Common Sense 101: The difference between probability and possibility

Published: November 4, 2016 at 9:28 am

Last Updated on December 18, 2021 at 10:55 pm

The notion of risk and reward is key to any investment plan. However, our understanding and expectation of risk and reward are often clouded by an inability to distinguish between probability and possibility. Here are a couple of examples that hopefully might bring out the difference.

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Can stock investors beat mutual fund managers?

First, does this question even make sense? Do people want guarantees before they start investing in stocks instead of mutual funds?!

It boils down to a matter of interest. I like something, I do it. I don’t, I don’t. Some of my choices can fail (if I choose to find out whether it did or not!) relative to other methods, but as long as I had fun doing it, and if my purpose is achieved, does it even matter?!

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Therefore, although the question does not make much sense, it can be used as an example to distinguish between probability and possibility.

Can stock investors beat mutual fund managers? A big resounding YES. As is the answer to “Can we reach the top of mount Everest?”. (No, I am not saying it is that hard, hang on).

As is the answer to “Can we reach the top of mount Everest?”. No, I am not saying beating funds is that hard, that would be a disrespect to the mountaineers. Hang on.

YES,  because the question is referring to the possibility of an event happening. So the answer is, “Yes, it is possible”.

Of course, this is extremely unhelpful. A better question to ask is,

“What does it take to beat an equity mutual fund manager?”.

Since something is possible, a set of steps to accomplish it can be stated. No issues there.

This does not mean the task is easy or hard. This does not mean, anyone who follows these instructions will achieve success and others would fail.

The answer to “Can stock investors beat mutual fund managers?” is not an off the cuff,

  • “it is hard”;
  • “it is easy”;
  • “I did it (and therefore no one can!)”;
  • “I could not do it (and therefore no one can!)” etc..

Simply because one requires data to gauge hard or easy. What data?

A study of, say about 100 (or more) stock investors vs a equal number of mutual fund investors who buy on the same days for a long enough period of time (say ten years) and repeat this experiment at least a few times over different time periods to calculate the probability of success or failure.

Even then, it is the probability of past performance! Even the choice of mutual funds to compare should not have biases (an index can be used). Even then all we can do is to state the result of the above study, assuming it is available and assuming the investors chosen had an IQ that was neither too low nor too high and reasonable common sense.

That sounds awful does it not?! Who will do such a study? Is it not easier to extrapolate our lone experience or the experience of a couple of people we know and make statements like, “it is unlikely”, “it is likely” etc? Many, including me, are guilty of such extrapolations.

Probability is the result of an unbiased and relevant study. Not a lazy extrapolation.

An unbiased study with statistically significant data.

I know, I know, it is academic nonsense that many disrespect without even a clue about what it stands for.

Assuming such a study is available for the above situation, should I extrapolate the results and decide to invest or not invest in direct equity? Possibly! With the understanding that

  1. Such results are often far from perfect and may not represent an actual probability – even if it is calculated like one!
  2. Even if the result shows 99% of investors could beat fund managers, it is possible that you could be part of the 1% who did not!

Just because an positive outcome has high proability, it does not exclude the possibility of a negative outcome! And vice versa. Example – LICs high claim settlement ratio!!

Related post: The difference between stock investing and mutual fund investing.

My point is, before worrying about an answer, we should first understand the difference between:

what is the probability that stocks investors can beat fund managers?

what is the possibility that stocks investors can beat fund managers

Since the questions are different, so are the answers!

Probability can only stem from  a big enough data set, not a single or few instances.

Possibility can be met with a simple (in this case) “yes, one can beat mutual fund returns with direct equity” even if a single investor* managed to beat a fund manager (over the same duration+dates).

* Many have, but since there is no systematic study associated, one cannot talk about a probability.

Even if no one managed to ascend mount Everest, it cannot technically be declared as impossible! It would just be very, very tough to climb. (More than 4000 people have managed to climb, but 280+ have died trying, so it is still very very tough!). Let me repeat, there is no correlation made between beating a fund manager and climbing mount Everest. That would be a disrespect to the mountaineers.


Probability can be high or low. Possibility is only a yes or no.

(hey it rhymes!)

A probability of 0% = impossible (black).

A probability of 100% = certain (white). The answer to the above question could be anything from 0% to 100% (shades of grey), depending on the decisions we make!!

Technically, there is no such thing as highly possible or very possible! That is just lack of data speaking! Either we have data or we don’t and stick to possibilities.

Here are two more example to highlight this point:

Can equity investing beat inflation?

If I were a salesman, I will say “most definitely” and move on. Unfortunately, I am not. So I am compelled to point out the difference between

Can equity investing beat inflation?  –> Yes, it is possible.

Will equity investing beat inflation? –> Yes, it is probable (by how much is grey area!!).

For both answers, the following rejoinder can be added:

Past performance reveals plenty of occasions when equity returns were less than fixed income returns and therefore active risk management is essential.

Is health insurance necessary?

Some people believe that health insurance is an expense and not very useful because the probability of a big-ticket hospital expense is low and that they can handle common hospitalisations without insurance.  This is again a confusion between probability and possibility.

Other examples

  • Will a SIP work?
  • Will going to a financial planner fetch me better returns?
  • Will my claim not be rejected if I buy from LIC?
  • Will DIY work? (like they say, everyone can DIY, but not everyone should!!). Read more: Reader Story: Are you sure you can be a DIY investor?
  • Equity funds returns 25% in the past and therefore history will repeat itself.
  • Why should I not invest in 100% equity since it will anyway give better returns in the long run?
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