Seminar Master Major Financial Economics : Quantitative Methods in Finance

Transcription

1 M. Sc. Theoplasti Kolaiti Leibniz University Hannover Seminar Master Major Financial Economics : Quantitative Methods in Finance Winter Term 2018/2019 Please note: The seminar paper should be 15 pages overall and contain a theoretical discussion of the respective topic/methods that summarizes the literature as well as an empirical application. The empirical application requires the use of statistical software such as R or Matlab - knowledge of which is required. The points listed under objectives are a suggestion meant as an inspiration and should not be understood as an outline. Similarly, the cited literature should be seen as a starting point. Topics 1. Regression based Tests of the Capital Asset Pricing Model Description: The Capital Asset Pricing Model is widely used in areas such as the evaluation of investment opportunities or the measurement of fund performance. It relates the expected return of an asset to the expected excess return of the market, the risk free interest rate and the covariance of the respective asset with the market portfolio. This implies several empirically testable predictions that have been extensively studied in the literature. Objective: Brief review of the testable predictions from the CAPM, discussion of the econometric issues encountered by tests based on time series regressions and cross-sectional regressions, economic interpretation of tests. Literature: Campbell et al. (1997), Fama and French (2004). 2. Multifactor Models for Asset Pricing Description: Multifactor models theoretically arise from the arbitrage pricing theory or the intertemporal CAPM (among others) and they generalize the CAPM in the sense that they allow for more than one priced risk factor. Empirically, it is found that multifactor models allow to explain more of the cross-sectional variation in expected stock returns than the simpler CAPM. On the other hand, multifactor models produce less testable hypotheses than the simpler model with an observable factor. Objective: Brief discussion of multifactor models, focus on the econometric issues involved in the estimation and testing of multifactor models for asset pricing. Literature: Campbell et al. (1997), Fama and French (1996), Fama and French (2004). 3. Present Value Relations for Stocks Description: Present value models relate the value of a stock to the future stream of dividends and a stochastic discount factor. Since the present value reacts more strongly to persistent changes in future dividends or the discount factor than it does to transitory changes, there is a natural connection between present value model and long horizon asset returns.

2 Objective: Discussion of the present value model for stock prices, long horizon asset return predictability and the econometric complications involved in testing long horizon predictability, such as overlapping observations. Literature: Campbell et al. (1997), Boudoukh et al. (2006), Koijen and Van Nieuwerburgh (2011). 4. Time Series Predictability in Stock Returns Description: The popular random walk model implies that stock returns are unpredictable. While this is a good approximation on a daily frequency, there are economic arguments that unites stock return predictability with the efficient market hypothesis insofar as predictor variables may co-vary with time-varying aggregate risk. There is empirical evidence in support of return predictability on monthly or quarterly horizons. However, there are several econometric issues that complicate inference on stock return predictability. Objective: Relationship between return predictability and efficient market hypothesis, bounds on the level of predictability, forecast methodology and associated econometric issues, forecast evaluation, summary of empirical evidence, role of data snooping. Literature: Breitung and Demetrescu (2015), Rapach et al. (2013). 5. Value at Risk and Extreme Value Theory Description: Determining the likelihood of extreme events is notoriously difficult, since - by definition - they are observed very rarely. This causes unusual challenges for their statistical analysis. However, this task is extremely important, for example to determine accurate risk measures such as VaR. Extreme value theory is a branch of statistics, that can be used to circumvent this problem by deriving the distribution of extremes from that of commonly observed events. Objective: Discussion of VaR and extreme value theory, estimation of the tail index, application of extreme value theory to financial risk management. Literature: Tsay (2005), Christoffersen (2012). 6. GARCH-Models Description: Generalized autoregressive conditional heteroscedasticity models are one of the most commonly applied volatility models in practice. In these models the variance of innovations is a function of the magnitude of previous innovations. Objective: Model definition, stationarity conditions, existence of moments, estimation, forecasting, testing for GARCH effects, extensions of the basic model. Literature: Tsay (2005) 7. Multivariate GARCH and Dynamic Conditional Correlations Description: Financial times series are known to exhibit features such as non-normality and volatility clustering. This is often modelled using conditional heteroscedasticity models such as GARCH. In financial applications it is often required to model the joint distribution of several variables, such as that of a stock portfolio and a bond portfolio. This requires multivariate extensions of the GARCH model that also capture time variation in the co-movement between these variables.

