0
Tutorial 3 : Risk and Return I
Conducted by : Mr Chong Lock Kuah, CFA

1
Key Points
•
The average rate of return on a single risky asset from historical
data is :
•
The Geometric average return or geometric mean rate of return,
(GM) on a single risky asset from historical data is :
n
R
......
R
R
R
n
R
R
n
3
2
1
n
1
t
t
1
1/n
n
3
2
1
)
R
)
.....
(1
R
)(1
R
)(1
R
(1
GM

2
Which to Use?
Consider the following investment :
Year
Beginning Value
Ending Value
Return (%)
1
$50.0
$100.0
100%
2
$100.0
$50.0
- 50%
We can calculate the arithmetic mean rate of return (AM) as follows :
AM
=
1.0 + (
–
0.5)
2
=
0.25
= 25%
Note that we started with $50 and ended with exactly the same amount
at the end of 2 years.
The investment brought no change in wealth and
therefore no return.
Yet, the AM computes a mean return of 25% !

3
Cont’d
From the previous data
Year
Beginning Value
Ending Value
Return (%)
1
$50.0
$100.0
100%
2
$100.0
$50.0
- 50%
We can calculate the geometric
mean rate of return (GM) as follows :
GM = { [ 1 + r
1
)( 1 + r
2
) …….. ]
1/n
–
1 } x 100
GM = { [ 1 + 1 )( 1
–
0.5 ) ]
1/2
–
1 } x 100
=
0
Note that GM accurately measures that the investment has not
yielded any return.
So which is correct, 0 percent or 25 percent?
Both are correct :
They just answer different questions.