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Using the data in the following table, and the fact that the correlation of A and B is 0
Using the data in the following table, and the fact that the correlation of A and B is 0.40, calculate the volatility (standard deviation) of a portfolio that is 80% invested in stock A and 20% invested in stock B. (Click on the following icon in order to copy its contents into a spreadsheet.) Year 2008 2009 2010 2011 2012 2013 Realized Returns Stock A Stock B -4% 22% 19% 28% 9% 5% - 1% -9% 5% - 14% 9% 30% The standard deviation of the portfolio is %. (Round to two decimal places.)
Expert Solution
First we will calculate standard deviation of both stock
Average return = Sum of returns/no. of periods
Standard deviation = √ (∑ (Return-Average return)^2)/(no. of periods - 1))
| Stock A | return | dev. =Return- AR (AR = 7.5946%) | squared dev. |
| 2008 | -4.0000% | -10.1667% | 1.0336% |
| 2009 | 19.0000% | 12.8333% | 1.6469% |
| 2010 | 9.0000% | 2.8333% | 0.0803% |
| 2011 | -1.0000% | -7.1667% | 0.5136% |
| 2012 | 5.0000% | -1.1667% | 0.0136% |
| 2013 | 9.0000% | 2.8333% | 0.0803% |
| Total | 37.0000% | 3.3683% | |
| Average Return =37.0000%/6 | 6.1667% | ||
| Standard deviation = |
√(3.3683%/(6-1)) |
||
| 8.2077% |
| Stock B | return | dev. =Return- AR (AR = 7.5946%) | squared dev. |
| 2008 | 22.0000% | 11.6667% | 1.3611% |
| 2009 | 28.0000% | 17.6667% | 3.1211% |
| 2010 | 5.0000% | -5.3333% | 0.2844% |
| 2011 | -9.0000% | -19.3333% | 3.7378% |
| 2012 | -14.0000% | -24.3333% | 5.9211% |
| 2013 | 30.0000% | 19.6667% | 3.8678% |
| Total | 62.0000% | 18.2933% | |
| Average Return =37.0000%/6 | 10.3333% | ||
| Standard deviation = |
√(18.2933%/(6-1)) |
||
| 19.1276% |
standard deviation of A (σA) =8.2077%
weight of A =80%
standard deviation of B (σB) =19.1276%
weight of B = 20%
correlaiton between A and B (rAB)=0.40
standard deviation or volatility of portfoliio (σp)= √((weigh A * σA ) ^2 + (weight B* σB )^ 2 +(2 * Weight A* Weight B*σA *σB* correlation AB))
= √((80%*8.2077%)^2 +(20%*19.1276%)^2 + (2*80%*20%*8.2077%*19.1276%*0.40))
=0.08822938373 or 8.82%
So standard deviation of portfolio is 8.82%
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