# Diversification, gambling and market forces

- 323 Downloads

## Abstract

Though simple and appealing, mean-variance portfolio choice theory does not describe actual diversification choices by investors, especially their propensity to gamble and the solvency constraints they face. Using 8 million trades realized by 90,000 individual investors, we show that diversification choices are in fact strongly driven by the skewness of returns, especially in bull markets, but also by the amount to be invested in risky assets. Increasing this amount by 10 % leads to increase by 3.8 % the number of stocks in investors’ portfolios, controlling for portfolio skewness. An important contribution of this paper is to show that the strength of the relationship between diversification and the skewness of returns is shaped by market forces. A strong negative relationship exists in bull markets but disappears in bear markets, a result not found in the literature. Our results survive several robustness checks, including controlling for individual heterogeneity and time-variability of stock price co-movements.

## Keywords

Individual investors Return skewness Diversification Gambling## JEL Classification

G02 G11## Notes

### Acknowledgments

We thank an anonymous referee for suggesting improvements in preceding versions of the paper. We also thank Laurent Deville, Gunter Franke, Burton Hollifield, Jens Jackwerth, Gregory Nini, Charles Noussair, Winfried Pohlmeier, Mark Seasholes, Pierre Six, Marc Willinger, the participants of the DMM meeting (2011, Montpellier), the Konztanz-Strasbourg Workshop (2011, Königsfeld), the Behavioral Insurance Meeting (2011, München), the French Finance Association Meeting (2014) for comments and suggestions. The financial supports of OEE (Observatoire de l’Epargne Européenne) and CCR Asset Management are gratefully acknowledged. We thank Tristan Roger for valuable research assistance and computer programming.

