In 'Simple Investing' you learnt about diversification - the act of spreading your savings among a variety of assets to reduce risk. There are good and not-so-good ways of doing this.

We explained that if you have enough money to buy two shares, and you want to diversify, it is intuitively sensible to buy two companies in different and unrelated industries. Two oil shares (Shell and BP, for example) will tend to go up and down together - responding to some common economic factors. But an oil share and a pharmaceutical (Shell and GlaxoSmithKline) will not. You could say that you get more diversification with Shell and Glaxo than you do with Shell and BP.

To expand on this we need two concepts: independence and correlation.

Independence

If the outcome of one event is not affected by the outcome of another the two events are independent. For example, the outcomes of two coin tosses are independent ("the coin does not remember"). If we have two shares we want their price movements to be independent.

The prices of oil and the share prices of BP and Shell are said to be 'positively correlated'. They tend to go up and down together. You don't want this in an investment portfolio. You are trying to smoothe out volatility, not reinforce it.

Correlation

You will get more diversification with Shell and Glaxo than you do with Shell and BP. The latter are said to be highly correlated: they tend to move about together. The former are not: they tend to move independently.

The correlation of Shell and BP arises from a common interest in the price of oil. In contrast Shell and Glaxo have different businesses. But they have some characteristics in common: for example they are both British companies. So they are not completely uncorrelated.

To diversify, we want shares that are as uncorrelated as possible - or, even better, negatively correlated (one price tends to go up when the other tends to go down). The benefits of diversification are diluted to the extent that investments are positively correlated.

It is possible to define the level of correlation between two variables to produce something called a correlation coefficient (CC), and there is some heavy mathematics to go with it. Completely independent variables have a CC of zero. Variables that move on lockstep have a CC of 1. Variables that always move in opposite directions have a CC of -1. Variables that sometimes move together and sometimes don’t have CCs between 1 and -1.

How much diversification?

So two shares are better than one. But how about three? five? 20? 500? The answer is that each additional share reduces the volatility of the portfolio, but most of the benefit comes with the first few extra shares then the benefits tail off quite quickly.

If considering shares alone, some advisers think that 10 carefully chosen shares are enough to build a well-diversified equity portfolio. Most advisers think that 20 are enough.

...and the implications for you are...

Once you have chosen equities as an asset class you will want to compare the costs (and work) of buying 20 different shares compared with the cost (and work) of investing in a few diversified trusts or funds.

If you chose the latter route there is no point in investing in a lot of different funds to obtain more diversification. Any single general fund already has as much diversification as you want. Incidentally that's why funds of funds do not necessarily add any value to pay for their higher costs.

Conclusion

Professors have won Nobel prizes for advances in the mathematics of diversification - called Portfolio Theory. So it can be a pretty heavy subject.

Just stay with the idea that you need to make your bets as uncorrelated as possible and as small as possible (so that you make more of them). But not so small that you give up your returns through diseconomies of scale. And diversification should not be used as a reason for plunging into fee-laden junk.

Here are some thoughts for diversifying your share portfolio:-

• spread your business sectors

• spread your country risk

• don't confine yourself to companies in businesses you know well. This is too restrictive. It might be good advice for stock-picking but that's not what you are doing here - you are trying to spread your bets.

We discuss diversifying among asset classes on the next page.