©2015, College for Financial Planning, all rights reserved.

Session 5Standard Deviation of a Portfolio, Concept and Calculation

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning

Session Details

Module 2

Chapter(s)

2

LOs 2-5 Identify covariance and correlation coefficient, know how to calculate one given the other, and understand their application and relevance when calculating the standard deviation of a portfolio.

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Portfolio Standard Deviation

Very important concept for the CFP ExamFor our purpose, a “portfolio” is only two assets.It’s important to understand how correlation impacts risk, with risk being measured by standard deviation.Example: You have invested in two funds:50% in Fund A, with a SD of 2050% in Fund B, with a SD of 10If the correlation coefficient is +1, what is the risk?Answer: 15, you can use a weighted average of the two standard deviations

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Portfolio Standard Deviation

Same scenario of 50% in each fund:What happens when they are no longer perfectly correlated, and the correlation coefficient is 0?

Answer: The lower the correlation, the lower the risk. The weighted average SD is 15% when the correlation coefficient is +1, and risk is going to go down as the funds become less correlated, so the standard deviation is going to be less than 15.

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Standard Deviation of a Portfolio

ijji2

j2

j2

i2

ip COVW2W σ W σW σ

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Covariance Formula

COV jiijij

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Portfolio Standard Deviation

Scenario:

40% in Security A with a 10% SD 60% in Security B with a 20% SDCorrelation between the two is 0.95

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Standard Deviation of a Portfolio Calculation

)95.0)(20)(10)(60)(.40(.2)20()60(.)10()40(.σ 2222p

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Standard Deviation of a Portfolio

As covariance (correlation) falls, so does risk as measured by standard deviation.

Correlation Coefficient

Standard deviation

+1.0 16

+0.5 14.4

+0.0 12.6

-0.5 10.6

-1.0 8.0

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The Composite PortfolioLess variable than individual stocks

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Question 1

Kerry owns the following two mutual funds:

The covariance between the two funds is -44. What is the standard deviation of Kerry’s portfolio?a. 17.1b. 19.6c. 21.3d. 25.0

Fund WeightingStandard Deviation

Octopus 50% 22

Squid 50% 28

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Question 2

Using the same fact pattern as in the previous question, what would the standard deviation of the portfolio be if the correlation coefficient between the two funds were +1.0?a. 17.1b. 19.6c. 21.3d. 25.0

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Question 3Your client has 50% in each fund. Fund A has an average return of 8.5% and standard deviation of 16. Fund B has an average return of 5.5% and a standard deviation of 8. The correlation between the two funds is 0.78. Which of the following answers is correct regarding the average return of both funds, and the portfolio standard deviation?a. 7% mean return, 12% std devb. 6.5% mean return, 12% std devc. 7% mean return, 11.4% std devd. 6.5% mean return, 11.4% std dev

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©2015, College for Financial Planning, all rights reserved.

Session 5End of Slides

CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAMInvestment Planning