## References

- Albuquerque R (2012) Skewness in stock returns: reconciling the evidence on firm versus aggregate returns. Rev Financ Stud 25:1630–1673CrossRefGoogle Scholar
- Ang A, Bekaert G (2002) International asset allocation with regime shifts. Rev Financ Stud 15:1137–1187CrossRefGoogle Scholar
- Ang A, Bekaert G (2004) How do regimes affect asset allocation? Financ Anal J 60:86–99CrossRefGoogle Scholar
- Arellano M, Bond S (1991) Some tests of specification for panel data: Monte carlo evidence and an application to employment equations. Rev Econ Stud 58:277–297CrossRefGoogle Scholar
- Baker M, Wurgler J, Yuan Y (2012) Global, local, and contagious investor sentiment. J Financ Econ 104:272–287CrossRefGoogle Scholar
- Bali TG, Cakici N, Whitelaw RF (2011) Maxing out: stocks as lotteries and the cross-section of expected returns. J Financ Econ 99:427–446CrossRefGoogle Scholar
- Barber B, Odean T (2000) Trading is hazardous to your wealth: the common stock investment performance of individual investors. J Finance 55(2):773–806CrossRefGoogle Scholar
- Barberis N, Huang M (2008) Stocks as lotteries: the implications of probability weighting for security prices. Am Econ Rev 98:2066–2100CrossRefGoogle Scholar
- Blume ME, Friend I (1975) The asset structure of individual portfolios and some implications for utility functions. In: Rodney L. White Center for Financial Research Working Papers 10–74. Wharton School Rodney L. White Center for Financial ResearchGoogle Scholar
- Brunnermeier MK, Gollier C, Parker JA (2007) Optimal beliefs, asset prices, and the preference for skewed returns. NBER Working Papers 12940. National Bureau of Economic Research IncGoogle Scholar
- Brunnermeier MK, Parker JA (2005) Optimal expectations. Am Econ Rev 95:1092–1118CrossRefGoogle Scholar
- Calvet LE, Campbell JY, Sodini P (2007) Down or out: assessing the welfare costs of household investment mistakes. J Polit Econ 115:707–747CrossRefGoogle Scholar
- Campbell R, Koedijk K, Kofman P (2002) Increased correlation in bear markets. Open Access publications from Maastricht University urn:nbn:nl:ui:27–19571. Maastricht UniversityGoogle Scholar
- Chamberlain G, Rothschild M (1983) Arbitrage, factor structure, and mean-variance analysis on large asset markets. Econometrica 51:1281–1304CrossRefGoogle Scholar
- Chen J, Hong H, Stein JC (2001) Forecasting crashes: trading volume, past returns, and conditional skewness in stock prices. J Financ Econ 61:345–381CrossRefGoogle Scholar
- Conrad J, Dittmar RJ, Ghysels E (2013) Ex ante skewness and expected stock returns. J Finance 68:85–124CrossRefGoogle Scholar
- Cook PJ, Clotfelter CT (1993) The peculiar scale economies of lotto. Am Econ Rev 83:634–643Google Scholar
- Deck C, Schlesinger H (2010) Exploring higher order risk effects. Rev Econ Stud 77:1403–1420CrossRefGoogle Scholar
- Ebert S, Wiesen D (2011) Testing for prudence and skewness seeking. Manag Sci 57:1334–1349CrossRefGoogle Scholar
- Eeckhoudt L, Schlesinger H (2006) Putting risk in its proper place. Am Econ Rev 96:280–289CrossRefGoogle Scholar
- Entrop O, McKenzie M, Wilkens M, Winkler C (2014) The performance of individual investors in structured products. Rev Quant Finance Account. doi: 10.1007/s11156-014-0479-8
- Forrest D, Simmons R, Chesters N (2002) Buying a dream: alternative models of demand for lotto. Econ Inq 40:485–496CrossRefGoogle Scholar
- Foucault T, Sraer D, Thesmar DJ (2011) Individual investors and volatility. J Finance 66:1369–1406CrossRefGoogle Scholar
- Francis JC, Kim D (2013) Modern portfolio theory: foundations, analysis and new developments. Wiley, New YorkGoogle Scholar
- Garrett TA, Sobel RS (1999) Gamblers favor skewness, not risk: further evidence from united states’ lottery games. Econ Lett 63:85–90CrossRefGoogle Scholar
- Goetzmann WN, Kumar A (2007) Equity portfolio diversification. Rev Finance 12:433–463CrossRefGoogle Scholar
- Gollier C (2005) Optimal illusions and decisions under risk. CESifo Working Paper Series 1382. CESifo Group MunichGoogle Scholar
- Harding MC (2008) Explaining the single factor bias of arbitrage pricing models in finite samples. Econ Lett 99:85–88CrossRefGoogle Scholar
- Harvey CR, Siddique A (1999) Autoregressive conditional skewness. J Financ Quant Anal 34:465–487CrossRefGoogle Scholar
- Harvey CR, Siddique A (2000) Conditional skewness in asset pricing tests. J Finance 55:1263–1295CrossRefGoogle Scholar
- Karolyi GA, Stulz RM (2003) Are financial assets priced locally or globally? In: Constantinides G, Harris M, Stulz RM (eds) Handbook of the economics of finance, volume 1 of Handbook of the Economics of Finance. chapter 16. Elsevier, Amsterdam, pp 975–1020Google Scholar
- Kelly M (1995) All their eggs in one basket: portfolio diversification of us households. J Econ Behav Organ 27:87–96CrossRefGoogle Scholar
- Kim WC, Fabozzi FJ, Cheridito P, Fox C (2014) Controlling portfolio skewness and kurtosis without directly optimizing third and fourth moments. Econ Lett 122:154–158CrossRefGoogle Scholar
- Kimball MS (1990) Precautionary saving in the small and in the large. Econometrica 58:53–73CrossRefGoogle Scholar
- Kraus A, Litzenberger RH (1976) Skewness preference and the valuation of risk assets. J Finance 31:1085–1100Google Scholar
- Kumar A (2007) Do the diversification choices of individual investors influence stock returns? J Financ Mark 10:362–390CrossRefGoogle Scholar
- Kumar A (2009) Who gambles in the stock market? J Finance 64:1889–1933CrossRefGoogle Scholar
- Lease RC, Lewellen WG, Schlarbaum GG (1974) The individual investor: attributes and attitudes. J Finance 29:413–433CrossRefGoogle Scholar
- Lesmond DA, Ogden JP, Trzcinka CA (1999) A new estimate of transaction costs. Rev Financ Stud 12:1113–1141CrossRefGoogle Scholar
- Lewis KK (1999) Trying to explain home bias in equities and consumption. J Econ Lit 37:571–608CrossRefGoogle Scholar
- Liu H (2014) Solvency constraint, underdiversification, and idiosyncratic risks. J Financ Quant Anal 49:1–39CrossRefGoogle Scholar
- Longin F, Solnik B (2001) Correlation structure of international equity markets during extremely volatile periods. J Finance 56:649–676CrossRefGoogle Scholar
- Menezes C, Geiss C, Tressler J (1980) Increasing downside risk. Am Econ Rev 70:921–932Google Scholar
- Mitton T, Vorkink K (2007) Equilibrium underdiversification and the preference for skewness. Rev Financ Stud 20:1255–1288CrossRefGoogle Scholar
- Nagel S (2005) Short sales, institutional investors and the cross-section of stock returns. J Financ Econ 78:277–309CrossRefGoogle Scholar
- Odean T (1999) Do investors trade too much? Am Econ Rev 89:1279–1298CrossRefGoogle Scholar
- Ortobelli S, Biglova A, Huber I, Racheva-Iotova B, Stoyanov S (2005) Portfolio choice with heavy-tailed distributions. J Concr Appl Math 3:353–376Google Scholar
- Shefrin H, Statman M (2000) Behavioral portfolio theory. J Financ Quant Anal 35:127–151CrossRefGoogle Scholar
- Shu PG, Chiu SB, Chen HC, Yeh YH (2004) Does trading improve individual investor performance? Rev Quant Finance Account 22:199–217CrossRefGoogle Scholar
- Stoyanov S, Rachev S, Racheva-Iotova B, Fabozzi F (2011) Fat-tailed models for risk estimation. J Portf Manag 37:107–117CrossRefGoogle Scholar
- Tarazona-Gomez M (2004) Are individuals prudent? An experimental approach using lottery choices. Technical Report, Copenhagen Business SchoolGoogle Scholar
- Tversky A, Kahneman D (1992) Advances in prospect theory: cumulative representation of uncertainty. J Risk Uncertain 5:297–323CrossRefGoogle Scholar
- Walker I, Young J (2001) An economist’s guide to lottery design. Econ J 111:700–722CrossRefGoogle Scholar
- Xu J (2007) Price convexity and skewness. J Finance 62:2521–2552CrossRefGoogle Scholar