You have £300,000 to invest and you areconsidering buying shares in one or both of two companies (Company X andCompany Y). The market price of each share is currently £15 for both Company Xand Company Y. Details of the possible present value of the return on eachshare are given below:

     Company X                                       Company Y                     

PV       Probability                           PV        Probability         

-£6         0.3                                     -£4             0.2

NIL         0.4                                      +£2            0.5

+£10      0.3                                     +£7             0.3

The above returns on the shares ofCompanies X and Y are independent.

Required：

a)    Calculate the expected valueand the standard deviation of the possible returns on each of the followinginvestments.

i)               All of the £300,000 is investedin the shares of Company X.

ii)              All of the £300,000 is investedin the shares of Company Y.

iii)             The £300,000 investment issplit equally in value between the shares of Company X and Company Y.

Note: Standard Deviation =

b)    In the context ofdiversification and portfolio theory, explain the similarities and differencesin your calculations in a) above.

请把详细过程也写下，many thanks