Investment risks
3. Risk assessment and measurement tools
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Investment returns
Investment risks
Measuring stand-alone risk
Portfolio risk and return
Diversifiable and market risks
Capital asset pricing model (CAPM) and
security market line (SML)
Outline
Investment returns measure the financial
results of an investment.
 Returns may be historical or prospective
(anticipated).
 Returns can be expressed in:

◦ Dollar terms
◦ Percentage terms
Investment Returns
Typically, investment returns are not
known with certainty.
 Investment risk pertains to the probability
of earning a return less than that
expected.
 The greater the chance of a return far
below the expected return, the greater
the risk.
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Investment Risk
Stock X
Stock Y
-20
0
15
Which stock is riskier? Why?
Probability Distribution
50
Rate of
return (%)

Expected Rate of Return

Standard Deviation

Coefficient of Variation
Measuring Stand-Alone Risk
^
 Portfolio Return, kp
 Portfolio Risk, p
◦
◦
◦
◦
Covariance
Portfolio Variance
Portfolio Standard Deviation
Correlation Coefficient
Portfolio Risk and Return
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Two stocks can be combined to form a
riskless portfolio if r = -1.0.
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Risk is not reduced at all if the two stocks
have r = +1.0.
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In general, stocks have r  0.65, so risk is
lowered but not eliminated.
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Investors typically hold many stocks.
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What happens when r = 0?
Two-Stock Portfolio
Company Specific
(Diversifiable) Risk
Stand-Alone Risk, p
Market Risk
10
20
30
40
2,000+
Diversifiable Risk versus Market
Risk
Market risk, which is relevant for stocks
held in well-diversified portfolios, is
defined as the contribution of a security to
the overall riskiness of the portfolio.
 It is measured by a stock’s beta
coefficient, which measures the stock’s
volatility relative to the market.
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Market Risk For Individual
Securities
Run a regression with returns on the
stock in question plotted on the Y axis and
returns on the market portfolio plotted on
the X axis.
 The slope of the regression line, which
measures relative volatility, is defined as
the stock’s beta coefficient, or b.

How Are Betas Calculated?
If b = 1.0, stock has average risk.
If b > 1.0, stock is riskier than average.
If b < 1.0, stock is less risky than
average.
 Most stocks have betas in the range of 0.5
to 1.5.
 Can a stock have a negative beta?
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How Are Betas Interpreted?
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CAPM indicates what should be the
required rate of return on a risky asset.
◦ Beta
◦ Risk aversion

The return on a risky asset is the sum of
the riskfree rate of interest and a
premium for bearing risk (risk premium).
The Capital Asset Pricing Model
(CAPM)
The CAPM when graphed is called the
Security Market Line (SML).
 The SML equation can be used to find the
required rate of return on a stock.
 SML: ki = kRF + (kM - kRF)bi

◦ (kM – kRF) = market risk premium, RPM
◦ (kM – kRF)bi = risk premium
Security Market Line (SML)
Security
HT
Market
USR
T-bills
Collections
Expected
return
17.4%
15.0
13.8
8.0
1.7
Risk, b
1.29
1.00
0.68
0.00
-0.86
 Which of the alternatives is best?
Expected Return versus Market
Risk
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Calculate beta for a portfolio with 50% HT
and 50% Collections.
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What is the required rate of return on the
HT/Collections portfolio?
Portfolio Risk and Return
 I = 3%
New SML
SML2
SML1
18
15
11
Original situation
8
0
0.5
1.0
1.5
2.0
Impact of Inflation Change on SML
Required Rate of
Return (%)
After increase
in risk aversion
SML2
kM = 18%
kM = 15%
18
SML1
 RPM = 3%
15
8
Original situation
1.0
Risk, bi
Impact of Risk Aversion Change
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Beta is an estimate.
Unrealistic assumptions.
Not testable.
CAPM does not explain differences in
returns for securities that differ:
◦ Over time
◦ Dividend yield
◦ Size effect
Drawbacks of CAPM