Stocks A and B have the following returns:
Stock A 
Stock B 

1 
0.09 
0.07 

2 
0.06 
0.01 

3 
0.12 
0.06 

4 
−0.02 
0.02 

5 
0.08 
−0.04 
a. What are the expected returns of the two stocks?
b. What are the standard deviations of the returns of the two stocks?
c. If their correlation is 0.47
what is the expected return and standard deviation of a portfolio of 75%
stock A and 25% stock B?
Year  Stock A  Stock B 
1  9.00%  7.00% 
2  6.00%  1.00% 
3  12.00%  6.00% 
4  2.00%  2.00% 
5  8.00%  4.00% 
a Average=  6.60%  2.40% 
b Standard dev=  5.27%  4.39% 
Where  
Average or Mean = Sum of all observations/Count of all observations  
Sample Standard deviation =((∑^{k=1 to N} (observation_{k} – average))/(N1))^(1/2) 
c
Expected return%=  Wt Stock A*Return Stock A+Wt Stock B*Return Stock B 
Expected return%=  0.75*0.066+0.25*0.024 
Expected return%=  5.55 
Variance  =( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB)) 
Variance  =0.75^2*0.0527^2+0.25^2*0.0439^2+2*0.75*0.25*0.0527*0.0439*0.47 
Variance  0.00209 
Standard deviation=  (variance)^0.5 
Standard deviation=  4.57% 
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