3 Objective: Review of multivariate GARCH models with special focus on the DCC model, discussion of model selection, estimation and testing. Literature: Tsay (2005), Christoffersen (2012), Engle (2002). 8. Risk Management using Copulas Description: Managing risks for multiple assets or portfolios requires to work with multivariate distributions. Copulas offer a particularly simple way to bind together several univariate distributions to flexible joint distributions. This has made them a popular tool in risk management. Objective: Introduction to copulas, discussion of their properties, estimation and specification testing. Literature: Christoffersen (2012), Mikosch (2006), Patton (2009). 9. Regression Analysis with Time Series Data Description: Regression analysis with time series data entails special challenges since the innovations are often heteroscedastic and exhibit serial correlation. Heteroscedasticity and autocorrelation consistent (HAC) estimates of the variance covariance matrix address these issues and provide robust standard errors. Objective: Discussion of different HAC estimators, their properties, lag selection, possibly fixed-bandwidth asymptotics, meaningful economic application. Literature: Martin et al. (2012), Kiefer et al. (2005), Andrews (1991). 10. TAR- and STAR-Models Description: Regime switching models allow for non-linear behavior in time series by linking different simple linear models with a transition function. Therefore, the behavior of the time series in threshold autoregressive (TAR) and smooth transition models depends on the magnitude of the previous observation. This kind of behavior is useful to model deviations from the purchasing power parity. Objective: Introduction to TAR and STAR models, discussion of their properties, tests for non-linearity, application to purchasing power parity. Literature: Teräsvirta et al. (2010) 11. Markov-Switching Models Description: Markov-switching models are another class of regime switching models that was originally developed to model asymmetric behavior of the unemployment rate in boom and bust periods. Here the transition between the regimes is driven by an unobserved state variable. Objective: Introduction and discussion of the Markov switching autoregressive model, properties of Markov chains, stationarity conditions, estimation, forecasting, application to economic time series. Literature: Hamilton (1989), Hamilton (1994) 12. Testing for Structural Breaks

4 Description: Economic and financial time series are subject to structural changes due to changing regulations, political events or social behaviors, among others. Testing for structural change is therefore an important part of econometric analyses. The CUSUM test for a single structural change is based on the partial sum of the residuals from a regression analysis, whereas the Bai-Perron procedure employs repeated F-tests to detect multiple structural breaks. Objective: Description and discussion of a selection of structural break tests, including the testing principles and limit distributions, application to meaningful economic example. Literature: Kleiber et al. (2002), Brown et al. (1975), Bai and Perron (1998), Bai and Perron (2003) 13. Unit Root Tests and Structural Breaks Description: Since many economic time series are highly persistent, there is an ongoing debate whether they are difference stationary or trend stationary, which has important implications for the impact of economic shocks. Tests for the null hypothesis of a difference stationary process can falsely reject if the series is also subject to structural change. Therefore, there are several extensions that allow for the presence of structural breaks. Objective: Discussion of difference and trend stationarity and standard unit root tests, overview of the most important unit root tests that allow for structural breaks, discussion of testing principles and their statistical properties, application to economic time series. Literature: Martin et al. (2012), Perron (1989), Perron (2006) 14. Vector-Autoregressive Models Description: VAR processes are a generalisation of univariate autoregressive models to vector-valued time series. This allows to model the relationship between several variables. The model class is often applied for macroeconomic forecasts. Objective: Introduction, different representations, stationarity conditions, estimation, possibly structural models or relationship to cointegration, application to macroeconomic forecasting. Literature: Hamilton (1994), Lütkepohl (2005), Martin et al. (2012) 15. Analysis of Cointegrated Time Series Description: A cointegrating relationship exists, if two or more non-stationary time series have a common stochastic trend, so that a stationary linear combination of the series exists. This concept is extremely important in economics, since it allows to model equilibrium relationships. Procedures to test for the existence of a cointegrating relationship include the Engle-Granger procedure, the Phillips-Ouliares test and the Johansen test. Deviations from the equilibrium relationship are modeled by vector error correction models. Objective: Definition and explanation of cointegration, discussion of selected testing procedures, estimation of the cointegrating vector, discussion of vector error correction models. Literature: Engle and Granger (1987), Phillips and Ouliaris (1990), Hamilton (1994), Martin et al. (2012)

