The average, also known as the arithmetic average or the mean of a set of values is a nice and simple number that is easy to calculate and interpret. However, it not valid under all circumstances and must be used with caution.
Given a set of numbers, we cannot blindly calculate the average – take the sum of the numbers and divided by the number of items in the set. I am guilty of doing this too.
What does the average represent?
Consider a set of students and the marks they have got. What does the average mark represent? The typical performance of the class? Yes, if most people got a mark close to the average? Then we could talk about above-average and below-average?
Yes, but under certain circumstances.
The bell curve
Most of us would have encountered the bell curve at some stage in life – eg. performance based increments. It is a probability distribution that has a peak and is symmetric on either side of the peak.
The peak represents the average and the fatness of the curve or the spread the standard deviation. These two quantities are derived from the probability distribution.
Yes, the arithmetic mean is a derived quantity. No one just came up with its formula.
The point is that the arithmetic mean is valid only for such symmetric distribution. So is the idea of standard distribution.
Mutual Fund Star Ratings are flawed!
Mutual fund risk and returns (or any security for that matter) are not normal. This automatically means quantities like alpha, beta, sharpe, Sortino etc are not valid. And in turn, means star ratings which use these metrics are not valid.
Mutual Fund Category Average
To elaborate the above point, consider the 5-year return distribution of multi-cap funds.
It should be immediately obvious that the distribution is not symmetric. Therefore a typical or average return is not of much use as it does not divide the distribution equally.
In fact, one should not even calculate the average in such a case.
Instead of the average one should use the median. This is a quantity that divides the distribution in half – 50% above the median and 50% below. For a bell curve, the average = median.
The median is also known as the second quartile. Any return above the median return falls in the top 50%.
One can also use the third quartile – top 75% of returns.
The whole point of this post is to suggest using the median and/or3rd quartile instead of the mean. The mean is “typically” invalid.
As mentioned above, I am guilty of using the category average returns too. I have now updated the mutual fund screener with median return instead of the mean.
Subscribe and join the freefincal Youtube community!
Connect with us on social media
- Twitter @freefincal
- Subscribe to our Youtube Videos
- Posts feed via: Feedburner
- We are also on Google PlusandPinterest
Do check out my books
You Can Be Rich Too with Goal-Based Investing
My first book is meant to help you ask the right questions, seek the right answers and since it comes with nine online calculators, you can also create customg solutions for your lifestye!Get it now. It is also available in Kindle format.Gamechanger: Forget Startups, Join Corporate & Still Live the Rich Life You Want
My second book is meant for young earners to get their basics right from day one! It will also help you travel to exotic places at low cost! Get it or gift it to a youngearnerThe ultimate guide to travel by Pranav Surya
This is a deep dive analysis into vacation planning, finding cheap flights, budget accommodation, what to do when travelling, how travelling slowly is better financially and psychologically with links to the web pages and hand-holding at every step. Get the pdf for ₹199 (instant download)Create a "from start to finish" financial plan with this free robo advisory software template
Free Apps for your Android Phone
All calculators from our book, “You can be Rich Too” are now available on Google Play!Install Financial Freedom App! (Google Play Store)
Install Freefincal Retirement Planner App! (Google Play Store)
Find out if you have enough to say "FU" to your employer (Google Play Store)
Well described. Using average has serious flaws in MF returns. It’s like saying if one leg is in the refrigerator and another is in the furnace, on an average a person is comfortable!
Yes … it can paint a picture which is quite different from reality and thus can very easily mislead.