Lottery Demand Research Articles

What Drives Demand for State-Run Lotteries? Evidence and Welfare Implications

Abstract We use natural experiments embedded in state-run lotteries and a new nationally representative survey to provide reduced-form and structural estimates of risk preferences and behavioural biases in lottery demand, and to explore the implications for optimal lottery design. We find that sales respond more to the expected value of the jackpot than to price but are unresponsive to variation in the second prize—a pattern that is consistent with probability weighting but is inconsistent with standard parameterizations. In the survey, we find that lottery spending decreases modestly with income and is strongly associated with measures of innumeracy, poor statistical reasoning, and other proxies for behavioural bias, which also decline with income. Regression predictions suggest that Americans would spend 43% less on lotteries if they were unbiased, while the remaining lottery demand is due to other factors such as anticipatory utility or entertainment value. We use these empirical moments to estimate a model of socially optimal lottery design. In the model, current multi-state lottery designs increase welfare but may harm heavy spenders.

Lottery demand, weather and the cross-section of stock returns

We investigate the role that weather-induced mood plays in underperformance of lottery stocks. We hypothesize that during pleasant weather conditions, investors are more likely to become risk-taking and optimistic, and invest more in lottery stocks. This results in overpricing and lower expected return for these stocks. We use sky cloud cover as a proxy for the weather condition and show that the MAX effect mainly exists following sunny weather; however, there is less evidence for the MAX anomaly following cloudy weather. Our finding is robust to using alternative constructions of MAX and skewness measures as well as other proxies for weather condition such as rain, wind and temperature.

Property crime and lottery-related anomalies

In this paper, we explore the association between property crime rate and lottery demand anomalies. Motivated by criminology literature that suggests a positive relation between crime and risk-taking, we conjecture that gambling propensity in the stock market is stronger (weaker) in regions with higher (lower) property crime rate. Consistent with our conjecture, we show that underperformance of lottery stocks, proxied by MAX, is more pronounced in the US regions with higher property crime rates compared to regions with lower property crime rates. Our results are robust to alternative proxies for lottery demand, such as alternative constructions of MAX and skewness measures, and various empirical tests. Our findings suggest variation in crime-induced gambling propensity affects financial market outcomes.

Lottery demand, lottery factor, and anomalies

AbstractWe provide an overview of the literature investigating (retail) investors' demand for lottery‐like stocks. We summarize different sets of lottery proxies and discuss their implications for cross‐sectional pricing of individual stocks. We present empirical evidence and summarize the findings including (i) the robustness of the lottery demand effect using an extended data set, (ii) the economic underpinnings of the lottery demand effect, and (iii) the explanatory power of the lottery preference factor for established stock market anomalies.

MAX, lottery-type stocks, and the cross-section of stock returns: Evidence from the Chinese stock market

This study empirically investigates a relationship between MAX and lottery-type stocks in the Chinese stock markets. We find that the lottery-type stocks, which are preferred for lottery demand of investors, are negatively priced in the Chinese market. Moreover, the MAX effect as a proxy for lottery stock is not strongly exhibited as the lottery behavior in the Chinese stock market. Our results show that the higher MAX stocks in the lowest price stocks are stronger than those in the highest price ones. This can explain why the MAX phenomenon of the Chinese market is different from that in the developed market regarding the candidate of the IVOL puzzle explanation.

Tail risk, beta anomaly, and demand for lottery: what explains cross-sectional variations in equity returns?

Tail risk, beta anomaly, and demand for lottery: what explains cross-sectional variations in equity returns?

Lottery Demand, Weather and the Cross-Section of Stock Returns

Lottery Demand, Weather and the Cross-Section of Stock Returns

Investor Heterogeneity and Time-varying Lottery Demand: Evidence from Repeated Experiments

Investor Heterogeneity and Time-varying Lottery Demand: Evidence from Repeated Experiments

