Good volatility, bad volatility, and time series return predictability

Abstract

We propose a least squares estimator weighted by a combination of lagged realized semivariances related to positive and negative returns (WLS-CRS) and use univariate models alone and in combination to reveal significant return predictability. For an investor with a mean-variance preference who allocates a portfolio based on an equal-weighted combination of WLS-CRS model forecasts, the annual certainty equivalent return is 242.8 basis points higher than that received by an investor whose portfolio is allocated based on historical average forecasts. In forecasting stock returns, WLS-CRS estimates outperform the popular ordinary least squares estimates in both statistical and economic evaluation frameworks. WLS-CRS also outperforms estimators based on least squares weighted by lagged realized volatility. We further demonstrate the dominant role of negative return semivariance in improved forecasting performance. Our main findings hold through several robustness checks, including alternative validation samples, different risk aversion coefficients, and various forecast combinations.

KEYWORDS:

• Return forecasting
• excess returns
• realized semivariance
• weighted least squares
• machine learning

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Earlier papers describing the detection of return predictability include but are not limited to Stambaugh (1986, 1999), Campbell (2000), Bossaerts and Hillion (1999), Goyal and Welch (2008), Lamoureux and Zhou (1996), Pesaran and Timmermann (1995), Avramov (2002), Patelis (1997), and Guo (2006).

2 VIX information is also used to derive ex-ante variance estimates after 1991.

3 http://www.hec.unil.ch/agoyal/

4 We thank the anonymous referee for this constructive suggestion.

5 These countries include Australia, Canada, France, Germany, Italy, Japan, Netherlands, Sweden, Switzerland, United Kingdom.

Additional information

Funding

This work is supported by the Major Program of the National Social Science Foundation of China (grant number 19ZDA105). Yudong Wang acknowledges the financial support from National Natural Science Foundation of China (numbers 71672081, 72071114), Fok Ying-Tong Education Foundation of China and Jiangsu Social Science Talent Grant.

Notes on contributors

Honghai Yu

Honghai Yu is a professor of finance in Nanjing University. He is interested in behavioral finance. His papers are published in international journals such as Management Science and Journal of Empirical Finance.

Xianfeng Hao

Xianfeng Hao is a graduate student of finance in Nanjing University. He is interested in financial forecasting. His papers are published in international journals such as Journal of Financial Markets and Energy Economics.

Yudong Wang

Yudong Wang is a professor of finance in Nanjing University of Science and Technology. He is interested in financial forecasting. His papers are published in international journals such as Management Science, Journal of Banking and Finance, Journal of Financial Markets and Journal of Empirical Finance.