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Stocks A and B have the following returns: (Click on the following icon in order to copy its contents into a spreadsheet
Stocks A and B have the following returns: (Click on the following icon in order to copy its contents into a spreadsheet.) 1 2 3 Stock A 0.08 0.06 0.14 -0.02 0.07 Stock B 0.07 0.04 0.05 0.01 -0.03 4 5 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 0.44, what is the expected return and standard deviation of a portfolio of 75% stock A and 25% stock B? The expected return for stock A is 0.066. (Round to three decimal places.) The expected return for stock B is 0.028 . (Round to three decimal places.) b. What are the standard deviations of the returns of the two stocks? The standard deviation of the return for stock Ais 0.0573. (Round to four decimal places.) The standard deviation of the return for stock B is 0.0390 . (Round to four decimal places.) c. If their correlation is 0.44, what is the expected return and standard deviation of a portfolio of 75% stock A and 25% stock B? The expected return for the portfolio is 0.0565. (Round to four decimal places.) The standard deviation of the return for the portfolio is 0.0046. (Round to four decimal places.)
Expert Solution
For the following data
|
Stock A |
Stock B |
|
|
1 |
0.08 |
0.07 |
|
2 |
0.06 |
0.04 |
|
3 |
0.14 |
0.05 |
|
4 |
-0.02 |
0.01 |
|
5 |
0.07 |
-0.03 |
Expected Avg return = Sum of return / N
|
Stock A |
Stock B |
|
|
1 |
0.08 |
0.07 |
|
2 |
0.06 |
0.04 |
|
3 |
0.14 |
0.05 |
|
4 |
-0.02 |
0.01 |
|
5 |
0.07 |
-0.03 |
|
Expected Return |
0.066 |
0.028 |
Stock A expected return = 0.08 + 0.06 + 0.14……+0.07 / 5 = 0.066
Stock b = 0.028
Standard Deviation
Std Dev = ((R1-Avg return )^2 +(R2-Avg return)^2 + (R3-Avg return )^2… upto R5 / n-1)^1/2
Std dev A = (0.08-0.066 )^2 +(0.06-0.066)^2 ……+ (R3-Avg return )^2… upto R5 / n-1)^1/2 = 0.057
Std dev of B = 0.039
|
Stock A |
Stock B |
|
|
1 |
0.08 |
0.07 |
|
2 |
0.06 |
0.04 |
|
3 |
0.14 |
0.05 |
|
4 |
-0.02 |
0.01 |
|
5 |
0.07 |
-0.03 |
|
Expected Return |
0.066 |
0.028 |
|
Standard Deviation |
0.057 |
0.039 |
Portfolio Standard Deviation
Standard Deviation of a portfolio of 2 Assets
***Std dev = ((w1^2)(sd1)^2) + (W2^2 sd2^2) + (2*w1*w2*sd1*sd2*correlation ) ) ^ ½***
Where the correlation is given to be 0.44
|
Asset |
Exp return |
Std dev |
|
|
A |
0.066 |
0.057 |
|
|
B |
0.028 |
0.039 |
|
|
Correlation |
0.44 |
||
|
Asset 1 |
Asset 2 |
Std Dev |
Exp Return |
|
75% |
25% |
0.048 |
0.057 |
Expected return of the portfolio = p1*r1 + p2*r2
=75%*0.066 +25% * 0..028 = 0.057
Std dev
Std dev = ((w1^2)(sd1)^2) + (W2^2 sd2^2) + (2*w1*w2*sd1*sd2*correlation ) ) ^ 1/2
Std dev = ((0.75^2)(0.057)^2) + (0.25^2 0.039^2) + (2*0.75*0.25*0.057*0.039*0.44 ) ) ^ ½
= 0.048
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