Reviewing Risk Measurement Concepts

1
Reviewing Risk Measurement Concepts

• First Affirmative Financial Network, LLC

R. Kevin OKeefe, CIMA
2
What we will cover

• Beta
• Standard Deviation
• Sharpe Ratio
• R-squared
• Correlation Coefficient
• How they interrelate

3
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

4
Beta

• A measure of a securitys 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.

5
Beta 1.0
6
Beta 0.5
7
Beta 2.0
8
Estimating Beta Fund 1

• R1 Rm
• -15 -20
• 30 40
• What is the slope (rise / run)?

9
Estimating Beta Fund 1
45
60
10
Estimating Beta Fund 1

• Rise / run 45 / 60 .75
• This is easy!
• But What happens when the data get more
  complex?

11
Estimating Beta Fund 2

• R2 Rm
• 3 -30
• 15 20
• 20 10
• -10 -40

12
Estimating Beta Fund 2
13
Estimating Beta Fund 2
Regression line
Beta .42
14
Beta Example

• Fidelity Select Gold Fund
• Beta 0.25
• Std Dev 31.28
• R-squared 2

15
(No Transcript)
16
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 gt
  1, and half have a beta lt 1.
• You cannot diversify away beta.

17
Standard Deviation

• Standard deviation defines a band around the mean
  within which an investments (or a portfolios)
  returns tend to fall. The higher the standard
  deviation, the wider the band.

18
Standard Deviation

• Assumes normal distribution (bell-shaped curve)

19
Standard Deviation
20
Standard Deviation
68.3
95.5
-1 SD
1SD
-2 SD
2 SD
21
Standard Deviation

• Q. What does it mean that a portfolios standard
  deviation is x?
• It means that x 1 standard deviation
• (which allows you, therefore, to say something
  statistically meaningful about the range of
  probable returns.)

22
Standard Deviation
68.3
95.5
-1 SD
1SD
-2 SD
2 SD
23
Standard Deviation

• Trick Question
• Which portfolio is riskiest?
• A B C
• Mean return 7 20 30
• Standard dev. 3 6 15

24
Standard Deviation

• Answer It depends on your definition of risk!
• Does risk mean
• Probability of loss?
• Magnitude of loss?
• Probability of underperforming target?

25
Standard Deviation

• Trick Question
• Which portfolio is riskiest?
• A B C
• Mean return 7 20 30
• Standard dev. 3 6 15

26
Beta vs. Standard Deviation

• Two Funds
• Same Slope
• Same Intersect
• Same Characteristic Line
• What statistical measure is identical for these
  two funds?

27
Two funds
28
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?

29
Beta vs. Standard Deviation

• Fund A
• Greater variability
• Higher standard deviation?
• Fewer securities
• Lower r-squared

• Fund B
• Less variability
• Lower standard deviation?
• More securities
• Higher r-squared

30
R-Squared

• Tightness of fit around the characteristic line
• OR, if you prefer, the percentage of a
  portfolios 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

31
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.

32
Correlation Coefficient

• Meaningful at the component level
• The Myth of Negative Correlation
• Correlation coefficients are cyclical they
  strengthen and weaken over time

33
Correlation Coefficients (3 year)
34
Correlation Coefficients (10 year)
35
Risk Adjusted Measures

• Total risk Market risk non-market risk
• All measures must be contextualized
• Standard Deviation
• 1. Dont forget to account for returns
• 2. Risk must be defined
• 3. Remember that standard deviation measures
  upside volatility as well as downside.

36
Risk Adjusted Measures

• Beta
• 1. Dont forget to account for R2.
• 2. A useful measure, but insufficient in
  portfolio construction

37
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).

38
Risk Adjusted Measures

• Correlation Coefficients
• 1. Fluctuate over time
• 2. Remember to factor in expected returns

39
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

40
Questions and Discussion

• ????