Using the options market as a case study, the authors explore how investors suffer from nominal price illusion by overestimating the growth potential for low-priced stocks relative to high-priced ones.
Nominal price levels influence investor behavior, but the reason is unclear. Investors systematically overestimate the skewness of low-priced stocks, placing an inordinate amount of emphasis on price when forming expectations of skewness and believing low-priced stocks to have more room to grow than higher-priced ones. The options market is a natural environment in which to examine this phenomenon of behavioral finance.
How Is This Research Useful to Practitioners?
The literature has documented how share price influences investor behavior, including how firms price IPOs and how share prices behave following stock splits. Time-varying investor preferences inform companies’ proactive management of share prices. Investment professionals have long known that investor perception affects stock prices. But why perception affects prices has been subject to much conjecture and undergone little, if any, empirical research.
The authors provide evidence of investors’ cognitive bias in the way that they perceive the ability of nominal share prices to produce future returns. Investors believe erroneously that low-priced stocks have more growth potential than higher-priced ones. The authors focus on the variable of skewness as a metric by which to assess investors’ expectations of share price appreciation. The options market serves as a natural laboratory for the authors to gauge these expectations.
Their investigation includes three tests, each of which independently supports investors’ overestimation of low-priced stock skewness. The first shows that in the entire cross section of stocks, investors place an undue emphasis on the role of price in formulating skewness expectations. In the second, the authors discover options portfolio mispricing that appears to support the same. In the third test, stock splits demonstrate that investors’ skewness expectations rise (fall) on the date of a stock split (reverse split) to a lower (higher) price.
Students of behavioral finance as well as analysts and traders would find this unique aspect of investor behavior helpful in decision making, analysis, and implementation, as would portfolio managers. Corporate finance directors could use these findings as additional fodder to support their efforts to maximize firm value by ministering to investors’ time-varying preferences.
How Did the Authors Conduct This Research?
The authors’ data include options price, volume, open interest, and implied volatility from IvyDB’s OptionsMetrics database for January 1996–December 2012. They scrub the data to remove options that lack best bid and offer prices as well as options with bid prices equal to or less than $0.05. Also removed are options with zero open interest, those that violate arbitrage bounds, those that have special settlement arrangements, and those whose underlying stock price is less than $10. CRSP is the source for share data as well as for stock splits.
To evaluate whether and to what extent nominal share prices systemically drive investors’ misperception of skewness, the authors use risk-neutral skewness (RNSkew) implied from options prices because it provides an unbiased and rational metric of expected skewness that captures how investors’ expectations of asymmetrical return distributions change.
They perform three separate tests, each of which supports their hypothesis that investors overestimate the skewness of low-priced stocks. In the first, the authors examine the entire cross section of optionable stocks and control for such firm characteristics as size and trading volume to remove how those traits may correlate with price. Using regressions, they analyze the co-movement between various skewness measures and price and find a strong inverse correlation between RNSkew and price. Investors continue to overweight price’s influence on skewness. Open interest and volume data on options support investors’ heightened optimism toward low-priced stocks; the ratio of call to put open interest and volume is much greater for low-priced stocks than for high-priced stocks.
In the second exercise, the authors test the hypothesis that investors suffer from nominal price illusion. Such misperception has pricing implications for options portfolios. Overemphasis on low-priced stocks’ expected skewness seems to infer that a portfolio of out-of-the-money (OTM) calls for low-priced stocks would be overvalued relative to OTM calls for high-priced shares. Estimation of returns to options portfolios reveals that overpricing in call options increases as the underlying stock prices decrease.
In the final experiment, the authors consider how investor expectations change around the time that a stock split occurs. RNSkew increases by more than 40% on the day of a split to a lower price level. The authors observe the opposite occurrence when a reverse split that results in higher price per share happens. Examination of implied volatilities after the split confirms biased expectations for low-priced stocks’ upward potential in the form of increased implied volatility of call options after a split.
Investor predilection for low-priced stocks appears to be an anomaly that contradicts the weak form of the efficient market hypothesis. Succumbing to nominal price illusion, investors place an inordinate amount of weight on the importance of price when developing skewness expectations. Options strategies that manage to exploit this investor preference produce outsized returns. To what extent other developed markets experience similar investor behavior with certain asset classes—through derivatives markets or the primary asset markets themselves—could be a subject for further inquiry.