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σ= n Σ ( Ri – R )2( Pi ) i=1 Standard Deviation σ, is a statistical
Deviation,
measure of the variability of a distribution
around its mean
around its mean.
It is the square root of variance.
Note, this is for a discrete distribution.
71 Certified Financial Controller CFC How to Determine the Expected
Return and Standard Deviation
Stock BW
BW
Ri
Pi
–0.15
0.10
–0.03
0.20
0.09
0.40
0.21
0.20
0.33
0.10 Sum
72 (Ri)(Pi)
–0.015
–0.006
0.036
0.042
0.033 1.00 0.090 Certified Financial Controller CFC 36 (Ri  R )2(Pi)
0.00576
0.00288
0.00000
0.00288
0.00576 0.01728 Determining Standard
Deviation (Risk Measure)
σ= n Σ ( Ri – R )2( Pi ) i=1 σ= .01728 σ = 0.1315 or 13.15%
13.15%
73 Certified Financial Controller CFC Coefficient of Variation
The ratio of the standard deviation of
ratio of the standard deviation of
mean
a distribution to the mean of that
distribution.
It is a measure of RELATIVE risk.
RELATIVE CV = σ/R
R
CV of BW = 0.1315 / 0.09 = 1.46
74 Certified Financial Controller CFC 37 Discrete versus. Continuous
Distributions
Discrete Continuous
0.035 0.4
0.35 0.03 0.3 0.025 0.25 0.02 0.2 0.015 0.15 0.01 0.1 0.005 0.05
–0.15 –0.03 75 9% 21% 33% 5 0 %
4 1 %
3 2 %
2 3 %
1 4 %
5 %
4%
13%
22%
31%
40%
49%
58%
67% 0 0 Certified Financial Controller CFC Continuous
Distribution Problem
• • 9.6%, –15.4%, 26.7%, –0.2%, 20.9%,
28.3%, –5.9%, 3.3%, 12.2%, 10.5% • 76 Assume that the following list represents the
that the following list represents the
continuous distribution of population returns
for a particular investment (even though
there are only 10 returns). Calculate the Expected Return and
Standard Deviation for the population.
Certified Financial Controller CFC 38 Risk Attitudes
Certainty Equivalent (CE) is the
Equivalent
is the
amount of cash someone would
require with certainty at a point in
time to make the individual
indifferent between that certain
indifferent between that certain
amount and an amount expected to
be received with risk at the same
point in time.
77 Certified Financial Controller CFC Risk Attitudes
Certainty equivalent > Expected value
equivalent Expected value
Risk Preference
Certainty equivalent = Expected value
Risk Indifference
Certainty equivalent < Expected value
Risk Aversion Most individuals are Risk Averse
Averse.
78 Certified Financial Controller CFC 39 Risk Attitude Example
You have the choice between (1) a guaranteed
have the choice between
guaranteed
dollar reward or (2) a coinflip gamble of
$100,000 (50% chance) or $0 (50% chance).
The expected value of the gamble is $50,000.
• Mary requires a guaranteed $25,000, or more, to
call off the gamble. • Raleigh is just as happy to take $50,000 or take
the risky gamble. • Shannon requires at least $52,000 to call off the
gamble. 79 Certified Financial Controller CFC Risk Attitude Example
What are the Risk Attitude tendencies of each?
are the Risk Attitude tendencies of each?
Mary shows “risk aversion” because her
“certainty equivalent” < the expected value of
the gamble.
.
Raleigh exhibits “risk indifference” because her
“certainty equivalent” equals the expected value
equivalent equals the expected value
of the gamble.
.
Shannon reveals a “risk preference” because her
“certainty equivalent” > the expec...
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This note was uploaded on 05/28/2013 for the course FINANCE economy taught by Professor Nill during the Fall '12 term at Bronx School Of Law And Finance.
 Fall '12
 nill
 Time Value Of Money

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