An Old Dog Learns New Tricks: Novel Applications of Kernel Density Estimators on Two Financial Datasets
Ginley, Matthew Cline
Ensor, Katherine B.
Doctor of Philosophy
In our first application, we contribute two nonparametric simulation methods for analyzing Leveraged Exchange Traded Fund (LETF) return volatility and how this dynamic is related to the underlying index. LETFs are constructed to provide the indicated leverage multiple of the daily total return on an underlying index. LETFs may perform as expected on a daily basis; however, fund issuers state there is no guarantee of achieving the multiple of the index return over longer time horizons. Most, if not all LETF returns data are difficult to model because of the extreme volatility present and limited availability of data. First, to isolate the effects of daily, leveraged compounding on LETF volatility, we propose an innovative method for simulating daily index returns with a chosen constraint on the multi-day period return. By controlling for the performance of the underlying index, the range of volatilities observed in a simulated sample can be attributed to compounding with leverage and the presence of tracking errors. Second, to overcome the limited history of LETF returns data, we propose a method for simulating implied LETF tracking errors while still accounting for their dependence on underlying index returns. This allows for the incorporation of the complete history of index returns in an LETF returns model. Our nonparametric methods are flexible-- easily incorporating any chosen number of days, leverage ratios, or period return constraints, and can be used in combination or separately to model any quantity of interest derived from daily LETF returns. For our second application, we tackle binary classification problems with extremely low class 1 proportions. These ``rare events'' problems are a considerable challenge, which is magnified when dealing with large datasets. Having a minuscule count of class 1 observations motivates the implementation of more sophisticated methods to minimize forecasting bias towards the majority class. We propose an alternative approach to established up-sampling or down-sampling algorithms driven by kernel density estimators to transform the class labels to continuous targets. Having effectively transformed the problem from classification to regression, we argue that under the assumption of a monotonic relationship between predictors and the target, approximations of the majority class are possible in a rare events setting with the use of simple heuristics. By significantly reducing the burden posed by the majority class, the complexities of minority class membership can be modeled more effectively using monotonically constrained nonparametric regression methods. Our approach is demonstrated on a large financial dataset with an extremely low class 1 proportion. Additionally, novel features engineering is introduced to assist in the application of the density estimator used for class label transformation.