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# Volatile substance

In my last article, I examined investment risk, the difference between average rates of return and volatility and, last, risk and reward.

In this, my second of three articles on planning a portfolio, I will look specifically at standard deviations, including the use of more than one standard deviation, preferred investment strategy and devising investment strategies.

Standard deviations give an indication of just how far away from an average rate of return an investment might deviate over any given period, measured over an historical period of time, typically three years.

The measurement of one standard deviation shows how far investment performance has deviated from the average over around 70 per cent of the period in question. An example should be helpful here.

Fund A

Let us say that, looking at fund A&#39s investment performance over the last 20 years, we find that the average annual return has been 9 per cent. We also note (from providers of investment performance statistics) that the standard deviation has been four. What does that number four indicate?

It indicates that in 70 per cent of the years under review, the investment return has never been lower than 4 per cent below the average rate of return nor higher than 4 per cent above the average rate of return. Thus, in 14 years out of the 20 years under review (70 per cent of the time), the annual rate of return to an investor has neither fallen below 5 per cent (the average of 9 per cent less the standard deviation of four) nor been higher than 13 per cent (the average of 9 per cent plus the standard deviation of four).

At this stage, we do not know either the lowest rate of return the investor would have suffered or the highest rate from which he benefited during the other 30 per cent of the time. We will return to this issue.

Would an investor consider this particular fund, with an average rate of return of 9 per cent and a standard deviation of four, to be volatile? The next question to ask must be volatile compared with what?

Let us make a comparison with another example fund.

Fund B

Fund B has grown over the last 20 years by an average of 11 per cent a year and we are told it has a standard deviation over that period of 16.

This means that in 70 per cent of the years under review (14 years out of 20), the investor could have suffered a loss of up to 5 per cent of his fund (the average gain of 11 per cent less the standard deviation of 16, which gives a minus number in this case) but may have enjoyed an investment gain of up to 27 per cent (this being the average rate of return of 11 per cent plus the standard deviation of 16).

Comparing the two investments, we can see not only that fund B&#39s average rate of return is higher than that of fund A but also that the volatility of fund B is higher and in some years brings with it the increased potential for higher losses or higher gains than might be suffered or enjoyed by fund A.

From these examples, you should be able to identify that the higher the standard deviation of an investment, the higher has been its volatility (noting again that standard deviations are usually calculated on an historical basis and may not necessarily be an accurate guide to future performance). Higher volatility, it should be stressed, does not indicate an inferior investment, simply that the investor might expect wider fluctuations in investment returns from one year to the next.

Some investors actively seek more volatile funds in the expectation over the longer period of higher average rates of return (the risk and reward relationship again) while others desperately want to avoid fluctuating returns.

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 four, we now discover that the figure for two standard deviations is seven.

This means that during 70 per cent of the time the investment return has deviated no more than 4 per cent from the average (giving an annual rate of return between 5 per cent and 13 per cent). But during 95 per cent of the time the return has deviated no more that 7 per cent away from the average, showing that only rarely (5 per cent of the time) has the annual rate of return been lower than 2 per cent (9 per cent minus seven) and no higher than 16 per cent (9 per cent plus seven).

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. You should note that 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 being 11 per cent and one standard deviation being 16, we have noted that during 70 per cent of the time the investment returns in any year would not have been lower than -5 per cent or higher than 27 per cent.

If we are now told that the measure for two standard deviations is 30, 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) but could have been as high as 41 per cent (11 per cent plus 30.

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.

By looking at the measure of one standard deviation and two standard deviations, we can arrive at a useful assessment of how investment returns have deviated away from the average most of the time (70 per cent – one standard deviation) and almost all the time (95 per cent – two standard deviations).

However, while statistics for one standard deviation are now widely and usually freely available, those for two standard deviations are much more difficult and usually costly to obtain.

Bearing in mind that the most important aspect of standard deviationss is to compare one investment against another and not to achieve mathematical precision with regard to either option, the majority of portfolio advisers content themselves with a sound knowledge, understanding and proper use of only the figures for one standard deviation.

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 did it get?” and “How good did it get?” before selecting investments which are likely to restrict the client&#39s downside risk to a level acceptable to requirements.

With cash deposits at the lower end of likely investment returns but also at the lower end of volatility, and with equities at the higher end both in terms of potential returns and volatility, the recommended investment strategy is crucial, not least to a pension drawdown decision.

There are investment analysis techniques which seek to predict future standard deviations for different asset classes (equities, property, deposits, gilts) although these can never claim the precision of historic measurements and are beyond the scope of this briefing note.

However, advisers should be able to identify that there will usually be very good reasons why certain funds and asset classes consistently have historical standard deviations either significantly above or below their peers, for example, as a result of management style, risk approach or other factors which can indicate that historical standard deviations can often be a guide to the future volatility of those investments.

Measurements of volatility are, therefore, an important aspect of portfolio planning which must be utilised just as frequently as average historical or expected rates of return.

In my next article, I will conclude by discussing investment strategies using standard deviations including asset, sector and fund selection.

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