Question

Consider the following 6 months of returns for 2 stocks and a portfolio of those 2 stocks: EEB Note: The portfolio is composed of 50% of Stock A and 50% of Stock B a. What is the expected return and standard deviation of returns for each of the two stocks? b. What is the expected return and standard deviation of returns for the portfolio? c. Is the portfolio more or less risky than the two stocks? Why? Stock A Stock B Jan 1% 0% Feb 4% -3% 7% 8% Apr 2% May -3% 4% Jun 29%. -2% 0.5% 0.5% 0.5% 0.5% 0.5% 0.5%

Answer 1

a. Expected return of Stock A = E(A) Sum of returns of stock A / No of months = (1% + 4% - 7% + 2% - 3% + 3%) / 6 = 0% / 6 = 0%

Standard deviation of Stock A =

Month	Ai	E(A)	Ai-E(A)	(Ai-E(A))2
Jan	1%	0%	1%	0.0001
Feb	4%	0%	4%	0.0016
Mar	-7%	0%	-7%	0.0049
Apr	2%	0%	2%	0.0004
May	-3%	0%	-3%	0.0009
June	3%	0%	3%	0.0009

0.0088 Standard deviation of Stock A-1

Standard deviation of Stock A- V0.001466666

Standard deviation of stock A = 0.038297 = 3.8297% = 3.83%

Expected return of Stock B= E(B) Sum of returns of stock B / No of months = (0% - 3% + 8% - 1% + 4% - 2%) / 6 = 6% / 6 = 1%

、 B-E(B)2 Standard deviation of Stock B-

Month	Bi	E(B)	Bi-E(B)	(Bi-E(B))2
Jan	0%	1%	-1%	0.0001
Feb	-3%	1%	-4%	0.0016
Mar	8%	1%	7%	0.0049
Apr	-1%	1%	-2%	0.0004
May	4%	1%	3%	0.0009
June	-2%	1%	-3%	0.0009
			Total	0.0088

0.0088 Standard deviation of Stock B-

Standard deviation of Stock BV0.001466666

Standard deviation of stock B = 0.038297 = 3.8297% = 3.83%

b. Expected return of Portfolio = E(P) = Weight of stock A x E(A) + Weight of stock B x E(B) = 50% x 0% + 50% x 1% = 0% + 0.5% = 0.5%

OT Standard deviation of Portfolio

Month	Pi	E(P)	Pi-E(P)	(Pi-E(P))2
Jan	0.5%	0.5%	0%	0.0000
Feb	0.5%	0.5%	0%	0.0000
Mar	0.5%	0.5%	0%	0.0000
Apr	0.5%	0.5%	0%	0.0000
May	0.5%	0.5%	0%	0.0000
June	0.5%	0.5%	0%	0.0000
			Total	0.0000

OT Standard deviation of Portfolio-V6

Standard deviation of Port folio- VO

Standard deviation of Portfolio = 0%

c. Risk of an asset is measured by standard deviation of returns.

Since the standard deviation of Portfolio is less than the standard deviation of two stocks, therefore portfolio is less risky than two stocks