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.