•
N actual observed returns are compounded
(1+R
1
) (1+R
2
) (1+R
3
)….. (1+R
N
)
•
The repeated geometric average return is
compounded N times
(1+R
GeomAvg
) (1+R
GeomAvg
) (1+R
GeomAvg
)….. (1+R
GeomAvg
)
= (1+R
GeomAvg
)
N
•
Set these 2 equal to one another
(1+R
GeomAvg
)
N
=(1+R
1
) (1+R
2
) (1+R
3
)….. (1+R
N
)
FIN 300 - Risk and Return Pt. 1
12

Geometric Average(or, Mean)
•
From the last slide
(1+R
GeomAvg
)
N
=(1+R
1
) (1+R
2
) (1+R
3
)….. (1+R
N
)
•
Solve for R
GeomAvg
Geometric Average Return
= [(1+R
1
) (1+R
2
) (1+R
3
)….. (1+R
N
)]
(1/N)
- 1
Aside: Note that the geometric average return will always be less
that the arithmetic average - unless the geometric average is
zero
FIN 300 - Risk and Return Pt. 1
13

Expected Return
•
Going back to our calculation of arithmetic return
–
Where we had assumed all returns as equally likely to
occur
•
What if we believe that some outcomes are more
likely than others
–
We will weigh the calculated average according to the
associated probability of each outcome
–
Thus the “expected return” is used when we calculate the
probability-weighted average of future possible outcomes
for an investment return
–
We will multiply each possible outcome by its associated
probability, before summing-up the terms
FIN 300 - Risk and Return Pt. 1
14

Expected Return Example
•
Given:
–
3 scenarios for earning an investment return over the next
year
•
Scenario 1:
–
Probability of 20% that you will earn a +20% return
•
Scenario 2:
–
Probability of 30% that you will earn a +5% return
•
Scenario 3:
–
Probability of 50% that you will earn a -10% return
(Note that the probabilities must sum to 100%!)
–
What is the
expected return
for the investment?
FIN 300 - Risk and Return Pt. 1
15

Expected Return Example
•
We multiply each return by its associated probability
•
And, then sum those terms up, to get the “expected” return
0.20 x 20% = 4%
0.30 x 5% = 1.5%
0.50 x -10% = -5%
Expected Return = 4% + 1.5% + (-5%) = 0.5%
•
Note that the
expected return
is not necessarily one of the
possible scenarios – that is okay, since the expected return is
nothing other than the
probability-weighted average
outcome
FIN 300 - Risk and Return Pt. 1
16

Expected Return
•
Expected return
is the
probability-weighted average
return
•
The outcomes have a probability distribution
–
Each of the outcomes is not (necessarily) equally likely
•
If repeated investments are made (each time having
one of the possible outcomes – think “spinning the
roulette wheel”), then the expected return may be
thought of as the average outcome over many
repeated investment opportunities
FIN 300 - Risk and Return Pt. 1
17

Expected Return Formula
N possible outcomes
=
•
FIN 300 - Risk and Return Pt. 1
18

Return vs. Risk
•
Any rational investor would prefer investments
with a higher return
•
However, there is a tradeoff
•
Generally speaking, investments offering a
higher return also come with a higher level of
risk
•
As investors, we have to balance the desire of
more return vs. the concern of taking on more
risk
FIN 300 - Risk and Return Pt. 1
19

Return vs. Risk
•
If I desire the utmost in safety in an investment, I
will put my money in an FDIC insured bank account
or T-Bills
–
However, I would expect to get very little return
•
If I am aiming for a higher investment return, I
might invest in the stock market
–

#### You've reached the end of your free preview.

Want to read all 45 pages?

- Fall '08
- Olander
- Finance, Standard Deviation, Corporate Finance, Return Pt.