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Actuarial Science and Insurance Series: investment-and-risk

Non-parametric prediction of stock returns based on yearly data - The long term view

Is it possible to predict equity returns and premiums with the use of empirical models? This is one of the most frequently pondered and studied questions in finance. This research examines the predictability of returns, taking the actuarial long term view and basing predictions on yearly data.

Author(s): Professor Jens Perch Nielsen - Cass Business School; Michael Scholz - Department of Economics, University of Graz; Stefan Sperlich - University of Geneva

One of the most studied questions in economics and finance is whether equity returns or premiums are predictable. Until the mid-1980's, the view of financial economists was that returns are not predictable, at least not in an economically meaningful way, and that stock market volatility does not change much over time.

In this paper we take the long term actuarial view and base our predictions on yearly data, predicting at a one year horizon. The objective of the research is to show that the prediction of excess stock returns can be improved by the approach of flexible non-parametric and semi-parametric techniques. We further propose a simple wild-bootstrap test which allows us to decide whether we can accept the parametric null hypothesis, that the historical mean is the right model, or whether we prefer the non- or semi-parametric alternative. After we have seen the usefulness of the non-parametric approach, we introduce a possibility to include prior knowledge in the estimation procedure. This can be, for example, a good economic model or likewise a simple parametric regression. We indicate that even the inclusion of the latter in a semi-parametric fashion can enormously improve the prediction of stock returns. To illustrate the potential of our method, we apply it to annual American stock market data. Our results conform to economic theory, namely that the most important part of stock returns is related to the change in interest rates and earnings.

To deliver a statistical insight into our method a non-parametric approach would suffer from the curse of dimensionality, bandwidth or boundary problems. A possible adjustment for this problem is the imposition of more structure. Our method contributes to this strategy due to its new and innovative idea - a model directly guided by economic theory. We achieve by a simple transformation the combination of bias and dimension reduction, i. e. more structure to circumvent the curse of dimensionality. This means in our case that a reliable prior captures some of the characteristics of the shape of the estimating function, and thus a multiplicative correction can cause a bias and dimension reduction in the remaining non-parametric estimation process of the correction factor. Thus, we present here a method which greatly improves non-parametric regression in combination with a simple parametric technique.

The full, draft research paper is available for download at the link below.

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{Nonparametric prediction of stock returns based on yearly data. The long term view.}{https://www.cass.city.ac.uk/__data/assets/pdf_file/0019/356212/predicting-equity-returns-cass-knowledge.pdf}
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