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08 Chapter model
10/7/2009 9:05
2/14/2006
Chapter 8. Risk and Rates of Return
Demand for
Probability
Rate of return on stock,
the firms
of this
if this demand occurs
Martin
U.S. Water
products
occurring
Martin Prod.
U.S. Water
Prob x Ret.
Prob x Ret.
Strong
30%
100%
20%
30.0%
6.0%
Normal
40%
15%
15%
6.0%
6.0%
Weak
30%
70%
10%
21.0%
3.0%
100%
Expected return =
15.0%
15.0%
MARTIN PRODUCTS
Demand for
Probability
(1)
(2)
(3)
the firms
of this
Return in
Deviation
Squared
Prob. X
products
occurring
this outcome
from mean
Deviation
Sq Deviation
Strong
30%
100%
85%
72.3%
21.7%
Normal
40%
15%
0%
0.0%
0.0%
Weak
30%
70%
85%
72.3%
21.7%
Sum of squared deviations (Variance) =
43.4%
(4)
Standard deviation =
65.8%
(5)
U.S. WATER
Demand for
Probability
(1)
(2)
(3)
the firms
of this
Return in
Deviation
Squared
Prob. X
products
occurring
this outcome
from mean
Deviation
Sq Deviation
Strong
30%
20%
5%
0.3%
0.1%
Normal
40%
15%
0%
0.0%
0.0%
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.
Standalone risk
(Section 8.1)
In explaining standalone risk, this model introduces probablity distributions and the
calculation of expected retuns, standard deviations, and coefficients of variation.
PROBABILITY DISTRIBUTIONS: CALCULATING EXPECTED RETURN
The probability distribution is a listing of all possible outcomes and the
corresponding probability.
The expected return is calculated by multiplying the
possible returns by their corresponding probabilities.
PROBABILITY DISTRIBUTIONS: CALCULATING STANDARD DEVIATION
Standard deviation measures the variability of a set of observations and is calculated
by finding the square root of a sum of squared deviations.
Sound confusing?
The
charts below calculate standard deviation for Martin and U.S. Water.
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View Full DocumentWeak
30%
10%
5%
0.2%
0.1%
Sum of squared deviations (Variance) =
0.2%
(4)
Standard deviation =
3.9%
(5)
SD for Martin
65.8%
SD for U.S. Water
3.9%
SAMPLE STANDARD DEVIATION CALCULATION
Realized
Deviation
Squared
Year
return
from mean
Deviation
2003
15%
5%
0.2%
2004
5%
15%
2.3%
2005
20%
10%
1.0%
Avg return =
10.0%
3.5%
Sum of squared deviations
1.75%
Divide by n, where n = 2
13.23%
Std deviation (take a square root)
Sample SD (Excel)
13.23%
COEFFICIENT OF VARIATION
CV for Martin
4.39
CV for U.S. Water
0.26
PORTFOLIO EXPECTED RETURN
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 Finance, Management

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