1. Session 5 Standard Deviation of a Portfolio, Concept and Calculation
CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning
Session 5 Standard Deviation of a Portfolio, Concept and Calculation

2. Session Details Module 2 Chapter(s) 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.
Let’s talk about the steps in the financial planning process…

3. Portfolio Standard Deviation
Very important concept for the CFP Exam For 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 20 50% in Fund B, with a SD of 10 If the correlation coefficient is +1, what is the risk? Answer: 15, you can use a weighted average of the two standard deviations

4. 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.

5. Standard Deviation of a Portfolio
Keep space beneath formula to show how there are three parts to the calculation.

6. Covariance Formula

7. Portfolio Standard Deviation
Scenario: 40% in Security A with a 10% SD 60% in Security B with a 20% SD Correlation between the two is 0.95

8. Standard Deviation of a Portfolio Calculation
Work problem in three sections.

9. 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

10. The Composite Portfolio
Less variable than individual stocks

11. Question 1 Octopus 50% 22 Squid 28
Kerry owns the following two mutual funds:
The covariance between the two funds is -44.
What is the standard deviation of Kerry’s portfolio?
17.1
19.6
21.3
25.0
Fund
Weighting
Standard Deviation
Octopus
50% 22
Squid 28
a is the correct answer.

12. 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?
17.1
19.6
21.3
25.0
d. Since this is a perfect positive correlation of +1, you can use a weighted average of the two standard deviations. If you calculate using the formula you will come up with the same answer.

13. Question 3
Your 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 Which of the following answers is correct regarding the average return of both funds, and the portfolio standard deviation?
7% mean return, 12% std dev
6.5% mean return, 12% std dev
7% mean return, 11.4% std dev
6.5% mean return, 11.4% std dev
c. is the correct answer. Calculate the mean return first, which comes to 7%. This leaves us with just answers a or c as possibilities. Then do a weighted average of the standard deviations, which comes to 12%. Since the correlation is less than 1 we know that the portfolio standard deviation would be less than 12%. The answer cannot be a – so then it must be c. This problem can be solved without doing the portfolio standard deviation calculation. If the calculation is done it would come out to

14. CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning
Session 5 End of Slides