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CHAPTER 10
Financial Risk and Return
Financial returns
Stand-alone risk
Portfolio risk
Corporate risk
Market risk
Risk and return
Copyright © 1999 by the Foundation of the American College of Healthcare Executives
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Financial Management Implications of
Risk and Return
Investors--both individuals and
businesses--dislike risk. Thus, risk
affects required returns.
Healthcare managers must
understand concepts of risk and
return in order to:
Understand financing costs.
Understand how service decisions
affect a business’ financial condition.
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Investment Returns
The financial performance of an
investment, whether made by an
individual or a business, is measured
by its return.
Investment returns can be measured
in two ways:
Dollar returns.
Percentage returns (rate of return).
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Investment Return Illustration
Suppose you buy 10 shares of stock
for $1,000 in total.
The stock pays no dividends, but
after one year you sell the stock for
$1,100.
0
1
-$1000
$1100
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Return Calculations
The dollar return is found as follows:
$ Return = Amount received - Amount invested
= $1,100 - $1,000 = $100
The rate of return is found as follows:
% Return = Dollar return / Amount invested
= ($1,100 - $1,000) / $1,000
= $100 / $1,000 = 0.10 = 10.0%
>>> Which one to use??
Copyright © 1999 by the Foundation of the American College of Healthcare Executives
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Financial Risk
Financial risk is present when there
is some chance of earning a return
on an investment that is less than the
amount expected. (not necessarily a
financial loss)
The greater the probability of a return
far below the expected return, the
greater the financial risk.
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Returns on Two Investments
Investment X
 Which investment is riskier?
Investment Y
0
15
Rate of
return (%)
Expected Rate of Return
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Risk Aversion
Investors can be:
Risk neutral.
Risk averse.
Risk seeking.
Most investors are risk averse:
If two investments have the same risk but
different returns, choose the higher return.
If two investments have the same return but
different risks, choose the lower risk.
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Probability (Risk) 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. Coin toss example:
Outcome
Head
Tail
Probability
0.50 or 50%
0.50 or 50%
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Expected vs. Actual Returns
Given the uncertainty of outcome with
regard to financial returns, need an
estimate of EXPECTED return that
incorporates the risk (probability)
associated with various financial
outcomes.
Comparison of expected return to
actual return as a proxy measure of
investment risk (post hoc).
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Expected Rate of Return - Example
Projected Returns for Two Proposed Projects:
Economic State
Very poor
Poor
Average
Good
Very good
Probability
of Occurrence
0.10
0.20
0.40
0.20
0.10
1.00
Rate of Return
MRI
Clinic
10%
0
10
20
30
20%
0
15
30
50
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What is each alternative’s
expected rate of return, E(R)?
E(R) =  (Pi) x (Ri)
E(RMRI) = (0.10 x [-10%]) + (0.20 x 0%)
+ (0.40 x 10%) + (0.20 x 20%)
+ (0.10 x 30%) = 10.0%.
E(Rclinic) = (0.10 x [-20%]) + (0.20 x 0%)
+ (0.40 x 15%) + (0.20 x 30%)
+ (0.10 x 50%) = 15.0%
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Realized Rates 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 (actual) 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 relevant when 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 represented by a lower case sigma, .
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Standard Deviation ()
=
Variance (Var) .
Var = P1 x (R1 - E[R])2 + P2 x (R2 - E[R])2
+ and so on .
VarMRI = 0.10 x (-10% - 10%)2 + … = 120.
MRI =
120 = 11.0%.
Clinic = 18.0%.
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Probability
MRI
Clinic
0
10 15
Rate of Return (%)
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Portfolio Risk and Return
Standard deviation 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 risk and
return is that of the entire portfolio.
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Portfolio Illustration
State
Prob
A
B
C
Very poor
Poor
Average
Good
Very good
0.10
0.20
0.40
0.20
0.10
1.00
-10%
0
10
20
30
30%
20
10
0
-10
-25%
-5
15
35
55
D
AB
AC
AD
15%
10
0
25
35
10% -17.5% 2.5%
10
-2.5
5.0
10
12.5
5.0
10
27.5 22.5
10
42.5 32.5
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 return on a portfolio, E(Rp), is
merely the weighted average of the
expected returns of each component:
E(RAB) = (0.5 x 10%) + (0.5 x 10%) = 10.0%.
E(RAC) = 12.5%.
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Alternative Method
____Estimated Return____
Economy
Recession
Below avg.
Average
Above avg.
Boom
Prob.
0.10
0.20
0.40
0.20
0.10
A
-10.0%
0.0
10.0
20.0
30.0
C
AC
-25.0%
-5.0
15.0
35.0
55.0
-17.5%
-2.5
12.5
27.5
42.5
E(RAC) = (0.10 x [-17.5%]) + (0.20 x [-2.5%])
+ (0.40 x 12.5%) + (0.20 x 27.5%)
+ (0.10 x 42.5%) = 12.5%.
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Portfolio Risk
Portfolio return is simply the
weighted average of the returns of
the components.
However, portfolio risk, which is
measured by the portfolio’s standard
deviation, is not merely the weighted
average of each component’s
standard deviation. It depends on
the relationships among the returns.
