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Aggregate idiosyncratic volatility, dynamic aspects of loss aversion, and narrow framing

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Abstract

We test the dynamic aspects of the loss aversion feature of Kahneman and Tversky (Prospect theory: an analysis of decision under risk. Econometrica 47:263–291, 1979) and find that idiosyncratic volatility is negatively associated with unrealized gains of stock returns. Moreover, we show that this negative relationship is stronger for stocks with high individual investors’ holdings. Finally, we show that controlling for firm age as defined by Fink et al. (What drove the increase in idiosyncratic volatility during the internet boom? J Financ Quant Anal 45:1253–1278, 2010) eliminates the significance of retail trading proportions as a driver of idiosyncratic volatility. These findings are robust to price, sentiment, and IPO dates. Bivariate vector auto-regression confirms the causality of unrealized gains of stock returns on idiosyncratic volatility.

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Notes

  1. Examples of such studies include Malkiel and Xu (2003), Bennett and Sias (2006), Brown and Kapadia (2007), Wei and Zhang (2006), Ang et al. (2006), Bali and Cakici (2008), Fu (2009), Bekaert et al. (2010), Brandt et al. (2010), Fink et al. (2010), Bali et al. (2011), Peterson and Smedema (2011) and Berrada and Hugonnier (2013).

  2. Please see page 1249 in Barberis and Huang (2001) for more elaborate explanation.

  3. According to Barberis and Huang (2001), investors in the economy of individual stock accounting (portfolio accounting) get utility from the gains and losses in the value of individual stocks (overall portfolio of stocks) they own.

  4. This data can be found at the following address: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/.

  5. Institutional Ownership is the sum of the shares held by all institutions at the end of every quarter divided by the total outstanding shares in Thomson Financial 13-F filing data.

  6. The authors show that Max defined as the average of the five highest returns of the month exhibits better properties consistent with lottery preferences.

  7. This data can be found at the following address: http://bear.warrington.ufl.edu/ritter/ipodata.htm.

  8. In Grinblatt and Han (2005) model, the reference price for a stock is obtained as the turnover weighted average of past stock price and past reference price. That is, \( RP_{i,t} = V_{i,t - 1} P_{i,t - 1} + (1 - V_{i,t - 1} )RP_{i,t - 1} \). The recursive substitution of past reference prices on the right hand side of the above equation leads to Eq. (3) with the exception that the summation is over infinite periods. For empirical implementation, we sum over the number of trading days in recent 3 years. Grinblatt and Han (2005), however, find robust results using 3, 5, or 7 years of data.

  9. Barberis and Huang (2001) considers two economies to study equilibrium firm-level stock returns. The first economy is one in which investors get direct utility not only from consumption but also from gains and losses in the value of their overall portfolio of stocks. The second economy is one in which investors which investors get direct utility not only from consumption but also from gains and losses in the value of individual stocks they own. They find that individual stock accounting can explain high mean and excess volatility.

  10. Computed as the product of daily idiosyncratic volatility and the square root of the number of trading days in the month.

  11. The investor sentiment (Sent) data is from Baker and Wurgler (2006) and downloaded from Wurgler’s website.

  12. We only report results based on equal-weighted idiosyncratic volatility from here on as they prove to be similar to those based on value-weighted idiosyncratic volatility.

  13. Fink et al. (2010) also suggest that this bias is particularly severe with the inclusion of Nasdaq firms in the CRSP database in the early 1970 s, several of which are included in Brandt et al. (2010) sample.

  14. We deeply appreciate the insightful comment from the anonymous referee on this.

  15. See Brandt et al. (2010).

  16. For brevity, we only report results pertaining to the lowest and highest portfolios.

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Authors and Affiliations

  1. Department of Economics and Finance, Louisiana Tech University, Ruston, LA, 71272, USA

    Jungshik Hur

  2. Department of Finance, University of Mississippi, Ruston, LA, 71272, USA

    Cedric Mbanga Luma

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  1. Jungshik Hur
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  2. Cedric Mbanga Luma
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Correspondence to Jungshik Hur.

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Hur, J., Luma, C.M. Aggregate idiosyncratic volatility, dynamic aspects of loss aversion, and narrow framing. Rev Quant Finan Acc 49, 407–433 (2017). https://doi.org/10.1007/s11156-016-0595-8

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