Wednesday, September 18, 2013

Calculating av. rate of return: Geometric mean is the king!

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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