Risk and Risk Aversion
BKM Chapter 6 – part 1
•
What is risk?
•
How do we measure risk?
•
The tradeoff between risk and return
•
Riskreturn assumptions of portfolio theory
•
Utility functions and indifference curves
Risk
Q) What is risk?
A)
Two definitions, both correct
:
Risk means more things can happen than will happen
 Elroy Dimson, a famous finance professor
My momma always said, “Life is like a box of chocolates. You never know
what you’ll get next.”
 Forrest Gump
Risk and Return: The tradeoff
Consider the following choice facing an investor with $100,000 to invest. She
has the choice of investing the $100,000 in a
riskfree
investment or a
risky
investment.
Possible payoffs of both investments are:
Riskfree investment
100,000
105,000
Risky
investment
150,000
100,000
80,000
The (simple) return on the riskfree investment is:
105,000
1
100,000
f
r
=

= 5%
2
The
expected return
on the risky investment is:
150,000
80,000
( )
0.6
1
0.4
1
22%
100,000
100,000
50%
20%
E r
�
�
�
�
=

+

=
�
�
�
�
�
�
�
�

%
1 442 4 43
1 442 4 43
Which investment should our investor choose? To try and make a decision, we
proceed in three steps:
Step 1
: Calculate the
risk premium
or
expected excess return
on the risky
investment.
Definition
: The
risk premium
on any risky asset is its expected return
over and above the riskfree rate:
(
)
(
)
( )
e
f
f
E r
E r
r
E r
r
=

=

%
%
%

For our risky investment,
(
)
(
)
0.6(50%
5%)
0.4( 20%
5%)
(
)
= 22%5% =17%
e
f
f
E r
E r
r
E r
r
=

=

+


=

%
%
%
Step 2
: Calculate the
risk
of the risky investment. It is traditional to use
variance
or
standard deviation
of an investment’s return as a measure of its
risk.

The variance of the riskfree investment is zero

The variance of the risky investment is:
2
2
2
( )
0.6 (0.50
0.22)
0.4 ( 0.20
0.22)
r
σ
�
�
�
�
=

+


=
�
�
�
�
%
0.1176
and, the standard deviation is
( )
0.1176
34.29%
r
σ
=
=
%
Step 3
: We need to decide whether the 17% risk premium is commensurate
with the 34.29% risk. i.e. we need a way of telling us whether 17% is adequate
compensation for this risk, more than adequate or less than adequate.
3

This is NOT an easy question to answer; the whole field of
asset pricing
has developed (and continues to expand) to answer this one question.
Asset
Pricing Models
like the CAPM and the APT are attempts to answer this
question.

Before we jump into asset pricing models, we need to learn portfolio
theory, and the first piece of this theory has to do with investors’ attitudes
towards risk. i.e. we need to make some assumptions regarding investors.