do negative interest rates make banks less safe?

The European Central Bank has implemented a number of unconventional monetary policies since the financial crisis and the subsequent sovereign debt crisis. One of the policies involves setting the official rate at which banks can park money at the ECB close to zero, or even below zero.
Was this a wise decision?

The idea of setting the official rate close to or below zero is that banks then have more incentive to *not* put money at the central bank. Rather, it would pay for banks to lend the money out, thus providing more financing to the people and businesses and helping the economy to grow again.

Then again, others argue that low interest rates squeeze the profit opportunities for banks, making them more vulnerable to new economic shocks and risking a new crisis in the financial sector.

In this paper, we investigate how markets percieved the effect of the ECB's decision to impose negative interest rates on the riskiness of banks. In particular, we are interested in whether some bank business models are more prone to the potential negative effects of ECB's policy than others.

We measure riskiness of the banks by well established methodology: the expected amount of capital that has to be injected into a troubled bank in case of an extreme market-wide shock. It is important to consider a situation of extreme market stress, as in that case injecting more capital into a troubled bank is most problematic and hurts most.

We find that policy rate cuts below zero trigger different SRisk responses than an equally-sized cut to zero. There is only weak evidence that large universal banks are affected differently than other banks in the sense that the riskiness of the large banks decreases somewhat more for rate decreases into negative territory.

Download the paper's published version in Economics Letters or see the Tinbergen Institute working paper version.