Non-Additivity of Subjective Expectations over Different Time Intervals

Abstract

We examine the additivity of stock-market expectations over different time intervals. When asked about a ten-year interval, survey respondents expect a stock-price change that is not equal to, but closer to zero than, the sum of their expectations over two shorter time intervals that cover the same ten years. Such sub-additivity is irrational in that it cannot stem from aggregating short-term expectations. Model estimates show that the pattern is consistent with a time perception where shorter time intervals have a proportionally larger weight. We also find that the respondents’ degree of additivity is correlated with making larger financial investments.