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hf5chap10.pptxCHAPTER 10 Financial Risk and Required Return
Two of the most important financial analysis concepts are risk and return. What is financial risk, how is it measured, and why is it so important to financial decision making? This chapter discusses basic risk and return concepts from the perspectives of both businesses and individual investors.
Copyright © 2012by the Foundation of the American College of Healthcare Executives 11/9/11 Version
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Financial Risk Basics
Financial risk is present whenever there is some chance of earning a return on an investment that is less than the amount expected.
In general, the greater the probability of a return far below that anticipated, the greater the risk.
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Risk Aversion
In their attitude towards investment risk, investors can be:
Risk neutral
Risk averse
Risk seeking
Most investors are risk averse.
This means that higher risk investments require higher rates of return.
It is risk aversion that makes risk concepts so important to financial decision making.
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Probability Distributions
The chance that an event will occur is called its probability of occurrence, or just probability.
A probability distribution lists all possible event outcomes along with their probabilities. For example, a coin toss:
Outcome Probability
Head 0.50 or 50%
Tail 0.50 or 50%
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Expected and Realized Rates of Return
Estimated Returns for Two Proposed Projects
Probability Rate of Return
Economic State of Occurrence MRI Clinic
Very poor 0.10 -10% -20%
Poor 0.20 0 0
Average 0.40 10 15
Good 0.20 20 30
Very good 0.10 30 50
1.00
Where do these estimates come from?
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Expected Rate of Return, E(R)
E(R) = Expected rate of return
E(RMRI) = (0.10 x [-10%]) + (0.20 x 0%)
+ (0.40 x 10%) + (0.20 x 20%)
+ (0.10 x 30%)
= 10.0%.
What is E(RClinic)?
= (P1 x R1) + (P2 x R2) + and so on.
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Realized Rate of Return
The expected rate of return is estimated before an investment is made.
After the fact, the return that is actually achieved is called the realized rate of return.
When risk is present, the realized rate of return rarely equals the expected rate of return.
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Stand-Alone Risk
Stand-alone risk is defined and measured assuming an investment will be held in isolation.
Stand-alone risk can be measured by the degree of “tightness” of the return distribution.
One common measure of stand-alone risk is the standard deviation of the return distribution, usually repre-sented by a lower case sigma, .
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Standard Deviation () and Variance (V)
= Variance .
V = P1 x (R1 - E[R])2 + P2 x (R2 - E[R])2
+ and so on.
VMRI = 0.10 x (-10% - 10%)2 + … = 120.
MRI = 120 = 11.0%.
Clinic = 18.0%.
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Probability
Rate of Return (%)
MRI
Clinic
0
10
15
A larger indicates more stand-alone risk
( =11%)
( =18%)
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Discussion Item
Here are the expected returns and standard deviations of the two investment alternatives:
E(R)
MRI 10% 11%
Clinic 15% 18%
Assuming the two projects are mutually exclusive, which one should be chosen?
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Coefficient of Variation (CV)
The coefficient of variation (CV) is defined as the standard deviation divided by the expected rate of return. It is a standardized measure of stand-alone risk.
CVMRI = 11% / 10% = 1.1.
CVClinic = 18% / 15% = 1.2.
Both the standard deviation and the CV indicate that the clinic investment is riskier than the MRI investment.
CV is most useful when comparing investments with widely differing returns.
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Portfolio Risk and Return
Standard deviation (or CV) is an applicable risk measure only when an investment is held in isolation.
Most investments are held as part of a collection, or portfolio, of investments.
When investments are held in portfolios, the relevant return, and hence risk, is that of the entire portfolio.
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Portfolio Illustration
State Prob A B C D AB AC AD
Very poor 0.10 -10% 30% -25% 15% 10% -17.5% 2.5%
Poor 0.20 0 20 -5 10 10 -2.5 5.0
Average 0.40 10 10 15 0 10 12.5 5.0
Good 0.20 20 0 35 25 10 27.5 22.5
Very good 0.10 30 -10 55 35 10 42.5 32.5
1.00
E(R) 10.0% 10.0% 15.0% 12.0% 10.0% 12.5% 11.0%
11.0% 11.0% 21.9% 12.1% 0.0% 16.4% 10.1%
Note: A, B, C, and D are single assets; AB, AC, and AD are equal weighted (50/50) portfolios of those single assets.
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Portfolio Return
The expected rate of return on a portfolio, E(Rp), is merely the weighted average of the components’ expected returns:
E(RAB) = (0.5 x 10%) + (0.5 x 10%) = 10.0%.
E(RAC) = 12.5%.
What is E(RAD)?
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Portfolio Risk
A portfolio’s return is simply the weighted average of the returns of the components.
However, a portfolio’s risk, which typically is measured by standard deviation, is not the weighted average of the component standard deviations. It depends on the relationships among the returns of the portfolio’s components.
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Portfolio Risk (Cont.)
Consider Portfolio AB.
Each component is risky when held in isolation ( = 10%), yet the portfolio has zero risk ( = 0%).
Why can Investments A and B be combined to form a riskless portfolio?
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Portfolio Risk (Cont.)
Consider Portfolio AC.
There is no risk reduction in this portfolio. Its standard deviation (16.4%) is the weighted average of the ’s of each component:
(0.50 x 11.0%) + (0.5 x 21.9%) = 16.4%.
Why is there no risk reduction here?
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Portfolio Risk (Cont.)
Consider Portfolio AD.
There is some risk reduction in this portfolio. The standard deviation (10.1%) is somewhat less than either of the component ’s and of the weighted average:
(0.50 x 11.0%) + (0.5 x 12.1%) = 11.6%.
Why is there some risk reduction here?