5 References Andrews, D. W. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica: Journal of the Econometric Society, pages Bai, J. and Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66: Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18:1 22. Boudoukh, J., Richardson, M., and Whitelaw, R. F. (2006). The myth of long-horizon predictability. The Review of Financial Studies, 21(4): Breitung, J. and Demetrescu, M. (2015). Instrumental variable and variable addition based inference in predictive regressions. Journal of Econometrics, 187(1): Brown, R. L., Durbin, J., and Evans, J. M. (1975). Techniques for testing the constancy of regression relationships over time. Journal of the Royal Statistical Society. Series B (Methodological), pages Campbell, J. Y., Lo, A. W.-C., and MacKinlay, A. C. (1997). The econometrics of financial markets. princeton University press. Christoffersen, P. F. (2012). Elements of financial risk management. Academic Press. Engle, R. (2002). Dynamic conditional correlation. Journal of Business & Economic Statistics, 20(3): Engle, R. F. and Granger, C. W. (1987). Co-integration and error correction: representation, estimation, and testing. Econometrica: Journal of the Econometric Society, pages Fama, E. F. and French, K. R. (1996). Multifactor explanations of asset pricing anomalies. The journal of finance, 51(1): Fama, E. F. and French, K. R. (2004). The capital asset pricing model: Theory and evidence. The Journal of Economic Perspectives, 18(3): Hamilton, J. (1994). Time Series Analysis, volume 2. Cambridge Univ Press. Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica: Journal of the Econometric Society, pages Kiefer, N. M., Vogelsang, T. J., et al. (2005). A new asymptotic theory for heteroskedasticityautocorrelation robust tests. Econometric Theory, 21(6):1130. Kleiber, C., Hornik, K., Leisch, F., and Zeileis, A. (2002). strucchange: An r package for testing for structural change in linear regression models. Journal of Statistical Software, 7(2):1 38. Koijen, R. S. and Van Nieuwerburgh, S. (2011). Predictability of returns and cash flows. Annu. Rev. Financ. Econ., 3(1): Lütkepohl, H. (2005). New introduction to multiple time series analysis. Springer Science & Business Media. Martin, V., Hurn, S., and Harris, D. (2012). Econometric modelling with time series: specification, estimation and testing. Cambridge University Press.

6 Mikosch, T. (2006). Copulas: Tales and facts. Extremes, 9(1): Patton, A. J. (2009). Copula based models for financial time series. In Handbook of financial time series, pages Springer. Perron, P. (1989). The great crash, the oil price shock, and the unit root hypothesis. Econometrica: Journal of the Econometric Society, pages Perron, P. (2006). Dealing with structural breaks. Palgrave Handbook of Econometrics, 1: Phillips, P. C. and Ouliaris, S. (1990). Asymptotic properties of residual based tests for cointegration. Econometrica: Journal of the Econometric Society, pages Rapach, D. E., Zhou, G., et al. (2013). Forecasting stock returns. Handbook of Economic Forecasting, 2(Part A): Teräsvirta, T., Tjøstheim, D., and Granger, C. W. J. (2010). Modelling nonlinear economic time series. Oxford University Press Oxford. Tsay, R. S. (2005). Analysis of Financial Time Series, volume 543. John Wiley & Sons.