

Money
& Banking MGT411
VU
Lesson
11
MEASURING
RISK
Measuring
Risk
Variance
and Standard Deviation
Value
at Risk (VAR)
Risk
Aversion & Risk Premium
Measuring
Risk
Most
of us have an intuitive sense for
risk and its
measurement;
The
wider the range of outcomes the greater the
risk
A
financial instrument with no
risk at all is a riskfree
investment or a riskfree
asset;
Its
future value is known with
certainty and
Its
return is the riskfree rate of
return
If
the riskfree return is 5 percent, a
$1000 riskfree investment
will pay $1050, its
expected
value,
with certainty.
If
there is a chance that the payoff
will be either more or less
than $1050, the investment
is
risky.
We
can measure risk by measuring the
spread among an investment's possible
outcomes. There
are
two measures that can be
used:
Variance
and Standard Deviation
Measure
of spread
Value
at Risk (VAR)
Measure
of riskiness of worst case
Variance
The
variance is defined as the probability
weighted average of the squared
deviations of the
possible
outcomes from their expected
value
To
calculate the variance of an investment,
following steps are
involved:
Compute
expected value
Subtract
expected value from each possible
payoff
Square
each result
Multiply
by its probability
Add
up the results
Compute
the expected value:
($1400
x ½) + ($700 x ½) = $1050.
Subtract
this from each of the
possible payoffs:
$1400$1050=
$350
$700$1050=
$350
Square
each of the
results:
$3502 =
122,500(dollars)2
and
($350)2 =
122,500(dollars)2
Multiply
each result times its
probability and adds up the
results:
½
[122,500(dollars)2]
+ ½ [122,500(dollars)2]
=
122,500(dollars)2
34
Money
& Banking MGT411
VU
More
compactly;
Variance
= ½($1400$1050)2 +
½($700$1050)2
=
122,500(dollars)2
Standard
Deviation
The
standard deviation is the square
root of the variance,
or:
Standard
Deviation (case 1)
=$350
Standard
Deviation (case 2)
=$528
The
greater the standard deviation, the
higher the risk
It
more useful because it is measured in the
same units as the payoffs
(that is, dollars and
not
squared
dollars)
The
standard deviation can then
also be converted into a
percentage of the initial
investment,
providing
a baseline against which we can measure
the risk of alternative
investments
Given
a choice between two investments with the
same expected payoff, most
people would
choose
the one with the lower
standard deviation because it
would have less risk
Value
at Risk
Sometimes
we are less concerned with
the spread of possible outcomes than we
are with the
value
of the worst outcome.
To
assess this sort of risk we
use a concept called "value
at risk."
Value
at risk measures risk at the
maximum potential
loss
Risk
Aversion
Most
people don't like risk and
will pay to avoid it;
most of us are risk
averse
A
riskaverse investor will always
prefer an investment with a
certain return to one with
the
same
expected return, but any amount of
uncertainty.
Buying
insurance is paying someone to
take our risks, so if someone
wants us to take on risk
we
must
be paid to do so
Risk
Premium
The
riskier an investment the higher
the compensation that investors require
for holding it
the
higher the risk
premium
Riskier
investments must have higher expected
returns
There
is a tradeoff between risk and expected
return;
You
can't get a high return
without taking considerable
risk.
35
Money
& Banking MGT411
VU
Figure:
The Tradeoff between Risk
and Expected
Return
Higher
Risk=Higher Expected Return
The
higher the risk, the
higher
the
expected return. The
risk
Risk
Premium
premium
equals the expected
return
on the risky investment
minus
the riskfree return.
Risk
Free Return
Risk
36
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