The beta anomaly in the Australian stock market and the lottery demand

Frazzini and Pedersen (2014) [Betting against beta. Journal of Financial Economics, 111(1), 1–25] report an insignificant performance for the betting against beta (BAB) strategy in the Australian equity market, suggesting that the beta anomaly does not exist in this market. We extend their sample period and find strong evidence for a low-beta effect. The arbitrage portfolio that takes long positions in low-beta stocks and short positions in high-beta stocks generates a significant abnormal return of 5.9% per year. The beta anomaly over 1995–2019 is strong and robust after controlling for risk factors and stock characteristics. Decomposition of the beta anomaly into stock and industry level components shows that the low-beta effect is driven by the firm, and not the industry level beta. We further find that lottery demand explains the low-beta effect. In a series of portfolio and cross-sectional analyses, we show that the abnormal returns related to the beta anomaly become insignificant after controlling for lottery demand. The findings are robust to different proxies for lottery demand, alternative beta estimation and regression analyses. There is no evidence that the beta anomaly can be explained by leverage constraints, coskewness risk or investment and profitability risk factors. We further show that beta anomaly is more pronounced during the upmarket than the downmarket periods and that lottery demand plays a role in its time-variation. The findings have important implications for retail and institutional investors who trade on beta.

Lottery demand and the asset growth anomaly

The negative relation between asset growth (AG) and future stock returns is particularly featured by the overvaluation of high AG stocks. We propose that such overvaluation is attributed to investors’ lottery demand toward stocks with high maximum daily returns (MAX), resulting in higher AG premium among high MAX stocks. Our empirical results confirm this prediction. Further evidence indicates that the impact of lottery preference on the AG anomaly is robust to several alternative explanations, including overinvestment, limits-to-arbitrage, and the q-theory. Our study provides a new insight into the understanding of the AG anomaly.

Option-implied lottery demand and IPO returns

We study the impact of time-varying lottery demand on first-day returns and the poor long-term performance of IPOs. Lottery demand – measured in terms of option-implied probability weighting – is associated with significantly higher first-day returns, tantamount to higher IPO underpricing and more money left on the table. Interacting the time variation in lottery demand with cross-sectional expected skewness reveals that IPO returns are particularly driven by the interaction between market-wide lottery demand and asset-specific lottery characteristics. When expected skewness meets low lottery demand, there is virtually no effect of skewness on first-day returns. In the long run, IPOs issued in high lottery demand regimes are more likely to perform poorly for up to five years after the IPO.

The Beta Anomaly in the Australian Stock Market and the Lottery Demand

The Beta Anomaly in the Australian Stock Market and the Lottery Demand

Does behavioral-motivated volatility effect explain the beta anomaly? Evidence from China

We find that the beta anomaly in the Chinese stock market is mainly driven by behavioral effects measured by lottery demand or idiosyncratic risk. The betting against volatility factor that is closely related to behavioral effects produces significant positive alpha, while the alpha of the betting against correlation factor related to leverage constraints is insignificant. When a lottery demand or an idiosyncratic risk factor is added to the well-established factor models, the beta anomaly disappears.

Adversity-hope hypothesis: Air pollution raises lottery demand in China

The empirical literature points to a stylized phenomenon of increased demand for hope following adversity. Clotfelter and Cook (1989) suggest that hope is a key sentiment underpinning recreational gambling. Chew and Ho (1994, this journal) offer the view of hope being experienced in lottery products when people enjoy delaying the resolution of uncertainty. Taking air quality as an indicator of subjective well-being, we hypothesize a positive causal relationship between air pollution and lottery sales. We test this hypothesis using data from China and find that air pollution measured by particle concentration increases demand for a popular lottery for which province-level daily sales records exist. The relationship can readily be seen on combining high-frequency, spatially resolved lottery sales and particle pollution data. Our findings support the adversity-hope hypothesis in the context of air quality and lottery sales and point to further tests using other measures of adversity and proxies of demand for hope.

Leverage constraints or preference for lottery: What explains the low-risk effect in India?

The study empirically investigates two theories that claim to explain the low-risk effect in Indian equity markets using a universe of stocks listed on the National Stock Exchange of India (NSE) from January 2000 to September 2018. Leverage constraints and preference for lottery are two major competing theories that explain the presence and persistence of the low-risk effect. While the leverage constraints theory argues that systematic risk drives low-risk anomaly and therefore risk should be measured using beta, lottery demand theory claims that irrational investor’s preference towards stocks with lottery-like payoffs is responsible for the persistence of the low-risk effect, and risk should be measured by idiosyncratic volatility. However, given that most of the risk measures are highly correlated, it is not easy to precisely measure a specific theory’s contribution to explaining the low-risk effect. The study constructs the Betting against correlation (BAC) factor to measure the contribution of leverage constraints to the low-risk effect. It further constructs the SMAX factor to untangle the contribution of lottery preference theory. The results show that leverage constraints theory predominantly explains the low-risk effect in Indian markets. This study contributes significantly to the body of literature, as this is the first such study on the Indian market, one of the major emerging markets, especially when the debate on theories explaining the low-risk effect is yet to settle.

