calculation HPR AND AM, GM

1. Investment and Portfolio Management
Presentation
7/11/2017

2. Example
Question: You are reviewing an investment with the following
price history as of January 1st each year.
 Calculate:
 The HPR for the entire period
 The annual HPRs
 The Arithmetic mean of the annual HPRs
 The Geometric mean of the annual HPRs
2001 2001 2003 2004 2005 2006 2007 2008
$ 100 $115 $118 $118 $112 $120 $122 $121
7/11/2017

3. N p0 p1 HPR HPY percentile
2001 100 115 1.15 0.15 15%
1002 115 118 1.026 0.026 2.6%
2003 118 118 1 0 0%
2004 118 112 0.94 - 0.06 - 6%
2005 112 120 1.07 0.07 7%
2006 120 122 1.01 0.01 1%
2007 122 121 0.99 - 0.01 - 1%
2008 121 -
1.186 0.186
HPR = Holding period return
P0 = Beginning value Investment
P1 = Ending value investment
N = Number of years the investment is held
7/11/2017

4. 𝐻𝑃𝑅 =
121
100
= 1.21 − 1 = 0.21 𝑖𝑡 𝑚𝑒𝑎𝑛𝑠 21%
AM =
0.15+0.026+0+(−0.06)+0.7+0.01+(−0.01)
7
= 0.026 𝑖𝑡 𝑚𝑒𝑎𝑛𝑠 2.6%
HPR calculation HPR =
𝑬𝑽
𝑩𝑽
− 𝟏
1 2 ... NR R R
AM
N
  

AM = Arithmetic Mean
7/11/2017

5. 𝐆𝐌 = (𝟏. 𝟏𝟓)(𝟏. 𝟎𝟐𝟔)(𝟏)(𝟎. 𝟗𝟒)(𝟏. 𝟎𝟕)(𝟏. 𝟎𝟏)(𝟎. 𝟗𝟗) 𝟏
𝟕
1.186 𝟏
𝟕 = 𝟏.𝟎𝟐𝟒 −𝟏= 𝟎.𝟎𝟐𝟒 𝒊𝒕 𝒎𝒆𝒂𝒏𝒔 𝟐.𝟒%
    
1
1 21 1 ... 1 1N
NGM R R R      
Geometric Mean
7/11/2017

6. 7/11/2017