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# Mean streets

We concluded last week&#39s article by starting to look at the concept of volatility in either the unit price of an investment or in its rate of growth.

This concept, rather than being simply a vague principle, can be quantified using the mathematical measurement of one standard deviation. Broadly, this measures how far and how often the price or rate of increase (or decrease) of a particular investment has deviated away from its mean over a given historical period of time.

You may remember from last week&#39s article that the one standard deviation measurement for an investment tells us how far the price or rate of increase has moved away from the average 70 per cent of the time.

Let me quickly give a couple of examples, first using investment values and then investment growth rates.

The Veritable equity fund&#39s average unit price over the past 10 years has been 50p. One standard deviation has been measured as being 10p.

This means its unit price has not deviated more than 10p away from its average for 70 per cent of the time over the past 10 years. In other words, its price has usually been within 40p and 60p.

The same trust&#39s average rate of growth over the same 10-year period has been 9 per cent and a calculation in this respect reveals a standard deviation of 3 per cent.

This means that for 70 per cent of the time its rate of growth has not deviated more than 3 per cent away from the average rate of growth, that is, it has been between 6 and 12 per cent.

Last week, I showed that the higher the calculated standard deviation figure, the more volatile the investment. You may wish to play with a few comparative figures for the above example to prove why a higher deviation means a greater move away from the average.

There are, however, a number of issues to take into account. First is relativity. If you were told a particular investment&#39s standard deviation was 8 per cent, would you judge this to have been a highly volatile, moderately volatile or relatively non-volatile investment? In fact, you could not make a judgement on such scant information without knowing the level of standard deviations of comparable investments.

If these were all showing standard deviations of 3 or 4 per cent, then the 8 per cent measurement would indicate a relatively very high level of past volatility.

But if the other similar investments showed standard deviations of 15 per cent and more, we could summarise that this investment has been of relatively low volatility.

This could be important in assessing future volatility when determining a portfolio with a structured approach to collective risk (remember the efficient frontier from these articles a few weeks ago, which we will pick up on again throughout the next few weeks?) Here, we might be comparing volatility of different asset classes, for example, gilts against equities, or sectors within those classes, such as UK equities against Japanese equities, or even individual funds within these sectors.

I hope you can see the fantastic potential for the use of standard deviation numbers in portfolio planning. It adds a quantitative tool to the more subjective issues typically used by portfolio planners.

The second issue to consider in using standard deviations is the time period over which the statistics have been compiled. Wherever you see mathematical values for risk in our financial papers and magazines, they are almost invariably related to one standard deviation taken over a three-year period.

Whether a longer period should be taken is open to debate but the main issue to bear in mind is to judge volatility on a comparative basis, using a constant time basis, between the competing investments under consideration.

Similarly, the adviser must also look at the number of values taken within the given time period. If, over a three-year period, the standard deviation is calculated using the investment&#39s daily value, the result will tend towards mathematical precision as it is easy to get near to the 70 per cent calculation with around 1,000 values to take into account.

However, if only one value each year were taken into consideration, you should be able to see the standard deviation number is likely to be meaningless, with only three values under consideration. Most standard deviation numbers use monthly figures but others use daily values.

So far, we have only assessed what has happened to the investment return 70 per cent of the time – the definition of one standard deviation. But what about the investment performance the other 30 per cent of the time?

It may be useful to look at the figure for two standard deviations, which explains how far from the average an investment has deviated during approximately 95 per cent of the time.

Fund A

With an average annual rate of return of 9 per cent and one standard deviation of 4 per cent, we now discover the figure for two standard deviations is 7 per cent. This means the investment return has deviated by no more than 4 per cent of the average during 70 per cent of the time, giving an annual rate of return between 5 and 13 per cent.

For 95 per cent of the time, it has not deviated more than 7 per cent away from the average. Only rarely (5 per cent of the time) has the annual rate of return been lower than 2 per cent (9 per cent minus 7 per cent) or higher than 16 per cent (9 per cent plus 7 per cent).

In other words, when the investment return has fallen outside the relatively narrow range covered by one standard deviation (70 per cent of the time) it has not done so by much. However, you should note we still do not know what has happened to fund performance for the remaining 5 per cent of the period in question.

Fund B

With the average annual rate of return at 11 per cent, we have already noted that during 70 per cent of the time the returns in any year would not have been lower than -5 per cent or higher than 27 per cent (one standard deviation being 16 per cent).

If we are now told the measure for two standard deviations is 30 per cent. This means that during 95 per cent of the time, the annual rate of return has been as low as -19 per cent (11 per cent minus 30 per cent) but could have been as high as 41 per cent (11 per cent plus 30 per cent).

This is further indication that Fund B has been much more volatile over the last 20 years than Fund A. Whether it is likely to remain so can be indicated by looking at its current declared investment strategy among other factors.

How can the concept of standard deviations help in devising an investment strategy and advising the client of potential risks? Even a small amount of thought should provide an answer to this question. We are now able to indicate to clients – albeit only from an historical perspective – how bad it got and how good it got. Then you can go on to select investments which are likely to suit the client&#39s risk requirements.

With cash deposits at the lower end of likely investment returns and also at the lower end of volatility, and with equities at the higher end in both terms, the recommended investment strategy is crucial.

In short, volatility measurements are an important aspect of portfolio planning which must be used just as frequently as average historical or expected rates of return.

In the coming weeks, my articles will look at each asset class (with some divided into sectors), taking into account their historical and predicted future returns and volatility, heading towards a more constructive and comprehensive visit to correlation-based portfolios aiming for the efficient frontier.

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