Again, assume that there are two i

nvestors, one being rational and the other one being

overconfident. Both investors correctly estimate the expected return and volatility of the market

portfolio, but they differ in their estimates about a stock X. All estimates are given below. The

risk f

ree rate is 4%.

Investor

Asset

E(r)

Rational

X

12.50%

50%

0.5

Overconfident

X

12.50%

30%

0.5

Market

Portfolio

16%

20%

a.

Please calculate the optimal weight to invest in stock X for each investor, in their optimal

risky portfolio (comprising of the market portfolio and stock X).

Notes: the calculation is introduced in lecture 7.

b.

Compare your results in part

a

.

for two investors. Can you make any inference regarding

the relation between overconfide

nce and under

-

div

ersification?