©2015, college for financial planning, all rights reserved. session 4 correlations & the...

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

Session 4Correlations & the “Correlation Pyramid”

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.

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

ReturnsAverage Returns

Coefficient of Variation

CovarianceStandard

Deviation of Portfolio

Standard Deviation

Sharpe Index

Treynor IndexCorrelation

Coefficient (R)

Coefficient of Determination

(R2)

Portfolio BetaCAPM

(Required Return)

Dividend Growth Module

Jensen Index (Alpha)

RS Rp Rm

W Rp Rf

Rp Rf

Beta

WRm

Rf

Rp

g

Do

4-4

The Pyramid

Covariance

Correlation Coefficient

(R)

– 1 0 + 1


(R – squared)

Coefficient of Variation (Variability)SD

M4-5

Covariance Formula

COV jiijij

4-6

Correlation Coefficient Formula

ijij

i j

COVR

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 +1.

4-9


- 1 + 10

4-10

Correlation Coefficients

AssetLarge-

CapSmall-

Cap

Large-Cap 1.00

Small-Cap 0.72 1.00

Inter. stocks 0.66 0.50

LT Corporate Bonds

0.29 0.15

T-Bills 0.11 0.05

Inflation -0.09 0.06

4-11

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


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



1.0

.95

.80

.50

.23

4-16


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

•What is the coefficient of determination telling you?



1.0 1.0

.95 .9025

.80 .64

.50 .25

.23 .0529

4-17

Correlation Coefficient Calculations

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



.98

.86

.70

.50

.40

4-18

Correlation Coefficient Calculations

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



.98 .9899

.86 .9274

.70 .8367

.50 .7071

.40 .6325

4-19

R and Beta

imm

i RS

Sβ

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 isa. 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. .61b. .77c. .88d. .94

4-22

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 4The 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. .53b. .60c. .66d. 1.00

4-24

©2015, college for financial planning, all rights reserved. session 4 correlations & the...

Documents

low correlation

rsquared measures

square r

covariance formula

particular asset

financial planning

good investment

standard deviation