Page 79 - DMGT207_MANAGEMENT_OF_FINANCES

Management of Finances

Notes Illustration 8: Mr. Marin provides the following informations, from the same compute his
expected return and standard deviation and variance.

Events 1 2 3 4
Probability .20 .40 .30 .10
Return (%) –10 25 20 10

Solution:
1. Calculating the Mean Absolute Deviation:
Event Probability Return P × Return Deviation Probability × Probability ×
(%) Deviation Absolute Deviation
(1) (2) (3) (4) (5) (6) (7)
A .20 -10 -2.0 -25.0 -5.0 5.0
B .40 25 10.0 10.0 4.0 4.0
C .30 20 6.0 .0 1.5 1.5
D .10 10 -1.0 -5.0 -0.5 0.5
Expected 0.0 Average = 10.0
Return = 5.0 Absolute
Deviation

2. Calculating the Standard Deviation:

Event Probability Deviation Deviation squared Probability × Deviation
(1) (2) (3) (4) = (3) (5) = (2) x (4)
2
A .20 -25.0 625.0 125.0
B .40 10.0 100.0 40.0
C .30 5.0 25.0 7.5
D .10 -5.0 25.0 2.4
Variation = Weighted average squared deviation = 175.0
Standard Deviation = square root of variance = 13.2287

When an analyst predicts that a security will return 15% next year, he or she is presumably
stating something comparable to an expected value. If asked to express the uncertainty about the
outcome, he or she might reply that the odds are 2 out of 3 that the actual return will be within
10% of the estimate (i.e., 5% and 25%). The standard deviation is a formal measure of uncertainty,
or risk, expressed in this manner, just as the expected value is a formal measure of a "best guess"
estimate. Most analysts make such predictions directly, without explicitly assessing probabilities
and making the requisite computations.
Illustration 9: The possible returns and associated probabilities of Securities X and Y are given
below:
Security X Security Y
Probability Return (%) Probability Return (%)
0.05 6 0.10 5
0.15 10 0.20 8
0.40 15 0.30 12
0.25 18 0.25 15
0.10 20 0.10 18
0.05 24 0.05 20

Calculate the expected return and standard deviation of securities X and Y.
Solution:

Calculation of expected return and standard deviation of Security X:

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