Bonus Ouestion (mandatory for ISE6300 students):\ 6. (20 pts) The prices of stocks

S_(1),S_(2),dots,S_(20)

are i.i.d. uniform random variables on

10,30

.\ a) Suppose that your portfolio consists of 1 share of each stock. What is the mean and variance of the total value

V

of your portfolio?\ b) Suppose that your portfolio consists of 20 shares of stock

S_(1)

only. What is the mean and variance of the total value

V

of your portfolio? Compare with a), which portfolio do you prefer? Why?\ c) Suppose that your portfolio consists of 10 shares of stock

S_(1)

and 10 shares of stock

S_(21)

, where the price of stock

S_(21)

is uniform on

10,30

but has perfect negative correlation (correlation

=-1

) with the price of

S_(1)

. What is the mean and variance of the total value

V

of your portfolio?

Bonus Question (mandatory for ISE6300 students): 6. (20 pts) The prices of stocks S1,S2,,S20 are i.i.d. uniform random variables on [10,30]. a) Suppose that your portfolio consists of 1 share of each stock. What is the mean and variance of the total value V of your portfolio? b) Suppose that your portfolio consists of 20 shares of stock S1 only. What is the mean and variance of the total value V of your portfolio? Compare with a), which portfolio do you prefer? Why? c) Suppose that your portfolio consists of 10 shares of stock S1 and 10 shares of stock S21, where the price of stock S21 is uniform on [10,30] but has perfect negative correlation (correlation =1 ) with the price of S1. What is the mean and variance of the total value V of your portfolio