Question

In: Finance

Suppose the return for stocks A and B for the last six months have been the...

Suppose the return for stocks A and B for the last six months have been the following:

A. B

3,2% 4,7%

4,1% 2,0%

-2,7% 1,4%

-0,5% -0,8%

6,7% 2,7%

5,5% -1,2%

a. What is the expected return, variance and standard deviation of the two stocks? What is the covariance and correlation among them?

b. What would the return and standard deviation of a portfolio that is 30% invested in stock A and 70% invested in stock B be?

Solutions

Expert Solution

STOCK A
R1 D1=R1-2.72 E1=D1^2
Period Return(%) Deviation from Mean Deviation Squared
1 3.2 0.48 0.2304
2 4.1 1.38 1.9044
3 -2.7 -5.42 29.3764
4 -0.5 -3.22 10.3684
5 6.7 3.98 15.8404
6 5.5 2.78 7.7284
SUM 16.3 SUM 65.4484
EXPECTED RETURN =MEAN=16.3/6= 2.72%
VARIANCE OF RETURN=65.4484/(6-1) 13.08968 %%
STANDARD DEVIATION=SQRT(VARIANCE) 3.62% (Square Root (13.08968)
STOCK B
R2 D2=R2-1.47 E2=D2^2
Period Return(%) Deviation from Mean Deviation Squared
1 4.7 3.23 10.4329
2 2.0 0.53 0.2809
3 1.4 -0.07 0.0049
4 -0.8 -2.27 5.1529
5 2.7 1.23 1.5129
6 -1.2 -2.67 7.1289
SUM 8.8 SUM 24.5134
EXPECTED RETURN =MEAN=8.8/6= 1.47%
VARIANCE OF RETURN=24.5134/(6-1) 4.90268 %%
STANDARD DEVIATION=SQRT(VARIANCE) 2.21% (Square Root (4.90268)
COVARIANCE AND CORRELATION D1=R1-2.72 D2=R2-1.47 F=D1*D2
Period Deviation from Mean(Stock A)(%) Deviation from Mean(Stock B)(%) Deviation StockA*Deviation StockB
1 0.48 3.23 1.5504
2 1.38 0.53 0.7314
3 -5.42 -0.07 0.3794
4 -3.22 -2.27 7.3094
5 3.98 1.23 4.8954
6 2.78 -2.67 -7.4226
SUM 7.4434
COVARIANCE OF RETURN A&B=7.4434/6- 1.240567 %%
CORRELATION=(COVARIANCE)/(STD DEVIATION A*STD DEVIATION B)
Correlation Coefficient=1.240567/(3.62*2.21) 0.155
b Return of Portfolio =Rp
Standard Deviation of Portfolio =Sp
Portfolio Variance =Vp
Rp=w1*R1+w2*R2
w1=Weight of stock A in the portfolio=30%= 0.3
w2=Weight of stock B in the portfolio=70%= 0.7
R1=Expected Return of Stock A 2.72%
R2=Expected Return of Stock B 1.47%
Rp=Portfolio Return =0.3*2.72+0.7*1.47= 1.84%
Vp=(w1^2)*(VarianceA)+(w2^2)*VarianceB+2*w1*w2*COVA&B*
Variance of Portfolio=(0.3^2)*13.08968+(0.7^2)*4.90268+2*0.3*0.7*1.240567= 4.1014224 %%
Sp=Portfolio Std Deviation=SQRT(Variance)= 2.03% Square Root (4.1014224)

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