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Chapter 8. Risk and Rates of Return
12/11/08
Table 81.
Probability Distributions and Expected Returns
Martin Products
U.S. Water
Rate of
Rate of
Economy,
Probability
Return
Probability
Return
Which
of This
If This
of This
If This
Affects
Demand
Demand
Product
Demand
Demand
Product
Demand
Occurring
Occurs
(2)x(3)
Occurring
Occurs
(5)x(6)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Strong
0.30
80%
24%
0.30
15%
4.5%
Normal
0.40
10%
4%
0.40
10%
4.0%
Weak
0.30
60%
18%
0.30
5%
1.5%
1.00
Expected return=
10%
1.00
Expected return=
10%
We use Excel to do the calculations shown in black boldface type.
TABLE 82. Calculating Martin Product’s Standard Deviation
Rate of
Deviation:
Economy,
Probability
Return
Actual 
Which
of This
If This
10%
Squared
Affects
Demand
Demand
Expected
Deviation
Deviation
Demand
Occurring
Occurs
Return
Squared
x Prob.
(1)
(2)
(3)
(4)
(5)
(6)
Strong
0.30
80%
70%
0.4900
0.1470
Normal
0.40
10%
0%
0.0000
0.0000
Weak
0.30
60%
70%
0.4900
0.1470
1.00
∑ = Variance:
0.29
Standard deviation = square root of variance: σ =
0.5422
Standard deviation expressed as a percentage: σ =
54.2%
TABLE 83. Finding σ Based On Historical Data
Deviation
from
Squared
Year
Return
Average
Deviation
The higher a security's risk, the higher its required return.
Risk can be thought of in
two ways: (1) Standalone risk, where the security is considered in isolation, and (2)
portfolio risk, where the security's risk is thought of as its contribution to a well
diversified portfolio.
In theory, only portfolio risk is important, but in practice both are
important.
Tables 81, 82, and 83 all pertain to standalone risk, after which we move
on to portfolio risk.
The standard deviation, σ, measures the variability of possible returns around the
mean, or expected return. We demonstrate its calculation in Table 82.
Excel paste functions are available for finding σ for an entire population (STDEVP) or a
sample from the population (STDEV), but not for finding σ with probabilities as in this case.
With probabilities you must go through the indicated calculations.
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