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Portfolio Evaluation
Rate of Return =
Amount you made
Amount you invested
Example: Buy a stock for $100 and at end of year it is worth $106, plus you received a $2
dividend.
Rate of Return = (106 – 100) + 2
=
8
=
8%
100
100
DollarWeighted Returns
At the end of the first year, you buy another share. At the end of the second year, you
receive another $2 dividend (per share) and the share price is $110.
100
____________106; +2
_________+4; +220
0
1
2
Find the Internal Rate of Return (IRR) to get the dollarweighted rate of return
0 =
100
–
106
+
2
+
4
+
220
=
100
–
104
+
224
1+r
1+r
(1+r)
2
(1+r)
2
1+r
(1+r)
2
r = 6.442%
It is dollarweighted because the second year (when more dollars are invested) gets more
weighting than the first year.
Timeweighted Returns
We already saw that the return in the first year was 8%. Find the return in the second year
in the same manner.
(220 – 212) + 4
=
12
=
5.66%
212
212
Now, average together the two returns:
8%
+
5.66%
=
6.83%
2
In this example, since the second year did worse than the first year, and there were more
dollars invested in the second year, the dollarweighted average is lower than the time
1
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View Full Document weighted average. If you did better in the time period when you had more money
invested, the dollarweighted average would be higher.
Most money managers are evaluated using timeweighted averages rather than dollar
weighted averages, because the amount of money they manage is generally not under
their control.
Arithmetic Averages vs. Geometric Averages
We covered this briefly in FINC 654.
Geometric Average Return – The compounded annual
return earned by an investor who
bought the security and held it for ‘T’ years. This is equivalent to earning this return each
year and reinvesting the earnings at the end of each year.
Geometric Average Return =
[Π (1+R
t
)]
1/T
– 1
Note that [Π (1+R
t
)] is often referred to as the buyandhold return.
Example: Let’s take the hypothetical returns for Freeman Corp.
2001
.05
2002
.09
2003
.12
2004
.20
f8e5
R
=
.05 + .09  .12 + .20
=
.22
=
.055
= 5.5%
=
Arithmetic Average Return
4
4
Geometric Mean = [(1.05) (1.09) (0.88) (1.20)]
1/4
– 1
=
4.85%
Note that the geometric average is always less than or equal to the arithmetic average.
The difference between the two becomes greater; the more variance there is in the
returns.
A general rule is that the geometric average is approximately equal to the arithmetic
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This note was uploaded on 03/09/2008 for the course FINC 725 taught by Professor Hansen during the Spring '08 term at Tulane.
 Spring '08
 Hansen
 Valuation

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