Mathematics can be boring. To make things interesting for you, I am going to keep all the mathematical and statistical jargons aside and describe concept in a fun way.

We all love cricket. Today, let’s spend some time connecting cricket with mathematics.

Graph above shows bowling length of Bumrah in the 2019 cricket world cub. Now let me ask you some questions:

What is the probability that next ball of Bumrah will be a short? It is 27%, quite an easy guess right?

Next, what is the probability that next ball will land either 2m or further away from the stumps? Easy, we just have to sum all earlier probabilities which is 27 + 24 + 15 + 16 = 82%. Other way to derive this probability would be 100 – 18 (probability of a full toss) = 82%.

What is the probability that the ball will land within 2m distance? Even easier, it is 18%.

Our mind finds it easier to associate probability with an outcome and that is why you did not have any difficulty answering above questions.

What if I tell you to reverse the direction? Can you tell me what would be the outcome, given the probability? This is where things start to become tricky. Lets give it a try.

Where will the ball land 18% of the time towards batsman’s end? It will be within 2m range.

Where will the ball land 34% of the time towards batsman’s end? It will be within 4m range.

We don’t really know where the next ball will land. It is highly random. In a way, we are trying to predict something which is highly unpredictable. Quite unintuitive right? If you are following me to this point, you are very close to understanding VaR. Remember, idea is to “predict outcome given the probability“.

This method of computing VaR is called historical method.

Ok, time for another example. This time, lets do some darting.

Imagine you have been throwing the dart all your morning. The board might look something like this:

You managed to hit the blue region quite a few times. Most of the time you landed in yellow, followed by green. Very few hits in the rose. If I had to draw a two-dimensional diagram of “no of occurrences” vs “distance from center”, it might look like this:

Now what if I ask you to compute the probability that your next dart lands in the rose? This can be calculated as “Region under rose divided by complete region under the bell curve”. That’s a pretty complex task for you and me. Fortunately some great mathematicians simplified this task for us by standardizing this calculation. It of course requires you to compute standard deviation but that is way more simple than calculating area in the graph. They created z-table that helps to quickly find the probability given the standard deviation.

Assuming z-table tells us that rose region is 5%, that means there is a 5% probability that your next dart will land in that region and 95% of the time you will be within green circumference. You see, we could “predict outcome given the probability“.

What if we assume rose region indicates losses and others indicate profitability? Your chance if being profitable is 95%. This is what the concept of VaR is. Given the probability, it tells whether you will incur losses or remain profitable based on the distribution of profit/loss data points gathered.

This method of computing VaR is called Parametric method.

VaR is much more than what I have described, but I also promised to not through any mathematical and statistical jargons. Though I could not keep the promise 100%. No matter how much we try, there is always a tail risk!