Nonparametric long term prediction of stock returns with generated bond yields

Abstract

Recent empirical approaches in forecasting equity returns or premiums found that dynamic interactions among the stock and bond are relevant for long term pension products. Automatic procedures to upgrade or downgrade risk exposure could potentially improve long term performance for such products. The risk and return of bonds is more easy to predict than the risk and return of stocks. This and the well known stock-bond correlation motivates the inclusion of the current bond yield in a model for the prediction of excess stock returns. Here, we take the actuarial long term view using yearly data, and focus on nonlinear relationships between a set of covariates. We employ fully nonparametric models and apply for estimation a local-linear kernel smoother. Since the current bond yield is not known, it is predicted in a prior step. The structure imposed this way in the final estimation process helps to circumvent the curse of dimensionality and reduces bias in the estimation of excess stock returns. Our validated stock prediction results show that predicted bond returns improve stock prediction significantly.

Forecasting benchmarks of long-term stock returns via machine learning

“…Several generalizations of Theorem 1 have been proposed in the literature. For example, Hansen (2006) proves the uniform and almost sure convergence of the NW estimator, while Scholz et al (2016) show the quasi-complete convergence of the estimator in the case of generated regressors and weakly dependent data. Li and Racine (2007) further show the asymptotic normality of the estimator by calculating the bias term…”

“…Scholz et al (2015) propose a semiparametric bias reduction method for the purpose of importing more structure based on a multiplicative correction with a parametric pilot estimate. Alternatively, Scholz et al (2016) make use of economic theory saying that the price of a stock is driven by fundamentals and investors should focus on forward earnings and profitability. They include information on the same years'-instead of last years'-explanatories and improve predictions.…”

“…The purpose of the current research is to make the first few investigations on suitable benchmark selection from an econometric perspective. We achieve this by machine learning based on the cross-validated time series approach of Nielsen and Sperlich (2003) , Scholz et al (2015) and Scholz et al (2016) to optimize the fully nonparametric statistical estimation and forecasting of the risky asset returns in excess of four different benchmarks: the risk free rate, the long-term interest rate, the earnings-by-price ratio, and the inflation. Our method lets the data speak in themselves via training and learning, while being intuitively informative so that we can identify the covariates driving the system.…”

Nonparametric prediction of stock returns based on yearly data: The long-term view

“…The problem which obviously occurs is that this information is unknown and must also be predicted in some way. For example, Scholz et al (2014) propose a two-step approach for the inclusion of the same years' bond yield, which is related to the change in interest rates. Furthermore, calendar effects or structural breaks, as described for linear models by Paye and Timmermann (2006) should be taken into consideration.…”

A Note on Combining Machine Learning with Statistical Modeling for Financial Data Analysis

“…The Editors of this Special Issue also urge practitioners not to ignore what has already been learned about financial data when using presumably fully automatic ML methods. Regarding financial data for example, Buch-Larsen et al (2005), Bolancé et al (2012), Scholz et al (2015Scholz et al ( , 2016, and Kyriakou et al (2019) (among others) have shown the significant gains in estimation and prediction when including prior knowledge in nonparametric prediction. The first two showed how knowledge-driven data transformation improves nonparametric estimation of distribution and operational risk; the third paper used parametrically-guided ML for stock return prediction; the fourth imputed bond returns to improve stock return predictions; and the last proposed comparing different theory-driven benchmark models regarding their predictability.…”