Reviewing Risk Measurement Concepts First Affirmative Financial Network, LLC R. Kevin OKeefe, CIMA.

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 = 0.5

-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 = 2.0

-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 1

-20

-10

0

10

20

30

40

-30 -20 -10 0 10 20 30 40 50

Market Return

Fund

Ret

urn

45

60


Rise / run = 45 / 60 = .75

This is easy!

But … What happens when the data get more complex?


R2 Rm

3 -30 15 20 20 10-10 -40



-15

-10

-5

0

5

10

15

20

25

-50 -40 -30 -20 -10 0 10 20 30

Market Return

Fu

nd

Ret

urn



-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.


Assumes normal distribution (bell-shaped curve)

Normal Distribution

Returns

Pro

ba

bili

ty


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



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



Trick Question:Which portfolio is riskiest?

A B C Mean return 7% 20% 30%Standard dev. 3% 6% 15%


Answer: It depends on your definition of risk!

Does “risk” mean …Probability of loss?Magnitude of loss?Probability of underperforming target?


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


Two Funds:

Which will exhibit greater variability (i.e., higher standard deviation)?

Which has more securities?

Which has the higher R2?


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.


Beta:

1. Don’t forget to account for R2.

2. A useful measure, but insufficient in portfolio construction …


Sharpe ratio:

1. Meaningless number, except as a way of comparing different portfolios over an identical period.

2. Measures absolute risk (vs. relative risk).


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

????

Reviewing Risk Measurement Concepts First Affirmative Financial Network, LLC R. Kevin OKeefe, CIMA.

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