Option Trading Blog

In part I, I wrote about the concept of VaR, Which is a tool to give us some metrics about our portfolio. This part will cover some (basic) calculations and instructions on how to compute the VaR. I’ll be adding also an excel file for your convenience, so feel free to go to the bottom of the post to download it.

Computing The VaR

A simple example

Suppose we have an initial investment of $10,000. We will want to compute that maximum amount we can lose with probability of 1%. Writing it in probability terms:

In the above equation, what does loss mean? If we have an initial investment of $10,000, and in the next period we have $9000, we have a loss of $1000. We want to connect the concept of loss with returns. Writing it in a more enlightening way:

From this we see that:

The Assumption of Normal Returns

Why did we need to express the Loss as the minus of return times the initial investment? because we are assuming returns are normally distributed, and hence we can manipulate the equation to give us something meaningful we can work with.

Note: If you want to avoid the computation presented here you can skip this part.

We recall from statistics, that if a random variable (Returns in our case), are normally distributed, then

has a standard normal distribution. In here, and denote the average and standard deviation of returns respectively.

This means that

Normalizing the last equation we get:

The last expression can be computed with excel! (assuming we have estimated the standard deviation and average)

The Excel File

I have added an excel file for your convenience. You can click here to download it.

In order to compute the VaR, you’ll have to put in the first column the probability you wish to calculate the maximum amount of loss you’d suffer.

In the second column, you’ll need to put either daily, weekly or monthly returns of your portfolio (if it’s a stock you could just put the historical prices of the stock) of the last 30 periods.

The last columns will tell you the average and standard deviation of the portfolio/stock. The VaR column is what is of interest to you and will report the maximum amount that could be lost under the given probability.