Question

Shares A and B have the following​ returns:

	Stock A	Stock B
1	0.09	0.05
2	0.07	0.03
3	0.13	0.04
4	−0.02	0.01
5	0.07	−0.02

a. What are the expected returns of the two​ shares?

b. What are the standard deviations of the returns of the two​ shares?

c. If their correlation is 0.44​, what is the expected return and standard deviation of a portfolio of 52​% share A and 48​% share​ B?

a. What are the expected returns of the two​ shares?

The expected return for share A is .................. (Round to three decimal​ places.)

The expected return for share B is .................. ​(Round to three decimal​ places.)

b. What are the standard deviations of the returns of the two​ shares?

The standard deviation of the return for share A is .................. ​(Round to four decimal​ places.)

The standard deviation of the return for share B is .................. ​​(Round to four decimal​ places.)

c. The expected return for the portfolio is .................. ​​​(Round to four decimal​ places.)

The standard deviation of the return for the portfolio is .................. ​​​(Round to four decimal​ places.)

Answer 1

Part a : Expected returns

Cases	Stock A returns	Stock A returns
1	0.09	0.05
2	0.07	0.03
3	0.13	0.04
4	-0.02	0.01
5	0.07	-0.02
Sum of return	0.34	0.11
Expected return ---> Sum of returns / no. of cases ---> returns / 5	0.068	0.022

Part b : Standard Deviation of Stock A

Cases	Stock A returns	Expected return	Deviation from expected return	Square of deviation from expected return
1	0.0900	0.0680	0.0220	0.0005
2	0.0700	0.0680	0.0020	0.0000
3	0.1300	0.0680	0.0620	0.0038
4	(0.0200)	0.0680	(0.0880)	0.0077
5	0.0700	0.0680	0.0020	0.0000
Step 1 : Sum of (square of deviation from expected return)	0.012
Step 2 : Step 1/ no. of cases --> Step 1 /5	0.002
Step 3 : Square root of step 2 ---> Standard deviation	0.049

Part b : Standard Deviation of Stock B

Cases	Stock B returns	Expected return	Deviation from expected return	Square of deviation from expected return
1	0.0500	0.0220	0.0280	0.0008
2	0.0300	0.0220	0.0080	0.0001
3	0.0400	0.0220	0.0180	0.0003
4	0.0100	0.0220	-0.0120	0.0001
5	-0.0200	0.0220	-0.0420	0.0018
Step 1 : Sum of (square of deviation from expected return)	0.003
Step 2 : Step 1/ no. of cases --> Step 1 /5	0.001
Step 3 : Square root of step 2 ---> Standard deviation	0.025

Part c : Standard Deviation of portfolio

Stock	Weight	Standard Deviation	Square of weights	Square of standard deviation	Square of weights x Square of standard deviation
A	52%	0.049	0.2704	0.0024	0.0007
B	48%	0.025	0.2304	0.0006	0.0001
Step 1 : Sum of (Square of weights x Square of standard deviation)	0.0008
Step 2 : 2 x weight of A x St. Dev. Of A x weight of B x St. Dev. Of B x Correlation between A and B	0.0003
Step 3 : Step 1 + Step 2	0.0011
Step 4 : Square root of Step 3 --> Standard Deviation of portfolio	0.033

Expected return of portfolio

Stock	Weight	Expected return	(Weight x expected return)
A	52%	0.0680	0.0354
B	48%	0.0220	0.0106
Sum of (weight x expected return) --> Portfolio expected return	0.046

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