Why Choose Us?
0% AI Guarantee
Human-written only.
24/7 Support
Anytime, anywhere.
Plagiarism Free
100% Original.
Expert Tutors
Masters & PhDs.
100% Confidential
Your privacy matters.
On-Time Delivery
Never miss a deadline.
Stocks A and B have the following historical retums: Yea Stock A returi Stock B retur 200 (24
Stocks A and B have the following historical retums: Yea Stock A returi Stock B retur 200 (24.25%) 55% 200 18.5% 26.73% 20038.67% 48.25% 200 14.33% (4.5%) 200: 39.13% 43.86% a) Calculate the average rate ofreturn for each stock during the period 2004 through 2008 Assume that someone held a portfolo consisting of 50% of Stock A and 50% of Stock What would the realized rate of retum on the portfolio have been in each year from 2004 through 2008? What would the average retum on the portfolio have been during that period? b) Calculate the standard deviation of retums for each stock and for the portfolo. c) Looking at the annual retums on the two stocks, would you guess that the correlation coefficient between the two stocks is closer to -6.8 or to -0.8? d) If more randomly selected stocks had been included in the portfolio, which of the following is the most accurate statement of what would have happened to p? Rwould have remained constant R would have been in the vicinity of 20% would have declined to zero fenough stocks had been included i. il.
Expert Solution
ANSWER -
The Expected return of the following data are calculated as follows
|
Year |
Stock A |
Stock B |
|
2004 |
-24.25% |
5.50% |
|
2005 |
18.50% |
26.73% |
|
2006 |
38.67% |
48.25% |
|
2007 |
14.33% |
-4.50% |
|
2008 |
39.13% |
43.86% |
|
Average return |
17.28% |
23.97% |
Expected Avg return = Sum of return / N
So
Expected return A = 17.28 %
Expected return B = 23.97%
For 50 % in A and 50 % in B
Return of the portfolio
|
Asset |
Exp return |
Std dev |
||
|
A |
17.28% |
25.84% |
||
|
B |
23.97% |
23.15% |
||
|
Correlation |
0.15 |
|||
|
Portfolio |
A Weight |
b Weight |
Exp Return |
|
|
1 |
50% |
50% |
20.63% |
|
Portfolio return = w1*r1 +w2*r2 = 20.63 %
Standard Deviation
Std Dev = ((R1-Avg return )^2 +(R2-Avg return)^2 + (R3-Avg return )^2… upto R5 / n-1)^1/2
|
Year |
Stock A |
Stock B |
|
2004 |
-24.25% |
5.50% |
|
2005 |
18.50% |
26.73% |
|
2006 |
38.67% |
48.25% |
|
2007 |
14.33% |
-4.50% |
|
2008 |
39.13% |
43.86% |
|
Average return |
17.28% |
23.97% |
|
Standard Deviation |
25.84% |
23.15% |
Standard Deviation of A = 25.84 %
Standard Deviation of B = 23.15 %
Portfolio Standard Deviation
|
Asset |
Exp return |
Std dev |
||
|
A |
17.28% |
25.84% |
||
|
B |
23.97% |
23.15% |
||
|
Correlation |
0.8 |
|||
|
Portfolio |
A weight |
B weight |
Std Dev |
Exp Return |
|
50% |
50% |
23.24% |
20.63% |
|
Standard Deviation of a portfolio of 2 Assets
Std dev = ((w1^2)(sd1)^2) + (W2^2 sd2^2) + (2*w1*w2*sd1*sd2*correlation ) ) ^ 1/2
So Standard deviation of the portfolio = 23.24 %
Correlation coefficient
By looking at the returns of both the stock we can observe
· When the returns of A rises ,so does the returns of B , Hence both the returns move in the same direction in comparison to the one another
· Hence the degree of correlation between the stocks must be positive as the movement In the returns of the stock are in the same direction
· So the Correlation must be close to +0.8
Archived Solution
You have full access to this solution. To save a copy with all formatting and attachments, use the button below.
For ready-to-submit work, please order a fresh solution below.