Past Stock Returns and the MAX Effect

This paper investigates how past stock returns affect investors’ lottery demand. We show that the maximum daily return (MAX) effect, first documented by Bali et al. (Maxing Out: Stocks as Lotteries and the Cross-Section of Expected Returns) is predominantly concentrated among stocks that have worst returns in the recent past. In contrast, for stocks that have recorded best past returns, the MAX effect becomes much weaker or even disappears. Our findings hold in the presence of a variety of control variables including the conventional return predictors, stock mispricing, stock price proximity to its 52-week high, and capital gains overhang. We interpret it as evidence that investors’ lottery demand intensifies in the presence of investment losses, consistent with the notion of time varying and state dependent nature of investors’ lottery preference. We further show that a self-financing portfolio that goes long in stocks with the worst past returns and low MAX and short in stocks with worst past returns and high MAX yields statistically and economically significant abnormal returns after risk adjustment by standard asset pricing models.

Adversity-Hope Hypothesis: Air Pollution Raises Lottery Demand in China

The empirical literature points to a stylized phenomenon of increased demand for hope following adversity. Clotfelter and Cook (1989) suggest that hope is a key sentiment underpinning recreational gambling. Chew and Ho (1994) offer the view of hope being experienced in lottery products when people enjoy delaying the resolution of uncertainty. Taking air quality as an indicator of subjective well-being, we hypothesize a positive causal relationship between air pollution and lottery sales. We test this hypothesis using data from China and find that air pollution measured by particle concentration increases demand for a popular lottery for which province-level daily sales records exist. The relationship can readily be seen on combining high-frequency, spatially resolved lottery sales and particle pollution data. Our findings support the adversity-hope hypothesis in the context of air quality and lottery sales and point to further tests using other measures of adversity and proxies of demand for hope.

MAX is not the max under the interference of daily price limits: Evidence from China

Proposing a proxy (MAX) for extremely positive returns (EPR) that trigger lottery demand, Bali et al. (2011) observe a negative relation between MAX and future stock returns in US. However, for China’s stocks with daily price limits, we observe that MAX understates EPR and their negative relation with future returns. By presenting a revised MAX (RMAX) explicitly considering price limits, we show that RMAX, free of such underestimations, exhibits persistent differences from MAX in explaining future returns. More importantly, attracted by stocks (consecutively) closing at the price limits, retail attention and subsequent retail trades contribute to the success of RMAX.

When to Bet Against Beta? Ask Google

In this paper, I document that investor attention negatively predicts betting against beta returns. Using Google Search Volumes toward US market indices as my proxy to attention, I find that this relation holds after controlling for competitive factors and different search terminologies and in most of the other G7 countries. The results also indicate that investor attention presents a unique capacity to explain future BAB performance that is not shared by other famous variables, such as liquidity constraints, sentiment, lottery demand or volatility. On aggregate, the findings suggest that individual investors are a relevant barrier to arbitrage strategies such as BAB.

Equity return anomalies in Turkish markets

Purpose- The purpose of this study is to investigate the predictive power of various anomalies in the cross-section of equity returns in Borsa Istanbul. Methodology- Covering a sample period between 1988 and 2018, this study implements univariate portfolio analyses. Specifically, each month, stocks are sorted into quintile portfolios based on one anomaly at a time. Next, the one-month-ahead equal- and value-weighted portfolio returns are calculated for each quintile to test whether the return spread between the extreme anomaly portfolios is economically and statistically significant. Findings- The findings using the whole sample document that market beta, firm size, lagged return and lottery demand have a significant and negative relation with future stock returns. In contrast, book-to-market ratio, investment and profitability have a strong positive relation with expected equity returns. Conclusion- All anomalies that are shown to predict U.S. equity returns are not documented in Turkey. Except for the investment anomaly, the directions of these anomalies are in line with the existing literature in the U.S.