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! 

Return on Investment : Mistakes to avoid

Hi Folks !

I have come across many times that, lot of people (educated & uneducated and even people with finance back ground - this is the motivation behind writing this article) in society get so much awfully surprised by word “returns on investment” and completely get carried away with out putting return on investment in context. I have one real example to share with you; (many of you already do it in right way- Great! & help spread awareness to those who don’t)

One of my relative came to me one day & said, “you know what! I earned cool 30% on particular investment!”  Another cousin seating next to me was like wow! Tell me I also want to invest.

A classic example of taking return of investment without any context & jump into investing.

What is missing in above statement “I earned 30% on particular investment”? From my perspective two things at the least; (there can be many more specially inflation-adjusted returns but these two comparison bench marks are never going to go away) 1.Time period 2. Risk involved.

Let me just ask you one simple question if your friend comes to you & say, “ I earned 40% returns on asset-A & I earned just 14% on asset –B, isn’t asset-A great asset?”  What is your answer?

My answer is I can not say whether asset-A is better as compared to asset-B, before I know in what time period return is generated & what was risk involved. The key point is with out knowing how long (time period) the investment was made & what was the risk in it, no body can ever say it is good or bad investment.

 Next time whoever you are facing, be it elder person from your family, friend, investment/mutual fund professionals, your professor etc. with the above question or asking you to invest with high return on investment asset check out on Time period & Risk involved first.

 In general terms here, risk means volatility or movement in the price of asset in particular time frame. So, in simple words, higher the volatility higher the risk. (Risk/volatility stuff is ugly for getting into details so I am just sticking to basic understanding here)

Now let me add in the above statement, “I earned 40% returns on asset-A & I earned just 14% on asset –B. I got 40% on asset-A after 8 years with 56% annual volatility(risk), while I got 14% on asset-B in 2 years with 5% annual volatility(risk).” Now what is your answer- which asset is better?

Let’s do bit of Maths;

1. To compare different time period assets we have to calculate annualized rate of return. So that we can compare on same time-scale.
2. To compare different risk-involved assets, we divide time adjusted rate of returns by volatility (risk). So, that we can compare on same risk-scale.

Asset-A

Annualized rate of return for 40% return over 8 year is 4.3%.( {(1+0.4)^ (1/8)}-1*100=4.3%)

So, effective after risk-adjusted rate of return (for taking 1% of risk you get this much % of returns) = 4.3 % / 56% = 0.076%

Asset-B

Annualized rate of return for 14% return over 2 year is 6.77 %.( {(1+0.14)^ (1/2)}-1*100=6.77%)

So, effective after risk-adjusted rate of return (for taking 1 % of risk you get this much % of returns) =  6.77 % / 5% = 1.35%

So, now when you compare for time period adjusted (as time period is different in both assets) & risk adjusted returns of assets A & asset-B, certainly asset-B is better as you get 1.35% return with compare to 0.076% return of asset-A, in the above context.

Friends! You are the king now. Never take returns on investment in absolute way from any one. We all make investments in different ways & in different phases of life, so next time any one says this is cool investment due to whatever return on investment, straight away ask for time period & risk involved in it or better calculate yourself the time & risk adjusted return & then only decide or make comment.

Hope by better thinking/understanding on the above stuff we can make our day to day life bit better!

Feel free to share any suggestion/question/doubt. Thanks!