One of the simplest models of stock prices is geometric brownian motion (GBM). This model gives rise to the idea of characterising a stock's performance by its mean annual return and volatility - which most of us are very familiar with.

But do we have a good grasp of what different values for volatility feel like? How much volatility are we comfortable with in a stock?

From the model you can derive several *theoretical *results about things like the expected drawdowns and likely daily movements, etc.

However, sometimes it helps to just *see *the effects of different values for these parameters in *reality*.

So here is a simple simulator of GBM which can be run in Excel/OpenOffice/LibreOffice. I can't post attachments so it is in the form of a table which you should be able to copy and paste into a spreadsheet starting at cell A1. You will then need to make a couple of quick modifications and the simulator is ready to go. The instructions are at the end of this article.

If you do it right it should look like this:

Each time you press **F9 **the simulator creates a year's worth of stock prices based on the values you supply for **mean annual return**,** annual volatility** and **df**. We'll come to **df** later.

If you set the volatility to zero you will see that the prices simply rise smoothly to achieve the desired final return. In fact I have included a "drift" column which plots this result as well as the stock price as a guide to the "underlying" behaviour.

Now change the volatility to (say) 12 (for 12% annual volatility). This is similar to the volatility of a 20-stock diversified portfolio such as NAPS. You will see that the stock price follows the drift reasonably closely. Every time you press F9 the simulator creates a new set of random numbers and a different solution - but they all follow the drift reasonably closely.

*Low Volatility example*

Now try a value for volatility of 50. This is similar to **Fevertree Drinks ** (LON:FEVR) or **Burford Capital ** (LON:BUR) . The price will swing wildly away from the drift.…

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