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principles of corporate finance chapter 7 question 17: What is the portfolio variance The table below...
principles of corporate finance chapter 7 question 17:
What is the portfolio variance
The table below shows standard deviations and correlation coefficients for eight stocks from different countries. Calculate the variance of a portfolio with equal investments in each stock. (Use decimals, not percents, in your calculations. Do not round intermediate calculations. Round your answer to 5 decimal places.)
| BHP | BP | Fiat Chrysler |
Heineken | Korea Electric |
Nestlè | Sony | Tata Motors | |
| BHP | 1.00 | .27 | .36 | .40 | .15 | .40 | .14 | .36 |
| BP | .27 | 1.00 | .36 | .15 | .14 | .35 | .46 | .19 |
| Fiat | .36 | .36 | 1.00 | .12 | .13 | .05 | .39 | .10 |
| Heineken | .40 | .15 | .12 | 1.00 | .22 | .49 | .32 | .31 |
| Korea Electric | .15 | .14 | .13 | .22 | 1.00 | −.29 | .29 | .08 |
| Nestlè | .40 | .35 | .05 | .49 | −.29 | 1.00 | .30 | .03 |
| Sony | .14 | .46 | .39 | .32 | .29 | .30 | 1.00 | .14 |
| Tata Motors | .36 | .19 | .10 | .31 | .08 | .03 | .14 | 1.00 |
| Standard deviation (%) | 24.80 | 34.10 | 48.06 | 23.04 | 32.83 | 14.70 | 49.84 | 44.11 |
Portfolio variance
Solutions
Expert Solution
Given information is shown below:
The covariance matrix is calculated in the following manner from the correlation matrix:
Since the portfolio is equally weighted, hence, the weights are calculated as: 1/Nuumber of stocks
= 1/8 = 0.125
The 2-stocks portfolio variance is calculated as:
In the similar manner, the 8-stock portfolio variance is calculated below:
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