Hi friends!
Generally we have natural
inclination towards arithmetic mean or simple average. Whenever we try to
calculate (or we are asked to calculate) average or mean for any data, many of
us with out second thought go for simple average. This is perfectly fine in
cases like; av. marks of students, av. height of group etc. but generally in
world of finance especially where return on investment is involved, calculating
simple average of return on investment for some number of years is full of
error and gives wrong perception about return rate on investment.
A good example will be worth
thousand words!
You bought 1 share of ABC Ltd
at Rs.100/- in year 2009. The share price for next 3 years;
Year Price
Return(%)
2009 100 -
2010 115 15% = (115-100)/100 * 100
2011 69 -40% = (69-115)/115 * 100
2012 89.7 30% =( 89.7-69)/69 * 100
Now if your friend asked you,
hey what’s average annual return rate on the above investment you made? Without thinking, you say well average annual
return on my investment is 1.66% due to simple average formula =(15 + (-40) +
30) /3.
Is this true average annual
rate of return or is this correct methodology of calculating av. annual rate of
return?
Friends just pause & think….if you have
invested Rs.100/- in 2009 & in 2012 you are getting only Rs.89.7, have you
actually earned anything for last 3 years time period on your investment? Of
course NOT, current price (Rs.89.7) is lower than what you invested (Rs.100) at
the start. So how can you ever have positive av. annual rate of return on your
investment?
That’s where the beauty of
Geometric mean/average or compound average of return comes to mesmerize us into
the world of finance.
If we calculate Geometric
mean/average for the above example;
Geometric mean = (1.15 * 0.6 * 1.3) ^1/3 , So by
solving, geometric or compound average annual rate of return on your investment
comes to negative 3.55% (-3.55%).
Note: Geometric mean takes
only positive numbers for calculation purpose so, what we do generally is add 1
to every yearly return so that we get away with negative number & after
calculating Geometric average deduct 1 from geometric average & multiply by
100 to get percentage(%).
The above geometric average
rate is more realistic as it is negative (which it should be as you are down
from what you invested at the start) & it takes into effect of compounding
which is very crucial in world of finance & price volatility gets reflected
in geometric average.
Geometric/compound average is
better because;
1.
It reflects more
economic reality in av. returns rate.
2.
Takes return
volatility into consideration.
3.
It is compounding
rate.
Always understand, whether
you are finance/investment professional or just any one, it is always more
truthful & realistic to present av. annual rate of return on investment to client
or anyone in terms of geometric average
So next time when anybody
says to you that this investment is good as it earned very good av. Rate of
return & you should invest, ask if that is compounding average or just
simple average (many times even
professional does not know & just blindly follows what is given) or better
if you have the details calculate compounding rate yourself. When you are
thinking to invent for more than one year & when your are looking for track
record of some investment, av. rate of return will surely come into picture.
Friends! Just by slight
change in our thinking & bit of better understanding you can see the
change. Always go for (or ask for) compound average while calculating average
rate of return on investment as it will not fool you like simple average.
Feel free to share any
suggestion/question/doubt. Thanks!
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