05model
9/16/2011 15:01
12/2/2002
Chapter 5. Model for Analyzing Risk and Rates of Return
The relationship between risk and return is a fundamental axiom in finance.
Generally speaking, it is totally logical to assume
that investors are only willing to assume additional risk if they are adequately compensated with additional return.
This idea
is rather fundamental, but the difficulty in finance arises from interpreting the exact nature of this relationship (accepting that
risk aversion differs from investor to investor).
Risk and return interact to determine security prices, hence its paramount
importance in finance.
PROBABILITY DISTRIBUTION
The probability distribution is a listing of all possible outcomes and the corresponding probability.
Demand for the
Probability of this
Rate of Return on stock
company's products
demand occurring
if this demand occurs
Martin Products
U.S. Water
Strong
30%
100%
20%
Normal
40%
15%
15%
Weak
30%
70%
10%
100%
EXPECTED RATE OF RETURN
The expected rate of return is the rate of return that is expected to be realized from an investment.
It is determined as the
weighted average of the probability distribution of returns.
Demand for the
Probability of this
Martin Products
U.S. Electric
company's products
demand occurring
Rate of Return
Product
Rate of Return
Product
Strong
30%
100%
30%
20%
6%
Normal
40%
15%
6%
15%
6%
Weak
30%
70%
21%
10%
3%
100%
EXPECTED RATE OF RETURN, k hat
15%
15%
MEASURING STANDALONE RISK: THE STANDARD DEVIATION
To calculate the standard deviation, there are a few steps.
First find the differences of all the possible returns from the
expected return.
Second, square that difference.
Third, multiply the squared number by the probability of its occurrence.
Fourth, find the sum of all the weighted squares.
And lastly, take the square root of that number. Let us apply this procedure to
find the standard deviation of Martin Products' returns.
Demand for the
Probability of this
Deviation from k hat
Squared deviation
Sq Dev * Prob.
company's products
demand occurring
Martin Products
Strong
30%
85%
72.25%
21.68%
Normal
40%
0%
0.00%
0.00%
Weak
30%
85%
72.25%
21.68%
Sum:
43.35%
Std. Dev.
=
Square root of sum
65.84%
Sq. root can be
65.84%
found in two ways
Probability of this
demand occurring
U.S. Electric
Strong
30%
5%
0.25%
0.08%
Normal
40%
0%
0.00%
0.00%
Weak
30%
5%
0.25%
0.07%
0.15%
Std. Dev.
=
Square root of sum
3.87%
Sq. root can be
3.87%
found in two ways
A
B
C
D
E
F
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View Full DocumentMEASURING STANDALONE RISK: THE COEFFICIENT OF VARIATION
The coefficient of variation indicates the risk per unit of return, and is calculated by dividing the standard deviation by the
expected return.
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 Spring '11
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 Standard Deviation, Interest

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