- #Weighted standard deviation of a portfolio how to
- #Weighted standard deviation of a portfolio professional
This is why diversification reduces risk. Σ i is the standard deviation of expected returns of security i, and,Ĭov ij is the covariance of expected returns of securities of i and j.Īssuming that the covariance is less than one (invariably true), this will be less than the weighted average of the standard deviation of the expected returns of the securities. W i is the proportion of the portfolio in security i, Where the sums are over all the securities in the portfolio, The standard deviation of the expected return on a portfolio is: The key result in portfolio theory is that the volatility of a portfolio is less than the weighted average of the volatilities of the securities it contains. It is often called modern portfolio theory or Markowitz portfolio theory. This problem can be solved without doing the portfolio standard deviation calculation.Portfolio theory deals with the value and risk of portfolios rather than individual securities. The answer cannot be a – so then it must be c. Since the correlation is less than 1 we know that the portfolio standard deviation would be less than 12%. Then do a weighted average of the standard deviations, which comes to 12%. This leaves us with just answers a or c as possibilities. Calculate the mean return first, which comes to 7%. 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. Fund B has an average return of 5.5% and a standard deviation of 8. Fund A has an average return of 8.5% and standard deviation of 16. If you calculate using the formula you will come up with the same answer.ġ3 Question 3 Your client has 50% in each fund. Since this is a perfect positive correlation of +1, you can use a weighted average of the two standard deviations.
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.ġ2 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. Kerry owns the following two mutual funds: The covariance between the two funds is -44. Scenario: 40% in Security A with a 10% SD 60% in Security B with a 20% SD Correlation between the two is 0.95Ĩ Standard Deviation of a Portfolio CalculationĪs covariance (correlation) falls, so does risk as measured by standard deviation. Keep space beneath formula to show how there are three parts to the calculation. 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. 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. 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 It’s important to understand how correlation impacts risk, with risk being measured by standard deviation. Very important concept for the CFP Exam For our purpose, a “portfolio” is only two assets. Let’s talk about the steps in the financial planning process…
#Weighted standard deviation of a portfolio how to
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.
#Weighted standard deviation of a portfolio professional
1 Session 5 Standard Deviation of a Portfolio, Concept and CalculationĬERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning Session 5 Standard Deviation of a Portfolio, Concept and CalculationĢ Session Details Module 2 Chapter(s) LOs 2-5