CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 4
Correlations & the
“Correlation Pyramid”
©2015, College for Financial Planning, all rights reserved.
Session Details
Module
2
Chapter(s) 2
LOs
2-5
2-6
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.
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
RS
Rp
Rm
Average
Returns
Returns
Coefficient of
Variation
Rp
W
Covariance
Standard
Deviation of
Portfolio
Standard
Deviation
Beta
W
Portfolio Beta
Do
g
Rp
Sharpe Index
Correlation
Coefficient (R)
Coefficient of
Determination
(R2)
Rf
Rf
Rm
Dividend
Growth
Module
Rf
Treynor Index
CAPM
(Required
Return)
Jensen Index
(Alpha)
Rp
4-4
The Pyramid
Covariance
Correlation Coefficient
(R)
–1
0
+1
Coefficient of Determination
(R – squared)
Coefficient of Variation (Variability)
SD
M
4-5
Covariance Formula
COV ij  iji j
4-6
Correlation Coefficient Formula
Rij 
COVij
i   j
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
Correlation Coefficient
-1
0
+1
4-10
Correlation Coefficients
Asset
Large-Cap
Small-Cap
Inter. stocks
LT Corporate Bonds
T-Bills
Inflation
LargeCap
1.00
0.72
0.66
0.29
0.11
-0.09
SmallCap
1.00
0.50
0.15
0.05
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
Return
Market Return
4-13
Negative Correlation
Return
Market Return
4-14
R & R-Squared
• The Correlation Coefficient is also referred to as “R”
and the Coefficient of Determination as “Rsquared.”
• 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
1.0
.95
.80
.50
.23
Coefficient of
Determination
4-16
Coefficient of Determination
Calculate the coefficient of determination, given
the following correlation coefficients between an
asset and a benchmark.
Correlation
Coefficient
1.0
.95
.80
.50
Coefficient of
Determination
1.0
.9025
.64
.25
.23
.0529
4-17
Correlation Coefficient Calculations
Calculate the correlation coefficient, given the
following coefficient of determinations between an
asset and a benchmark.
Coefficient of
Determination
.98
.86
.70
.50
.40
Correlation
Coefficient
4-18
Correlation Coefficient Calculations
Calculate the correlation coefficient, given the
following coefficient of determinations between an
asset and a benchmark.
Coefficient of
Determination
.98
.86
.70
.50
.40
Correlation
Coefficient
.9899
.9274
.8367
.7071
.6325
4-19
R and Beta
Si
β
 Rim
Sm
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. .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 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. 1.00
4-24
CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 4
End of Slides
©2015, College for Financial Planning, all rights reserved.