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# 3.2.1 Understanding portfolio theory

The last section sets out the benefit of diversification when investing. You’ll now take this analysis further forward, by looking at how a portfolio can be constructed. This is called portfolio theory.

The animation introduces a key statistical concept which is important in investment management: ‘standard deviation’. This is a measure of the dispersion, or spread, of data around an average or mean number. The greater the standard deviation, the more varied or dispersed are the data around the average. The risk/return positions C & D shown at the end of this section’s animation will be explored further in the next section.

Interactive feature not available in single page view (see it in standard view).

Standard deviation can be calculated by following the steps below:

1. Obtain the average (or mean) of all the (daily) share prices over the period in question. To do this, add up all the daily recordings of the share price and divide by the number of those daily recordings.
2. For each share price, work out its difference from this mean and then square this difference. So if the difference is 4 pence, the square would be 16 and so on.
3. Once you have done the second step for all the share prices, add up all these ‘squares’.
4. Divide the total you get in the third step by the total number of share prices. So if the total of the ‘squares’ is 10000 and the number of share price recordings is 100, you end up with 10000/100 = 100.
5. Find the square root of the outcome from the fourth step. So if the outcome from the fourth step is 100, then the square root of this is 10 pence. This is the Standard deviation and it can either be expressed as an absolute number (i.e. 10 pence) or as a % of the mean share price.

The statistical meaning of a (that is, one) standard deviation is that it captures 68% of the individual recorded prices. So if the standard deviation in the example above is 10 pence, then 68% of the share prices are within 10 pence of the average (or mean) share price (either higher or lower).

Thsi information can also be downloaded in the supporting document How to calculate standard deviation and what does it mean? [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]