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Correlation
The movement relationship between two variables is called correlation.
Correlation is measured by the correlation coefficient, r:
r = +1 = perfect positive correlation, such as in Portfolio AC.
r = -1 = perfect negative correlation, such as in Portfolio AB.
r = 0 = zero correlation.
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“Real World” Correlations
It is difficult to generalize about correlations among investment returns.
However, it is rare (if not impossible) to find r = +1, r = -1, or even r = 0.
The correlation between two randomly chosen investments is likely to range from +0.4 to +0.8.
Why?
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Impact of Portfolio Size
The risk of a portfolio (sp) decreases as more and more investments are randomly added.
However, the incremental risk reduction from each new investment decreases as more assets are added.
Considerable risk remains regardless of the number of assets added.
Why?
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Many Stocks ( = 18%)
0
15
Probability
A Few Stocks ( = 30%)
One Stock ( = 35%)
Illustration Using
Stock Returns
Return
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Number of Assets in Portfolio
10 20 30 40
Portfolio Risk
sp
sp (%)
1
18
35
Diversi-
fiable
Risk
Note: The standard deviations shown are for an average 1-asset,
2-asset, 3-asset, and so on, portfolio.
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Stand-alone Portfolio Diversifiable
Stand-alone risk is the risk of an individual investment when it is held in isolation.
Diversifiable risk is that part of the stand-alone risk that can be eliminated by diversification.
Portfolio risk is that part of the stand-alone risk that cannot be eliminated by diversification.
risk risk risk
= + .
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Implications for Investors
It is not rationale for an investor, whether an individual or business, to hold a single investment.
Because an investment held in a portfolio is less risky than when held in isolation, stand-alone risk measures (i.e., s) are not relevant for investments held in portfolios.
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Beta Coefficients
The most widely used measure of risk for investments held in portfolios is the beta coefficient, or just beta.
Beta measures the volatility of the investment’s returns relative to the returns on the portfolio.
Because beta is a relative measure of risk, it depends on both the investment and the portfolio.
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Beta Illustration
Rate of Return if State Occurs _
Year H M L Portfolio (P)
1 35% 15% 8% 15%
2 5 5 5 5
3 -18 -5 2 -5
4 40 25 18 25
5 50 35 19 35
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Return on P (%)
-20 -10 10 20 30 40
40
30
20
10
-10
-20
Return on
H, M, and L
(%)
H (b = 1.5)
M (b = 1.0)
L (b = 0.5)
?What does the distance of the points from the regression line indicate?
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If beta = 1.0, investment has average risk, where average is defined as the riskiness of the portfolio.
If beta > 1.0, investment has above-average risk.
If beta < 1.0, investment has below-average risk.
Most investments have betas in the range of 0.5 to 1.5.
Beta Illustration (Cont.)
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Beta Components
b = ri,M .
i
M
The beta of an investment depends on:
Its standard deviation relative to the standard deviation of the portfolio.
Its correlation with the portfolio.
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Portfolio Risk
If the investor is an individual, the investments are individual securities (stocks), the portfolio is the market portfolio, and the relevant risk of each asset is called market risk.
If the investor is a business, the investments are real assets (projects), the portfolio is the entire business, and the relevant risk of each asset is called corporate risk .
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In for-profit businesses, projects have both corporate risk and market risk.
The risk of the project as seen by the business’s managers (and other stakeholders) is corporate risk, which is measured by its corporate beta.
The risk of the project as seen by the business’s shareholders is market risk, which is measured by market beta.
This topic will be explored in more depth when we cover capital budgeting analysis.
Portfolio Risk (Cont.)
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Portfolio Betas
The beta of portfolio is simply the weighted average of the betas of the component investments.
This concept applies regardless of whether the portfolio is an individual investor’s stock portfolio or a business’s portfolio of projects.
For example, combining H and L:
bp = (0.70 x bH) + (0.30 x bL)
= (0.70 x 1.5) + (0.30 x 0.5) = 1.20.
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Risk and Required Return
Defining and measuring risk is of no value if we cannot relate risk to required rate of return.
The relationship between risk and required rate of return on a stock investment is given by the Security Market Line (SML) of the Capital Asset Pricing Model (CAPM):
R(Re) = RF + [R(RM) - RF] x b.
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SML Illustration Using Asset H
Assume RF = 6%.
Assume R(RM) = 10%.
b = 1.5.
R(Re) = RF + [R(RM) - RF] x b
= 6% + (10%- 6%) x 1.5
= 6% + (4% x 1.5)
= 6% + 6.0% = 12.0%.
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What is the required rate of return on Investment L?
What is the required rate of return on Investment M?
Note that the term [R(RM) - RF] is called the market risk premium. It is the amount above the risk-free rate that investors require to assume average (b = 1) risk.
SML Illustration (Cont.)
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SML
R(RH) = 12
R(RM) = 10
R(RL) = 8
RF = 6
0 0.5 1 1.5
SML: R(Re) = 6% + (10% - 6%) x b.
R(Re) (%)
Risk, b
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A Word of Caution About the CAPM
The CAPM is based on a very restrictive set of assumptions.
It has not been empirically verified.
It is based on investor expectations, but the inputs used in the model typically are based on historical data.
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Some Good News About the CAPM
The CAPM provides investors with a very rational way of thinking about required rates of return..
R(Re) is composed of:
The risk-free rate, which compensates investors for the time value of money.
A risk premium, which compensates investors for the amount of portfolio risk assumed.
Should an investor who holds a stock in isolation expect to receive his or her required rate of return?
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This concludes our discussion of Chapter 10 (Financial Risk and Required Return).
Although not all concepts were discussed in class, you are responsible for all of the material in the text.
Do you have any questions?
Conclusion
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