Question

You have been given the following return​ data:

               Expected Return      
Year   Asset A   Asset B   Asset C
2021          7%       8%           2%
2022          9%       6%           4%
2023          11%      4%   6%
2024          13%      2%           8%

on three assets-​A, ​B, and C over the period 2021--2024

Using these​ assets, you have isolated three investment​ alternatives:

Alternative   Investment          
1   100%   of asset A      
2   50%      of asset A and 50% of asset B
3   50%      of asset A and 50% of asset C

a. Calculate the average portfolio return for each of the three alternatives.

b. Calculate the standard deviation of returns for each of the three alternatives.

c. On the basis of your findings in parts a and b​, which of the three investment alternatives would you​ recommend? Why?

Answer 1

Standard deviation for each asset :

Year	A	B	C
2021	7%	8%	2%
2022	9%	6%	4%
2023	11%	4%	6%
2024	13%	2%	8%
	40%	20%	20%
	40%/4	20%/4	20%/4
Mean	10%	5%	5%
Std Deviation	2.58%	2.58%	2.58%

Correlation	A	B	C
A	1	-1	1
B		1	-1
C			1

For portfolio ,

Average Return

Standard Deviation

Answer a)  

Option	A	B	C	Return
1	100%	0%	0%	100%*10%	10%
2	50%	50%	0%	50%*10%+50%*5%	7.500%
3	50%	0%	50%	50%*10%+50%*5%	7.500%

Answer b)

Option	A	B	C	Standard Deviation
1	100%	0%	0%	(100%^2*2.58%^2)^0.5	2.58%
2	50%	50%	0%	(50%^2*2.58%^2+50%^2*2.58%^2+2*50%*50%*2.58%*2.58%*-1)^0.5	0.000%
3	50%	0%	50%	(50%^2*2.58%^2+50%^2*2.58%^2+2*50%*50%*2.58%*2.58%*-1)^0.6	0.000%

Answer c) I would recommend to make investment in Option 1 for getting better return, as the risk is just 2.58%.