Interests:  Quantitative Finance  |  Asset Pricing  |  Non-Linear Phenomena | Financial Economics

Working Papers (available upon request)

Which is Worse: Heavy Tails or Volatility Clusters? (Schadner W. and Traut J.)

Shadow Interest Rates in the Euro Area (Lang S., Reynard S. and Schadner W.)

Crypto's Expected Randomness (Schadner W. and Liebi L.)

Return Auto-Correlation as Implied by Option Prices (Schadner W.)


W. Schadner and J. Traut (2022) in Mathematics

This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex-ante believes for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in a mathematical and in an economical sense are developed. An evaluation of existing models reveals that none can comply with the developed conditions consistently. This study overcomes this pitfall and provides two estimation models via exploiting the underlying factor structure of returns. The first solution reformulates the task into a constrained nearest correlation matrix problem. This method can be used either as a stand-alone instrument or as a repair tool to re-establish feasibility of another model's estimate. One of these properties is matrix invertibility, which is especially valuable for portfolio optimization tasks. The second solution transforms common risk factors into an implied correlation matrix. The solutions are evaluated upon empirical experiments of S&P 100 and S\&P 500 data. They turn out to require modest computational power and comply with the developed constraints. Thus, they provide practitioners with a reliable method to estimate realistic implied correlation matrices.

Keywords: Risk Factors, Implied Correlation, Equity Risk, Factor Analysis, Invertible Matrix, Correlation Matrix

Journal IF: 2.6

W. Schadner (2022) in Chaos, Solitons & Fractals

This paper studies the long-range dependence and multifractal content of U.S. political time-series to gather a deeper understanding of sociophysic phenomena. Specifically, multifractal detrended fluctuation analysis (MF-DFA) is applied upon data in the context of (i) president approval (polls), (ii) president online attention (Google Trends) and (iii) election-win probabilities (prediction markets). All analyzed series are characterized by anti-persistence, which may be interpreted as a nervous and overreacting behavior. We further detect significant multifractality with true non-linear correlation remaining after correcting for spurious sources. Importance from understanding the multifractal behavior arises from the fact that all three data types are used in practice for the prediction of election outcomes. We further argue that variation in local persistence (as implied by multifractality) can be both beneficial and destructive in different real world scenarios. We draw parallels to simple examples like the timing of political campaigns or trading on prediction markets. On the methodological side, the article implements recent improvements of MF-DFA such as focus-based regression and overlapping segments.

Keywords: Multi-Scaling, Sociophysics, Google Trends, President Approval, Prediction Markets, MF-DFA 

Journal IF: 9.9

W. Schadner (2021) in Physica A

This paper applies multifractal detrended fluctuation analysis to study the multifractal property and temporal persistence of U.S. and European stock market sentiment, providing deeper insights into investor behavior. The findings indicate that the average sentiment is anti-persistent, understood as a general tendency for investors to overreact. The multifractal property is clearly pronounced in both markets. The significant width of the multifractal spectra indicates a substantial variation in local sentiment persistence. Analyses show that the current sentiment persistence is positively related to the level of market mood. Hence, investor fear is related to overreacting, while optimism is more closely related to a random walk. Conclusions are drawn from financial option and survey data. 

Keywords: Multifractal, MF-DFA, Long-term memory, Investor sentiment, Financial crisis, Implied volatility

JEL Classification: C58 , C22, G01, G40, G14 

Journal IF: 3.8

W. Schadner (2021) in Quantitative Finance and Economics

Equity returns are typically higher correlated during market downturns than during bullish times. This paper develops a novel approach how investor expectations for such correlation asymmetries can be quantified from forward-looking data. Based on option implied volatilities, it is found that the correlation asymmetry is significant, rejecting the use of the classic mono-correlation assumption. Further, the spread between expected down and up correlations is time-varying and positively dependent on the current market mood: stock diversification is more difficult when it is needed the most. Thus, the three main advantages of the proposed model are (ⅰ) the distinction between up- and down-correlations, (ⅱ) it actually captures investor expectations as traded in current market prices and (ⅲ) the immediate response to the current market outlook. Practical relevance of this paper is highlighted by the computation of expected up-/down CAPM betas. 

Keywords: implied correlation,  dual-beta, implied volatility,  forward-looking risk, asymmetric dependence

JEL Classification: C58, G11, G17


S. Lang and W. Schadner (2021) in Finance Research Letters (2021)

The economic crisis spurred by the Corona virus (COVID-19) confronts central banks worldwide with new kinds of challenges, as in many countries a stop in production and sales due to lock downs meets enormous fiscal and monetary impulses to overcome the crisis. In Europe the situation is more than ever complicated, as a multitude of monetary policy emergency measures implemented during the financial and European debt crisis of 2007 to 2012 are still in place, such as negative interest rates and central bank bond buying programs. Especially the bond buying programs have been intensified once more during the current Corona crisis. This article contributes to the existing knowledge by proposing a new theoretic trilemma model for the case of a monetary union. Accordingly, there exists a trade-off between stabilizing a monetary union, maintaining free capital mobility and reducing expansionary monetary policy. The results underscore the importance of resolving the trilemma without jeopardizing the currency and financial stability. 

Keywords: European Central Bank, Policy trilemma, Euro area, Free capital mobility, Monetary policy, Financial stability, Corona crisis

JEL Classification: E52, E61

Journal IF: 9.8

W. Schadner (2020) in Finance Research Letters

This paper develops a method to improve estimation accuracy of the equity implied correlation matrix. The advantages of implied versus historical correlations are (i) that they actually reflect investor expectations and (ii) they are able to adopt for sudden changes in the market. While the complete solution to the matrix remains impossible, we address the puzzle from a factor pricing perspective and argue that certain structures are obligatory. Given so, the matrix can be refined into clusters of similar firm characteristics where coefficients are assessable. This allows to enhance the estimation precision while keeping the benefits from being fully forward-looking. 

Keywords: Implied Correlation, Equity, Expected Risk, Risk Factors, Option Implied Volatility

JEL Classification: G12, C58

Journal IF: 9.8

W. Schadner (2020) in Finance Research Letters

This study models a link between ex-ante autocorrelation in expected returns and risk-neutral momentum, enabling a straightforward interpretation of market sentiment. Correspondingly, concepts of fractal Brownian motion are applied to option implied volatility term structures. Based on an empirical investigation of daily SP500 and Euro Stoxx 50 data (2006–2018), we find that the expected return momentum varies over time, as fear spreads much faster than investor confidence can be regained. Thus, we conclude that risk-neutral momentum is a novel perspective for further research in the fields of risk management, asset allocation, and behavioral finance. 

Keywords: Momentum, Sentiment, Implied volatility, Long-term memory, Fractal Brownian motion, Market fear

JEL Classification: C22, G01, G12

Journal IF: 9.8