Do you know your uncle’s shoe size?
That’s what I was asked when I wanted to understand the “bell curve.”
What would your answer be to that question?
You might get confused with counter-questions like:
- Which uncle are you talking about?
- How would I know my uncle’s shoe size?
But surprisingly, my professor answered the question by the basic principle of the “bell curve.”
How does a Bell Curve find my uncle’s shoe size?
He asked me further two more questions,
- What is the average height of an Indian? I answered 5.5 Feet.
- So, there is a high probability that your uncle’s height falls within the range of 5.5 feet, right? I said yes. –
And there is the answer, the shoe size of my uncle can fall under the average shoe size of a 5.5-foot man.
I, being curious, asked, “But what if my uncle’s height is 6 feet?”
The professor responds, “Yes, that’s possible, but the probability of your uncle being 6 feet tall is relatively low, only about a 13.6% chance.”
Understanding the Bell Curve Graphically
To illustrate this concept further, the professor unrolls a paper and draws a bell curve. Here’s how it works:
Imagine your uncle falls into the age range of 40-50 years old. The professor explains that if we were to measure the heights of all Indians in this age group, we’d find that most of them have an average height of 5.5 feet.
The center of the bell curve corresponds to the average height of 5.5 feet. The curve peaks at this point because the majority of people fall into this height range.
He then introduced the concept of standard deviation (SD).
For instance, if we consider a deviation of 0.5 feet from the average (5.5 feet), we have:
- People shorter than 5.5 feet by 0.5 feet are marked at the “-1 point” on the curve (representing 5 feet tall).
- Taller people, those who are 0.5 feet taller than 5.5 feet, are marked at the “+1 point” on the curve (representing 6 feet tall).
- Now I know the people who fall close to the average height of 5.5 feet are about 68.20%.
- And people who deviate from the average, either higher or lower are about 26.12%
- People who deviate by larger size., which means rarely short or rarely tall are just about 4.2%
How to use this concept in Mutual Fund schemes?
As we know we can process all the data on the heights of Indian men. We can replace the data with “Returns from mutual funds”.
What will we find if we replace the data with a mutual fund scheme?
We can find the “Average Return” of the scheme first [5.5 Feet]. Then we can find the “How much it can deviate from the ‘average return’, on both sides -ve and +ve. That we can name as -1 Standard Deviation and +1 Standard Deviation.
For example;
If the A fund has an average return of 10% historically, and it went up to 15% in some periods and gave 5% in some periods. My standard deviation is 5%. That means, at any point in time this scheme can give me a only 5% return or a maximum of 15% return if invested.
End of Part 1;
We discuss – How to compare funds based on Standard Deviation in Part 2