Is there a "pessimistic" bias in individual beliefs ? Evidence from a simple survey

It is an important issue for economic and finance applications to determine whether individuals exhibit a behavioral bias toward pessimism in their beliefs, in a lottery or more generally in an investment opportunities framework. In this paper, we analyze the answers of a sample of 1,540 individuals to the following question: Imagine that a coin will be flipped 10 times. Each time, if heads, you win 10 Euros. How many times do you think that you will win? The average answer is surprisingly about 3.9 which is below the average 5, and we interpret this as a pessimistic bias. We find that women are more "pessimistic" than men, as are old people relative to young. We also analyze how our notion of pessimism is related to more general notions of pessimism previously introduced in psychology.