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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%).
The reason is that the expected
returns for each asset are perfectly
negatively correlated with one
another so that risk is cancelled out.
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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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Return Distributions for Two Perfectly
Negatively Correlated Assets (r = -1.0) and
for 50/50 Portfolio WM
.
Asset W
Asset M
.
.
.
.
0
.
.
Portfolio WM
.
. . . . .
0
0
.
.
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Return Distributions for Two Perfectly
Positively Correlated Assets (r = +1.0) and
for 50/50 Portfolio WW’
.
Asset W
.
.
Asset W’
.
.
0
.
.
.
Portfolio WW’
.
.
.
0
0
.
.
.
.
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Statements About Portfolio Risk
It is difficult to generalize about “real
world” correlations.
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.
Cumulative economic effects
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Portfolio Effects on Risk
p decreases as more assets are added.
However, the incremental risk reduction
decreases as more assets are added.
Considerable risk remains regardless of
the number of assets added.
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Probability
Many Assets
Illustration Using
Stock Returns
A Few Assets
One Asset
0
15
Return
Even with a large number of stocks, p 20%.
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p (%)
Stand-Alone Risk, p
Diversifiable Risk
Portfolio Risk
10
20
30
40
# Assets in Portfolio
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Stand-alone Portfolio Diversifiable
= risk +
.
risk
risk
Portfolio risk is that part of an asset’s
stand-alone risk that cannot be
eliminated by diversification.
Diversifiable risk is that part of an
asset’s stand-alone risk which can be
eliminated by diversification.
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Implications for Investors
It is not rational to hold a single
investment. (unless risk seeking)
Stand-alone risk measures are not
generally relevant when assets are
held in portfolios.
The need for measure(s) of relative
risk of individual assets held in
larger asset portfolios.
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Beta Coefficients
The most widely used measure of
risk for assets held in portfolios is
the beta coefficient, or just beta.
Beta measures the volatility of the
asset’s returns relative to the returns
on the portfolio.
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Beta Illustration
Year
1
2
3
4
5
Rate of Return if State Occurs _
H
M
L
Portfolio (P)
20%
5
-10
35
50
15%
5
-5
25
35
10%
5
0
15
20
15%
5
-5
25
35
Plot expected returns for each single asset vs.
the expected returns for the portfolio over time.
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Return on
H, M, and L
H (b = 1.5)
M (b = 1.0)
40
L (b = 0.5)
30
20
10
-20
-10
0
10
20
30
40
Return on P
-10
-20
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If beta = 1.0, asset has average risk,
where average is defined as the
riskiness of the portfolio.
If beta > 1.0, asset is more risky
than average.
If beta < 1.0, asset is less risky than
average.
Most assets have betas in the range
of 0.5 to 1.5.
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Relevant Measures of Portfolio Risk
If the investor is an individual, the
assets 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
assets are real assets (business
lines), the portfolio is the entire
business, and the relevant risk of
each asset is called corporate risk .
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Note that business assets incorporate
elements of both corporate risk and
market risk.
The risk of the asset as seen by the
business’ managers (and other
stakeholders) is corporate risk, which is
measured by the asset’s corporate beta.
The risk of the asset as seen by the
business’ shareholders is market risk,
which is measured by the asset’s market
beta.
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Portfolio Betas
The beta of a given portfolio is
simply the weighted average of the
betas of the component assets.
This concept applies regardless of
whether the portfolio is an
individual investor’s stock portfolio
or a business’ portfolio of real
assets.
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Calculate the beta for a portfolio with
70% in Asset H and 30% in Asset L
bp = Weighted average
= (0.70 x bH) + (0.30 x bL)
= (0.70 x 1.5) + (0.30 x 0.5)
= 1.20.
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Relationship Between Risk and Return
Contemporary asset valuation
methods require consideration of
both risk and return.
The relationship between risk and
required rate of return on a stock
investment is given by Security
Market Line (SML) of the Capital
Asset Pricing Model (CAPM):
R(Ri) = RF + [R(RM) - RF] x bi.
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CAPM Definitions
Where:
R(Ri) = required return on asset i
RF = risk free rate of return
R(Rm) = required market return
bi = market beta value for asset I
Both RF and R(Rm) rates are
determined by current marketplace
conditions
RF -- U.S. treasury rates (10 yr)
R(Rm) -- avg. expected market returns
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SML Illustration Using Asset H
Assume RF = 6%.
Assume R(RM) = 10%.
bH = 1.5.
R(RH) = RF + [R(RM) - RF] x bH
= 6% + (10% - 6%) x 1.5
= 6% + (4% x 1.5)
= 6% + 6.0% = 12.0%.
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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.
Represents the premium that
investors are currently requiring to
assume commensurate risk.
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SML: R(Ri) = 6% + (10% - 6%) x bi .
R(Ri) (%)
SML
R(RH) = 12
R(RM) = 10
R(RL) = 8
RF = 6
0
0.5
1
1.5
Risk, bi
Copyright © 1999 by the Foundation of the American College of Healthcare Executives