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First Affirmative Financial Network, LLC
Reviewing Risk Measurement Concepts
R. Kevin O’Keefe, CIMA
What we will cover
 Beta
 Standard Deviation
 Sharpe Ratio
 R-squared
 Correlation Coefficient
 How they interrelate
Limitations and Uses
Limitations:
Cannot predict specific events
Are historical, backward-looking
Uses:
Can help improve portfolio construction
Can help identify unwanted exposure
Can help defend investment decisions
Beta
A measure of a security’s sensitivity to market
movements
It is a relative measure, not an absolute measure
of volatility
It does not tell you enough; you need to know the
R-squared.
Beta = 1.0
Beta = 1.0
15
10
Portfolio
5
0
-15
-10
-5
0
-5
-10
-15
Market
5
10
15
Beta = 0.5
Beta = 0.5
8
6
Portfolio
4
2
0
-14 -12 -10
-8
-6
-4
-2-2 0
-4
-6
-8
Market
2
4
6
8
10
12
14
Beta = 2.0
Beta = 2.0
14
12
10
8
6
Portfolio
4
2
0
-14 -12 -10 -8
-6
-4
-2-2 0
-4
-6
-8
-10
-12
-14
Market
2
4
6
8
10 12 14
Estimating Beta: Fund 1
R1
Rm
-15
30
-20
40
What is the slope (rise / run)?
Estimating Beta: Fund 1
Estimating Beta: Fund 1
40
Fund Return
30
20
45
10
0
-30
-20
-10
-10
0
10
60
-20
Market Return
20
30
40
50
Estimating Beta: Fund 1
Rise / run = 45 / 60 = .75
This is easy!
But … What happens when the data get more
complex?
Estimating Beta: Fund 2
R2
Rm
3
15
20
-10
-30
20
10
-40
Estimating Beta: Fund 2
Estimating Beta: Fund 2
25
Fund Return
20
15
10
5
0
-50
-40
-30
-20
-10
-5 0
-10
-15
Market Return
10
20
30
Estimating Beta: Fund 2
Estimating Beta: Fund 2
25
Fund Return
Regression line
20
15
10
Beta = .42
5
0
-50
-40
-30
-20
-10
-5 0
-10
-15
Market Return
10
20
30
Beta : Example
Fidelity Select Gold Fund
Beta: 0.25
Std Dev: 31.28
R-squared: 2
Beta: The Details
 The beta of a portfolio is the weighted
average of the individual betas of the
securities in the portfolio.
 Half the securities in the market have a
beta > 1, and half have a beta < 1.
 You cannot diversify away beta.
Standard Deviation
Standard deviation defines a band around
the mean within which an investment’s
(or a portfolio’s) returns tend to fall. The
higher the standard deviation, the wider
the band.
Standard Deviation
Assumes normal distribution (bell-shaped curve)
Probability
Normal Distribution
Returns
Standard Deviation
Probability
Normal Distribution
Mean
Standard Deviation
Probability
Normal Distribution
68.3%
95.5%
-2 SD
-1 SD
Mean
+1SD
+2 SD
Standard Deviation
Q. What does it mean that a portfolio’s
standard deviation is x%?
A. It means that x = 1 standard deviation
(which allows you, therefore, to say something
statistically meaningful about the range of
probable returns.)
Standard Deviation
Probability
Normal Distribution
68.3%
95.5%
-2 SD
-1 SD
Mean
+1SD
+2 SD
Standard Deviation
Trick Question:
Which portfolio is riskiest?
Mean return
Standard dev.
A
7%
3%
B
C
20% 30%
6% 15%
Standard Deviation
Answer: It depends on your definition of risk!
Does “risk” mean …
Probability of loss?
Magnitude of loss?
Probability of underperforming target?
Standard Deviation
Trick Question:
Which portfolio is riskiest?
Mean return
Standard dev.
A
7%
3%
B
C
20% 30%
6% 15%
Beta vs. Standard Deviation
Two Funds:
Same Slope
Same Intersect
Same Characteristic Line
What statistical measure is identical for these two
funds?
Two funds
Fund B
Fund Return
Fund Return
Fund A
Market Return
Market Return
Beta vs. Standard Deviation
Two Funds:
Which will exhibit greater variability (i.e.,
higher standard deviation)?
Which has more securities?
Which has the higher R2?
Beta vs. Standard Deviation
Fund A
Fund B
Greater variability
Higher standard
deviation?
Fewer securities
Lower r-squared
Less variability
Lower standard
deviation?
More securities
Higher r-squared
R-Squared
“Tightness of fit around the characteristic line”
OR, if you prefer, “the percentage of a portfolio’s
fluctuations that can be explained by fluctuations
in its benchmark index”
Relates to beta, not standard deviation
Tells you how much significance there is to the beta:
higher R2 = greater significance
Sharpe Ratio
Sharpe Ratio =
Excess Return*
Standard Deviation
*Above the risk-free rate
1.The number is meaningless except in a relative
context.
2.Based on Standard Deviation, not Beta, thus more
meaningful at the portfolio level rather than at the
component level.
Correlation Coefficient
Meaningful at the component level
The Myth of Negative Correlation
Correlation coefficients are cyclical; they
strengthen and weaken over time
Correlation Coefficients (3 year)
Correlation Coefficients (10 year)
Risk Adjusted Measures
Total risk = Market risk + non-market risk
All measures must be contextualized
Standard Deviation:
1. Don’t forget to account for returns
2. “Risk” must be defined
3. Remember that standard deviation measures upside
volatility as well as downside.
Risk Adjusted Measures
Beta:
1. Don’t forget to account for R2.
2. A useful measure, but insufficient in portfolio
construction …
Risk Adjusted Measures
Sharpe ratio:
1. Meaningless number, except as a way of
comparing different portfolios over an identical
period.
2. Measures absolute risk (vs. relative risk).
Risk Adjusted Measures
Correlation Coefficients:
1. Fluctuate over time
2. Remember to factor in expected returns
Limitations and Uses
Limitations:
Cannot predict specific events
Are historical, backward-looking
Uses:
Can help improve portfolio construction
Can help identify unwanted exposure
Can help defend investment decisions
Questions and Discussion
? ??