Can the Market Multiply and Divide? Non‐Proportional Thinking in Financial Markets
研究发现投资者更多按价格变化金额而非百分比思考，导致低价股对新闻反应更极端；价格翻倍会使波动率和贝塔下降20%-30%，股票分割后波动率跳升，这有助于解释规模-波动率关系、杠杆效应谜题等资产定价现象。
ABSTRACT We hypothesize that investors partially think about stock price changes in dollar rather than percentage units, leading to more extreme return responses to news for lower‐priced stocks. Consistent with such non‐proportional thinking, we find a doubling in price is associated with a 20% to 30% decline in volatility and beta (controlling for size/liquidity). To identify a causal price effect, we show that volatility jumps following stock splits and drops following reverse splits. Lower‐priced stocks also respond more strongly to firm‐specific news. Non‐proportional thinking helps explain asset pricing patterns such as the size‐volatility/beta relation, the leverage effect puzzle, and return drift and reversals.