𝐸𝐴𝑝𝑝𝐴𝑝𝑖𝑝𝑖𝑅𝑦
𝑝𝑜
𝑅ℎ𝐴
𝑖
𝑡ℎ
𝐴𝐴𝑅𝑅𝐴𝑅
𝑅
𝑖
=
𝑖
𝑡ℎ
𝐴𝐴𝑅𝑅𝐴𝑅
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
–
However, I would have to be willing to bear
significantly more risk
•
Much of what we do in finance centers on how to
make our investment choices and negotiate the
tradeoff between risk and return
FIN 300 - Risk and Return Pt. 1
20

Measuring Risk
•
In finance, we use statistical measures to
measure risk and return
•
We use the concept of mean to describe the
return
•
Now, we will use variance and standard
deviation to measure the risk, or volatility, of
investment returns
FIN 300 - Risk and Return Pt. 1
21

Statistics Formulas
𝑀𝐴𝐴𝑅
=
𝜇
=
𝑅
�
=
1
𝑁
� 𝑅
𝑖
𝑁
𝑖=1
𝑃𝐴𝐴𝑖𝐴𝑅𝑚𝐴
=
𝜎
2
=
1
𝑁−1
∑
𝑅
𝑖
− 𝑅
�
2
𝑁
𝑖=1
𝑆𝑅𝐴𝑅𝐸𝐴𝐴𝐸
𝐷𝐴𝐴𝑖𝐴𝑅𝑖𝑝𝑅
=
𝜎
=
𝜎
2
=
𝑃𝐴𝐴𝑖𝐴𝑅𝑚𝐴
The above formulas are known as the
sample mean
,
sample
variance
, and
sample standard deviation
Also, these formulas assume the outcomes to be equally weighted
We typically use such formulas to measure (actual observed)
historical returns
FIN 300 - Risk and Return Pt. 1
22
Returns are equally weighted

Standard Deviation and Variance with
Probabilities
•
Let’s return to our previous example, where we
calculated the expected (or, probability-weighted
average) return
•
Now, let’s calculate the variance and standard
deviation for that set of probable scenarios
FIN 300 - Risk and Return Pt. 1
23

Standard Deviation w/Probabilities
•
Scenario 1: 20% probability earning a +20% return
•
Scenario 2: 30% probability earning a +5% return
•
Scenario 3: 50% probability of earning a -10% return
Steps to obtain the standard deviation:
1)
Calculate the
expected (mean) return
as we did before
2)
For each scenario, subtract the mean from the scenario
return (this gives us the “
deviation
” for each scenario)
3)
For each scenario, square the deviation (this gives us the
“
squared deviation
” for each scenario)
4)
Now, calculate the
probability-weighted average of the
“squared deviations”
(this gives us the variance)
5)
Finally, take the square root to obtain the
standard
deviation
!

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