reviewing risk measurement concepts first affirmative financial network, llc r. kevin okeefe, cima
TRANSCRIPT
Reviewing Risk Measurement Reviewing Risk Measurement ConceptsConcepts
First Affirmative Financial Network, LLC
R. Kevin O’Keefe, CIMA
What we will coverWhat we will cover
Beta Standard Deviation Sharpe Ratio R-squared Correlation Coefficient How they interrelate
Limitations and UsesLimitations 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
BetaBeta
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 = 1.0Beta = 1.0
Beta = 1.0
-15
-10
-5
0
5
10
15
-15 -10 -5 0 5 10 15
Market
Port
folio
Beta = 0.5Beta = 0.5
Beta = 0.5
-8
-6
-4
-2
0
2
4
6
8
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Market
Po
rtfo
lio
Beta = 2.0Beta = 2.0
Beta = 2.0
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
-14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14
Market
Port
folio
Estimating Beta: Fund 1Estimating Beta: Fund 1
R1 Rm
-15 -20 30 40
What is the slope (rise / run)?
Estimating Beta: Fund 1Estimating Beta: Fund 1
Estimating Beta: Fund 1
-20
-10
0
10
20
30
40
-30 -20 -10 0 10 20 30 40 50
Market Return
Fund
Ret
urn
45
60
Estimating Beta: Fund 1Estimating Beta: Fund 1
Rise / run = 45 / 60 = .75
This is easy!
But … What happens when the data get more complex?
Estimating Beta: Fund 2Estimating Beta: Fund 2
R2 Rm
3 -30 15 20 20 10-10 -40
Estimating Beta: Fund 2Estimating Beta: Fund 2
Estimating Beta: Fund 2
-15
-10
-5
0
5
10
15
20
25
-50 -40 -30 -20 -10 0 10 20 30
Market Return
Fu
nd
Ret
urn
Estimating Beta: Fund 2Estimating Beta: Fund 2
Estimating Beta: Fund 2
-15
-10
-5
0
5
10
15
20
25
-50 -40 -30 -20 -10 0 10 20 30
Market Return
Fu
nd
Ret
urn
Regression line
Beta = .42
Beta : ExampleBeta : Example
Fidelity Select Gold Fund
Beta: 0.25Std Dev: 31.28R-squared: 2
Beta: The DetailsBeta: 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 DeviationStandard 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 DeviationStandard Deviation
Assumes normal distribution (bell-shaped curve)
Normal Distribution
Returns
Pro
ba
bili
ty
Standard DeviationStandard Deviation
Normal Distribution
Mean
Pro
ba
bili
ty
Normal Distribution
Mean
Pro
ba
bili
ty
68.3%
95.5%
-1 SD +1SD-2 SD +2 SD
Standard DeviationStandard Deviation
Standard DeviationStandard 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.)
Normal Distribution
Mean
Pro
ba
bili
ty
68.3%
95.5%
-1 SD +1SD-2 SD +2 SD
Standard DeviationStandard Deviation
Standard DeviationStandard Deviation
Trick Question:Which portfolio is riskiest?
A B C Mean return 7% 20% 30%Standard dev. 3% 6% 15%
Standard DeviationStandard Deviation
Answer: It depends on your definition of risk!
Does “risk” mean …Probability of loss?Magnitude of loss?Probability of underperforming target?
Standard DeviationStandard Deviation
Trick Question:Which portfolio is riskiest?
A B C Mean return 7% 20% 30%Standard dev. 3% 6% 15%
Beta vs. Standard DeviationBeta vs. Standard Deviation
Two Funds:
Same SlopeSame IntersectSame Characteristic Line
What statistical measure is identical for these two funds?
Two fundsTwo funds
Fund A
Market Return
Fu
nd
Ret
urn
Fund B
Market Return
Fu
nd
Retu
rn
Beta vs. Standard DeviationBeta 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 DeviationBeta vs. Standard Deviation
Fund A
Greater variabilityHigher standard
deviation?Fewer securitiesLower r-squared
Fund B
Less variabilityLower standard
deviation?More securitiesHigher r-squared
R-SquaredR-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 RatioSharpe 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 CoefficientCorrelation Coefficient
Meaningful at the component level
The Myth of Negative Correlation
Correlation coefficients are cyclical; they strengthen and weaken over time
Correlation Coefficients (3 Correlation Coefficients (3 year)year)
Correlation Coefficients (10 Correlation Coefficients (10 year)year)
Risk Adjusted MeasuresRisk 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 MeasuresRisk Adjusted Measures
Beta:
1. Don’t forget to account for R2.
2. A useful measure, but insufficient in portfolio construction …
Risk Adjusted MeasuresRisk 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 MeasuresRisk Adjusted Measures
Correlation Coefficients:
1. Fluctuate over time
2. Remember to factor in expected returns
Limitations and UsesLimitations 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 DiscussionQuestions and Discussion
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