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Chapter 6
Foundation Of Risk Analysis
®1999 South-Western College Publishing
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How Do Asset Prices Change
With Risk?
• The Higher the Volatility (Risk)
• The Higher the E(R)
• The Lower the Price
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Market Scenario
Certainty
1. The mean return equals
the riskless interest rate.
2. The variance is 0.
Uncertainty
1. The mean return is greater than
the riskless interest rate.
2. The variance is greater than 0.
3. The risk premium is zero. 3. The risk premium is positive.
(with risk aversion)
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• Certainty
There is only one future return that is
known with a probability of 1.
• Uncertainty
There is more than one possible future
return. The probability of each
outcome is unknown.
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Probabilities
• Objective Probability
– Actual probabilities are known
• Subjective Probability
– Probability estimates
• Actual probabilities are not known
– Based on historical data
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Have different
average rates of
return
Assets
Requires
criteria for
selection
Have different
degrees of risk
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Investment Criteria
• MRC
– Selects the asset with the highest rate of
return
– Does not rank investments
• MERC
– Compares assets with uncertain returns
– Gives a clear ranking of investments
– Chooses highest E(R)
– Does not relate risk to return
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Attitudes Toward Risk
• Risk Averters Most investors
– Dislike volatility or risk
– Require a risk premium for taking on
additional risk
• Risk Neutral
Use MERC
– Ignore variance
– Decisions based only on E(R)
• Risk Seekers Buy lottery tickets
– Like risk and variance
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E(R) = Mean Rate of Return + Risk
on Riskless Asset
Premium
Risk Premium is Required by the Market to
Compensate Investors for Risk
Variance and Standard Deviation
Measures Risk
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Calculating Variance and
Standard Deviation
• Variance
– Measure of the dispersion around the mean
m
2 =  Pi[Ri - E(R)]2
i=1
• Standard Deviation
– Measure of how much the actual return is
likely to deviate from its expected return
 = Square root of the variance
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Mean-Variance Criterion
MVC
• Most Investors are Risk Averse
• Risk Aversion Characteristics
– Select assets with the lowest variance for
the same E(R)
– Select assets with the highest E(R) for the
same variance
• Assumes
– Investors like higher E(R’s)
– Investors dislike higher variances
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MVC
Return
C
A
.
B
.
.
(see next slide)
Risk
Investors prefer investments A and C to B
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• C Gives a Greater Return Than B for the
Same Level of Risk.
C
B
• A Gives the Same Return as B for a Lower
Level of Risk.
A
B
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Risk-Return Relationship
• Confirmed by Historical Returns
– The higher the risk
• Higher variance and standard deviation
– The higher the average rates of return
• An Asset’s Variability Determines its Risk
Premium
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