樂透股對股價錯估影響之研究

Abstract

許多文獻指出人們對於樂透、或是一些賭博遊戲的熱愛，投資人也較偏好以及喜愛風險性資產(Bali et al. (2011), Thaler and Ziemba (1988))。本研究透過每月最高的個股日報酬率漲跌幅，定義樂透性股票，同時使用Stambaugh, Yu, and Yuan (2015)所整理的股價錯估指標，將樣本資料進行獨立分組，並進行橫斷面分析，分析套利風險以及股價錯估所帶來的套利不對稱之結果。 本研究實證發現樂透股性質以及股票預期報酬之間存有負向關係。由於具有樂透股性質的股票，其容易因為投資人的投資偏好，形成較強的套利風險，並且其風險在套利限制存在的情況之下，將形成程度較大的股價錯估情形。 除此之外，樂透性股票造成的套利風險，也受到套利不對稱的影響，且該影響除了受到個股層面差異之影響外，也受到投資人層面差異之影響。對於一些法人投資人較傾向持有的股票標的，其套利限制較少，遇到股價高估時較容易透過放空的方式調整股票價值；反之對於法人投資人持有較少的標的其套利限制則較多，因此當股價被高估時，則不易調整股價，使得股價預期報酬較法人持股較高之投資組合低。 本研究也在引入Baker and Wurgler (2006)所提出的投資人情緒指標替代變數，並且發現套利不對稱的效果應在市場情緒較高時會有更顯著的增強。而在實證結果中，同樣是股價最被高估，且最具樂透股性質之投資組合，其在投資人情緒較高時的預期股價報酬，皆顯著低於投資人情緒較低時期。實證結果中也可以發現，投資人情緒的替代變數，其對投資組合的報酬率影響為負，表示當投資人情緒越高，越容易使得股價被高估，同時在套利限制的情況下，其股價預期報酬越低。最後一節的實證結果也證實樂透股性質以及股價錯估對於股票預期報酬之影響，在排除小公司的情況下也依然穩健。

Many studies have indicated that people have a strong affinity for lotteries and certain gambling games, and investors also tend to prefer and enjoy riskier assets (Bali et al. (2011), Thaler and Ziemba (1988)). In this research, we define "lottery stocks" based on the monthly maximum daily stock return, and we use the Mispricing Score provided by Stambaugh, Yu, and Yuan (2015) to independently group the sample data for cross-sectional analysis. We analyze the results of arbitrage risk and the arbitrage asymmetric resulting from stock mispricing. The empirical findings of this study reveal a negative relationship between the lottery stocks and their expected returns. Lottery stocks are more likely to have greater arbitrage risk due to investors' preferences, and this risk leads to a significant stock mispricing when arbitrage constraints are present. Furthermore, the arbitrage risk caused by lottery stocks is also influenced by arbitrage asymmetric, which are affected not only by stock-level differences but also by investor-level differences. Stocks favored by institutional investors tend to have fewer arbitrage constraints, making it easier to adjust their stock values through short-selling when they are overvalued. Conversely, stocks less favored by institutional investors face more constraints, making it difficult to adjust their stock prices when overvalued, resulting in lower expected returns compared to portfolios with higher institutional ownership. This study also introduces the investor sentiment proxy provided by Baker and Wurgler (2006) and finds that the effect of asymmetric arbitrage is enhanced during periods of higher market sentiment. In the empirical results, portfolios with the most overpriced stocks and lottery stocks show significantly lower expected stock returns during periods of higher investor sentiment compared to periods of lower investor sentiment. The results also demonstrate that the sentiment proxy has a negative impact on portfolio returns, indicating that higher investor sentiment tends to lead to overvalued stock prices and lower expected returns under arbitrage constraints. Finally, the empirical findings in the last section confirm that the impact of lottery stock and mispricing on expected stock returns remains robust even after excluding small companies.