Wize University Introduction to Finance Textbook > Risk, Return & Portfolio Theory
Portfolio Standard Deviation (Special Cases)
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Standard Deviation with Perfect Correlations
Investments are said to be perfectly correlated or negatively correlated if their correlation coefficient is equal to 1 or -1. In these cases, the following rules apply:
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Example: Portfolio Standard Deviation with Perfect Correlations
Compute the standard deviation of a portfolio with 70% invested in Stock X and the rest in Stock Y. The standard deviations of stocks X and Y are 14.4% and 8.65% respectively and the correlation coefficient between the stocks is 1 (perfect positive correlation).
Practice: Portfolio Standard Deviation with Perfect Correlations
The standard deviation of a portfolio containing stocks G and F is 8.95%. Stock G has a standard deviation of 7.5% and stock F has a standard deviation of 12%. Stocks G and F have a perfect positive correlation. If the portfolio has $10,000 in it, how much of that is invested in stock G?
Round your final answer to 2 decimal places.
| Amount invested in Stock G | $ |
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Standard Deviation with No Correlation
When two stocks are said to be completely unrelated, this means that the covariance and correlation between them is 0.
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Example: Portfolio Standard Deviation with No Correlation
Stock G has a standard deviation of 15% and Stock H has a standard deviation of 22%. The stocks are unrelated and you combine them in a portfolio by investing $7,500 into Stock G and $2,500 into Stock H.
What is the standard deviation of the portfolio?
Practice: Portfolio Standard Deviation with No Correlation
You've constructed a portfolio with a standard deviation of 18.4% using two completely unrelated stocks, Stocks A and B. The portfolio contains twice as much Stock A as it does Stock B. If the standard deviation of Stock A is 15%, what is the standard deviation of stock B?
Round your final answer to 2 decimal places
| Standard deviation of Stock B | % |
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Standard Deviation of Portfolio with a Risk-Free Asset
In a 2 asset portfolio that contains a risk-free asset and a risky asset, the standard deviation of the portfolio is the found using only the risky asset.
Wize Concept
This is because a risk free asset has a standard deviation (risk) of zero.
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Example: Portfolio Standard Deviation with a Risk-Free Asset
You wish to construct a portfolio using shares of Amazon and US treasury bills. Amazon's stock is known to have a standard deviation of 15.6%. If you plan to invest equally into both assets, what will be the standard deviation of your portfolio?
Practice: Portfolio Standard Deviation with a Risk-Free Asset
You've constructed a portfolio with a standard deviation of 25% using Apple Inc.'s stock and US treasury bills. The standard deviation of Apple's stock is 22%. What percentage of your portfolio is invested in Apple's stock and what percentage is invested in the treasury bills?
Round your final answer to 2 decimal places
| Weight of Apple stock | % | |
| Weight of Treasury Bills | % |