Question

1.- Modern Portfolio Theory: A Portfolio of Risky Securities Is Not Necessarily a Risky Portfolio.

Given the portfolio investments and the price changes below, compute the returns on the whole portfolio. Assume that you have the same amount invested in each stock. The initial amount is $2000 on each company for a total investment of $10,000.

            Initial Price      Shares Bought End of Year Price    Value at End of Year     Returns

Co. A                $40                                          $20     

Co. B                $80                                          $0

Co. C                $20                                          $50

Co. D                $60                                          $90

Co. E                 $50                                          $70

a) How many shares of each company are held in the portfolio given that the amount invested in each company is $2000?

b) What is the value of each security and the total portfolio at the end of the year?

c) What is the total portfolio return for the year?

d) Confirm the answer in part c) by calculating the weighted average portfolio return.                           Portfolio Returns = W_A*R_A + W_B*R_B + ….

Answer 1

a)

Company	Number of shares purchased [Amount invested/Issue price]
A	2000/40=50
B	2000/80=25
C	2000/20=100
D	2000/60=33.33333 (rounded to 33)
E	2000/50=40

b)

Company	Number of shares purchased	End of year price	Number of shares* end of year price
A	2000/40=50	20	1000
B	2000/80=25	0	0
C	2000/20=100	50	5000
D	2000/60=33.33333 (rounded to 33)	90	3000
E	2000/50=40	70	2800
Total value of portfolio at end of year			11800

c)Total portfolio return = Value at end - Initial amount invested

                   = 11800 - (2000*5)

                  = 11800 - 10000

                 = 1800

Return (%) =Return in $ /initial amount invested

          = 1800/10000

          = .18 or 18%

d)

Company	Value at end [A]	amount invested [B]	Return($) [A-B]	Return (%) [return in $ /B]	Weight	Return(%) *weight
A	1000	2000	-1000	-1000/2000=- .50 or -50%	2000/10000=.2	-10% (-50*.2)
B	0	2000	-2000	-2000/2000 = -100%	.2	-20%   (-100*.2)
C	5000	2000	3000	3000/2000= 1.5 or 150%	.2	30%
D	3000	2000	1000	1000/2000=.50 or 50%	.2	10%
E	2800	2000	800	800/2000=.40 or 40%	.2	8%
		10000
Total portfolio return						18%