Equities

Estimating the Risk-Return Trade-Off With Overlapping Data Inference

Topics - Equities

${ numberSection } ${ text }
Estimating the Risk-Return Trade-Off With Overlapping Data Inference

Netspar Discussion Paper                              

When financial economists empirically investigate the predictions of their models, they must choose the horizon over which the agents in the model hold their investments. For example, Merton’s Intertemporal Capital Asset Pricing Model (ICAPM) is a theoretical continuous-time model, but empirical researchers usually choose a one-month or one-quarter horizon as the most appropriate test environment even though daily data are available.

The most popular methods for modeling the conditional variances and covariances that are the sources of risk in these models are generalized autoregressive conditional heteroskedasticity (GARCH) and mixed data sampling (MIDAS), which are usually implemented with maximum likelihood estimation (MLE) by sampling the data at the same frequency as the horizon chosen for the model.

Here the authors demonstrate that when the data are sampled more finely than the horizon of the model, reearchers can use all of the available data to lower the standard errors of the estimates and improve the power of the tests of the theories by using overlapping data inference (ODIN). Their insight is to use the first order conditions of MLE as orthogonality conditions of Hansen’s Generalized Method of Moments (GMM).

The authors estimate the parameters of the model from the average of the overlapping MLE samples and construct appropriate standard errors that account for the serial correlation induced by the overlapping data.

AQR Capital Management, LLC, (“AQR”) provide links to third-party websites only as a convenience, and the inclusion of such links does not imply any endorsement, approval, investigation, verification or monitoring by us of any content or information contained within or accessible from the linked sites. If you choose to visit the linked sites, you do so at your own risk, and you will be subject to such sites' terms of use and privacy policies, over which AQR.com has no control. In no event will AQR be responsible for any information or content within the linked sites or your use of the linked sites.

 

The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees. This information is not intended to, and does not relate specifically to any investment strategy or product that AQR offers. It is being provided merely to provide a framework to assist in the implementation of an investor’s own analysis and an investor’s own view on the topic discussed herein. Past performance is not a guarantee of future results.

 

Hypothetical performance results have many inherent limitations, some of which, but not all, are described herein. The hypothetical performance shown was derived from the retroactive application of a model developed with the benefit of hindsight.  Hypothetical performance results are presented for illustrative purposes only.

 

Diversification does not eliminate the risk of experiencing investment loss.

 

Certain publications may have been written prior to the author being an employee of AQR.

This material is intended for informational purposes only and should not be construed as legal or tax advice, nor is it intended to replace the advice of a qualified attorney or tax advisor.