Module 6

What is a portfolio?

Standard Deviation

Standard deviation is a measure of how volatile a stock is, compared to its average return.

Highly volatile stocks will deviate away from their average return often, while less volatile stocks will move only slightly away from their average return.

For example, as seen below, if a highly volatile stock has an average annual return of 20%, then it may deliver returns as low as 2% and as high as 40%. On the other hand, a less volatile stock may deliver returns as high as 25% and as low as 15%.  

Standard deviation is measured as a percentage and indicates how far a stock moves from its average return over time. A higher standard deviation % means that the stock deviates greatly from the average. 

Stocks that have a higher standard deviation are seen as being more risky, as they are less predictable. This opposite is true for stocks with a lower standard deviation.

Calculating standard deviation

Being able to calculate standard deviation will help you to understand how risky a stock may be.

Before starting to calculate anything, you need to gather the historic stock prices of a particular stock, over the last 5 years. This information is available on Yahoo Finance, where you can download it as an excel file.

It is best to get monthly stock prices over a period of the last 5 years.

Then, you need to calculate the percentage change between each pairing.

This is done by using the following formula.

C = \frac{x_2 - x_1}{x_1}

For example, if a stock is price at $100 in January 2022 and $120 in February 2022, the calculation would be: ($120 – $100) ÷ $100 =  20%.

You need to do this calculation for each pairing of stock prices, in chronological order.

Once you have done that, you need to find the average return. You do that by adding all percentage changes together and dividing it by the number of percentages.

For example: (5% + 10% + 5% + 3%) ÷ 4 = 5.75%.

In order to calculate standard deviation, the following formula can be used.

\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}

It may look complicated but it is not too difficult.

The first step is to subtract the average return from each individual percentage change, then you need to square the sum of that.

Next, after squaring, you need to add all of the percentages together and divide it by the number of percentages.

This number is then square rooted to find the standard deviation.  

Weaknesses of standard deviation

Standard deviation is a useful method to get an understanding of the risk of a stock. However, it has its weaknesses.

Firstly, the standard deviation calculation relies on historic information, which means that it may not be useful when it comes to examining what will happen in the future.

As a result, standard deviation needs to be used in combination with other methods.

In addition, the outcome of the standard deviation formula changes depending on the period of time chosen by the investor.

At one period of time, a stock may be more volatile than it is in another. Therefore, standard deviation may give you the wrong impression about the risk profile of a stock.

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