Discount curve estimation by monotonizing McCulloch Splines

In this paper a new and very simple method for monotone estimation of discount curves is proposed. The main idea of this approach is a simple modification of the commonly used (unconstrained) Mc-Culloch Spline. We construct an integrated density estimate from the predicted values of the discount curve. It can be shown that this statistic is an estimate of the inverse of the discount function and the final estimate can easily be obtained by a numerical inversion. The resulting procedure is extremely simple and we have implemented it in Excel and VBA, respectively. The performance is illustrated by three examples, in which the curve was previously estimated with an unconstrained McCulloch Spline. --

New backtests for unconditional coverage of the expected shortfall

We present a new backtest for the unconditional coverage property of the ES. The test statistic is available for finite out-of-sample size which leads to better size and power properties compared to existing tests. Moreover, it can be easily extended to a multivariate test

Diversification effects between stock indices

During the World Financial Crisis it became obvious that classical models of portfolio theory significantly under-estimated risks, especially with regard to stocks. Instabilities of correlations and volatilities, the relevant parameters characterizing risk, led to overestimation of diversification effects and consequently to under-estimation of risks. In this article, we analyze diversification effects concerning stocks during different market periods of the previous decade. We show that parameters and risks significantly change with market periods and find that the impact of fluctuations and estimation errors is 5 times larger for volatilities than for correlations. Moreover, it turns out that diversification between sectors is more efficient than diversification between countries

Some practical aspects of sequential change point detection

In this report we investigate the finite sample properties of a new online monitoring scheme which was recently introduced by Gösmann et al. (2020) by means of a simulation study and a real data example. We also develop an algorithm which can be used in an active risk management. We start with an introduction in the basic notation and an explanation of the monitoring procedure, continue with an extensive simulation study to provide recommendations for the choice of several tuning parameters. Finally we present some illustration analyzing the Standard & Poor’s 500, MSCI World and MSCI Emerging Markets indices

Stabilität von Diversifikationseffekten im Markowitz-Modell

Im Zuge der Finanzkrise wurde deutlich, dass das Risiko in klassischen Modellen zur Portfoliotheorie deutlich unterschätzt wurde. Die Instabilität der relevanten Risikoparameter, also Korrelationen und Volatilitäten, führte dazu, dass Diversifikationseffekte über- und somit Risiken unterschätzt wurden. Ziel dieses Beitrags ist es, Diversifikationseffekte in verschiedenen Marktphasen des letzten Jahrzents zu untersuchen und die Auswirkungen für das Risikomanagement zu quantifizieren. Dabei zeigt sich, dass sich die Parameter bzw. Risiken sehr deutlich mit der jeweiligen Marktphase ändern und eine Parameterschätzung aus historischen Mittelwerten nicht zielführend ist. JEL-Klassifikation: C 52, G 11; G 3

An empirical study of correlation and volatility changes of stock indices and their impact on risk figures

During world financial crisis it became obvious that classical models of portfolio theory significantly under-estimated risks, especially with regard to stocks. Instabilities of correlations and volatilities, the relevant parameters characterizing risk, led to over-estimation of diversification effects and consequently to under-estimation of risks. In this article, we analyze the relevant risk parameters concerning stocks during different market periods of the previous decade. We show that parameters and risks significantly change with market periods and find that the impact of fluctuations and estimation errors is ten times larger for volatilities than for correlations. Moreover, it turns out that diversification between sectors is more efficient than diversification between countries

Evaluating value-at-risk forecasts

We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect first-order instationarities in the matrix of VaR-violations. Second, we propose χ 2-tests for detecting cross-sectional and serial dependence in the VaR-forecasts. Moreover, we combine our new backtests with a test of unconditional coverage to yield two new backtests of multivariate conditional coverage. In all cases, a bootstrap approximation is possible, but not mandatory in terms of empirical size and power

Automated Portfolio Optimization Based on a New Test for Structural Breaks

We present a completely automated optimization strategy which combines the classical Markowitz mean-variance portfolio theory with a recently proposed test for structural breaks in covariance matrices. With respect to equity portfolios, global minimum-variance optimizations, which base solely on the covariance matrix, yield considerable results in previous studies. However, financial assets cannot be assumed to have a constant covariance matrix over longer periods of time. Hence, we estimate the covariance matrix of the assets by respecting potential change points. The resulting approach resolves the issue of determining a sample for parameter estimation. Moreover, we investigate if this approach is also appropriate for timing the reoptimizations. Finally, we apply the approach to two datasets and compare the results to relevant benchmark techniques by means of an out-of-sample study. It is shown that the new approach outperforms equally weighted portfolios and plain minimum-variance portfolios on average

A completely automated optimization strategy for global minimum-variance portfolios based on a new test for structural breaks

We present a completely automated optimization strategy which combines the classical Markowitz mean-variance portfolio theory with a recently proposed test for structural breaks in co- variance matrices. With respect to equity portfolios, global minimum-variance optimizations, which base solely on the covariance matrix, yield considerable results in previous studies. However, nancial assets cannot be assumed to have a constant covariance matrix over longer periods of time. Hence, we estimate the covariance matrix of the assets by respecting potential change points. The resulting approach resolves issues like timing or determining a sample for parameter estimation. Moreover, we apply the approach to two datasets and compare the results to relevant benchmark techniques by means of an out-of-sample study. It is shown that the new approach outperforms equally weighted portfolios and plain minimum-variance portfolios on average

A new online-test for changes in correlations between assets

We apply a new test to determine whether correlations between assets are constant over time. The test statistic is a suitably standardized maximum of cumulative empirical correlation coefficients. An empirical application to various assets suggests that the test performs well in applications. We also propose a portfolio strategy based on our test which hedges against potential financial crises and show that it works in practice. JEL Classification: C12, C14, G01, G1