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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