©2015, College for Financial Planning, all rights reserved. Session 4 Correlations & the “Correlation Pyramid” CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning

Session Details Module2 Chapter(s)2 LOs2-5 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. 2-6 Identify the coefficient of determination, and know how to calculate and understand it applications. 4-2

Efficient Frontier Example 4-3

Investment Risk/Return Relationships 4-4

The Pyramid Covariance Correlation Coefficient (R) – Coefficient of Determination (R – squared) Coefficient of Variation (Variability) SD M 4-5

Covariance Formula 4-6

Correlation Coefficient Formula 4-7

Coefficient of Determination Formula R-squared – just square R! 4-8

Covariance & Correlation Coefficient Covariance measures the tendency of two assets to move in the same or different directions over time. Covariance is needed in the standard deviation of a portfolio calculation. The Correlation Coefficient (R) is a standardized version of covariance, and ranges from –1 to

Correlation Coefficient

Correlation Coefficients Asset Large- Cap Small- Cap Large-Cap1.00 Small-Cap Inter. stocks LT Corporate Bonds T-Bills Inflation

Changing Correlations Correlations change over time. Correlations increase in down markets. Some correlations can be harder to measure than others, such as hedge funds and alternative investments. A low correlation with a portfolio does not necessarily mean that it is a good investment. 4-12

Positive Correlation Market Return Return 4-13

Negative Correlation Market Return Return 4-14

R & R-Squared The Correlation Coefficient is also referred to as “R” and the Coefficient of Determination as “R- squared.” The Coefficient of Determination (R-squared) is found by squaring the Correlation Coefficient (R). R-squared is the amount of systematic risk, with the balance being unsystematic risk. R-squared measures how much of the price movement of a particular asset is explained by the benchmark to which it is being compared. 4-15

Coefficient of Determination Calculate the coefficient of determination, given the following correlation coefficients between an asset and a benchmark. Correlation Coefficient Coefficient of Determination

Coefficient of Determination Calculate the coefficient of determination, given the following correlation coefficients between an asset and a benchmark. What is the coefficient of determination telling you? Correlation Coefficient Coefficient of Determination

Correlation Coefficient Calculations Calculate the correlation coefficient, given the following coefficient of determinations between an asset and a benchmark. Coefficient of Determination Correlation Coefficient

Correlation Coefficient Calculations Calculate the correlation coefficient, given the following coefficient of determinations between an asset and a benchmark. Coefficient of Determination Correlation Coefficient

R and Beta 4-20

Question 1 Seth is considering the purchase of the Delta Fund, which has a correlation coefficient of.92 with the S&P 500. He asks you how much unsystematic risk he is taking by investing in this fund. You would tell him that the percentage of unsystematic risk is a.8%. b.15%. c.85%. d.92%. 4-21

Question 2 Stock ABC has a standard deviation of 16 and beta of 1.1. Stock XYZ has a standard deviation of 9, and a beta of 0.7. The covariance between the two stocks is +88. What is the correlation coefficient between the two stocks? a..61 b..77 c..88 d

Question 3 Your client, Glenda, is a conservative investor and has found a stock that she is considering purchasing. She informs you that even though the stock has a standard deviation of 32, the beta is just.35. She tells you that she likes the fact that the stock has approximately one-third the volatility of the overall market. You would advise Glenda that she a.is correct that the low beta would be a good match for her conservative risk tolerance. b.needs to check further; the low beta is misleading and may be the result of a low correlation between the stock and the market. c.needs to take into account the high standard deviation, which would result in an adjusted beta of over 1. d.is a conservative investor, so any stock with a beta of less than 1 would be appropriate for purchase. 4-23

Question 4 The market has an expected return of 14% and a standard deviation of 19. The fund you are considering has an expected return of 10% with a standard deviation of 14. The coefficient of determination between the market and the fund is.81. Which one of the following is closest to the fund’s beta? a..53 b..60 c..66 d

©2015, College for Financial Planning, all rights reserved. Session 4 End of Slides CERTIFIED FINANCIAL PLANNER CERTIFICATION PROFESSIONAL EDUCATION PROGRAM Investment Planning