Bidirectional relationship between investor sentiment and excess returns: new evidence from the wavelet perspective

ABSTRACT

We propose to use the wavelet concept of the phase angle to determine the lead–lag relationship between investor sentiment and excess returns that are related to the bubble component of stock prices. The wavelet phase angle allows for decoupling short- and long-run relations and is additionally capable of identifying time-varying comovement patterns. Based on the monthly S&P500 index and two alternative monthly US sentiment indicators, we find that in the short run (until 3 months), sentiment is leading returns whereas for periods above 3 months the opposite can be observed. Moreover, the initially strong positive relationship becomes less pronounced with increasing time horizon, thereby indicating that the over- or undervaluation in the short run is gradually corrected in the long run.

KEYWORDS:

• Wavelet phase angle
• wavelet analysis
• sentiment indicator
• excess returns
• speculative bubble
• stock market

JEL CLASSIFICATION:

• G11
• G14
• C22
• C32

Notes

¹ The focus on excess returns is in line with Brown and Cliff (2005), who also relate investor sentiment to some indicator of stock market mispricing.

² The data for the S&P500 index and dividends are obtained from Robert Shiller’s website: http://www.econ.yale.edu/~shiller/data.htm. The source for the consumer price index and the Moody’s 30-year BAA corporate bond yield is the FRED database: http://research.stlouisfed.org/fred2/.

³ This index can be downloaded from http://people.stern.nyu.edu/jwurgler/.

⁴ Download sources and availability of original time series in the time span 1970:01–2014:09:

1. BBS (1970:01–2014:09) and CCI (1970:01–2014:09, until 1978 bimonthly): Thomson Reuters Datastream;

2. ADV, ADVVOL, DECL and DECLVOL (1970:01–2014:09): http://unicorn.us.com/avdec;

3. NYSE short interest (1970:01–2010:04) and margin debt (1970:01–2014:09): http//nyxdata.com/Data-Products/Facts-and-Figures;

4. VIX (1990:01–2014:09): http://finance.yahoo.com;

5. MFF (1984:01–2014.M9): Thomson Reuters Datastream;

6. IPO number and first-day returns (1970:01–2014:09): Jay Ritter’s website http://site.warrington.ufl.edu/ritter/ipo-data.

⁵ Data on the industrial production index, the unemployment rate and the Purchasing Managers Index have been downloaded from http://research.stlouisfed.org/fred2/.

⁶ The computation of ϕ_xy (τ, s) is carried out in MATLAB using the ASToolbox by Aguiar-Conraria and Soares (2011).

⁷ The boundary at 3 years represents a compromise between interpretability and accuracy of results. On the one hand, increasing the boundary could contaminate findings with information of long-run lead–lag relation which can hardly exist. On the other hand, a too low upper bound reduces the number of phase angle values involved in the calculation of the mean values.