Question
In: Finance
Using the data in the following table, answer parts (i) – (v). Year Stock X Stock...
Using the data in the following table, answer parts (i) – (v).
|
Year |
Stock X |
Stock Y |
|
2012 |
-11% |
-5% |
|
2013 |
15% |
25% |
|
2014 |
10% |
15% |
|
2015 |
-5% |
-15% |
|
2016 |
5% |
-5% |
|
2017 |
8% |
-2% |
|
2018 |
7% |
10% |
|
2019 |
5% |
15% |
|
Average return |
||
|
Standard deviation |
||
|
Correlation between Stock X and Stock Y |
0.7567 |
|
- Estimate the average return for each stock.
- Calculate the standard deviation of returns for Stocks X and Y.
- For a portfolio that is 75% weighted in Stock X, and 25% weighted in Stock Y, calculate the expected return of the portfolio.
- Calculate the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (iii).
- Suppose the correlation between Stocks X and Y has reduced to 0.35, does it increase or reduce the standard deviation of your portfolio based on the weights of Stocks X and Y stated in part (iii). Explain your answer.
Solutions
Expert Solution
i. The average return for stock X, 
is
= 4.25%
The average return for stock Y, 
is
= 4.75%
Hence, the average return for stock X is 4.25 and stock Y is 4.75%.
---------------------------------------------------------------------------------------------------------------------
ii. The standard deviation for stock X, 
is
= 8.362
The standard deviation for stock Y, 
is
= 13.488
Hence, the standard deviation for stock X is 8.362% and stock Y is 13.488%.
------------------------------------------------------------------------------------------------------------------------------------
iii. The expected return of the portfolio, 
is
= 4.375%
Therefore, the expected return of the portfolio is 4.375% .
--------------------------------------------------------------------------------------------------------------------------------
iv. The standard deviation of the portfolio, 
is
= 9.095%
Therefore, the standard deviation of the portfolio is 9.095%
-----------------------------------------------------------------------------------------------------------------------------
v. If the correlation is reduced to 0.35, we compute the standard deviation
= 8.094%
Thus, we can say that when the correlation is reduced to 0.35, the standard deviation of the portfolio is also reduced.
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