Consider a market with two types of investors: rational investors and overconfident investors. Both types correctly estimate the expected return of the market portfolio, E(rM). However, overconfident investors underestimate its standard deviation, M (so overconfident investors are overconfident about the precision of their estimates of returns), whereas rational investors have a correct estimate of it. Both investor types have a risk aversion parameter, A = 4 and preferences represented by the utility function,

E(U) = E(r) 12*A2

The true values of relevant market variables and the corresponding estimates of the two investor types are given in the table below.

a. What fraction of their wealth will each of the investor types invest in the market portfolio? (Note: the optimal fraction of wealth invested in the optimal risky portfolio, i.e., the market portfolio, is discussed in Lecture 4).

b. What is the resulting expected utility for each investor type?

c. Now assume that overconfident investors revise their expectation about the market expected return up by 2%, while their estimate of market volatility remains unchanged. Please calculate the optimal fraction of wealth the overconfident investor invests in the market portfolio with these revised expectations.

d. Now redo part c by assuming it is rational investors who revise up their expectation about the market expected return by 2%.

e. Compare results in parts c and d, and please comment on the relationship between overconfidence and excessive trading.