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Just rewards

Over the last few weeks, I have been looking at the concepts of diversification within an investment portfolio, the reduction of risk or volatility arising from this diversification and, most important, the issues of correlation between assets.

The nirvana of achieving a mix of investments approaching the efficient frontier has been explained and discussed.

Here, I would like to continue where we left off last week, noting an investment portfolio within a pension drawdown contract which suff- ered horrible returns over the first few years but recovered (at least in terms of annual percentage performance) in later years. Unfortunately, of course, as Fred&#39s fund had been so depleted by the time the fund&#39s performance recovered, he did in fact not reap the benefits of that turn-round.

In these circumstances, it is no surprise that Fred complains, claiming he has been given bad advice. His financial adviser revisits the original file only to discover that the original illustration indicated that an average rate of growth in excess of 8 per cent should have made the drawdown strategy profitable.

Adding up each year&#39s investment gains in percentage terms, deducting losses and then dividing the total by the number of years of the contract, the adviser arrives at an average annual return over the 15-year period of, say, 20 per cent.

This high average has arisen as there were some very high investment gains towards the end of the drawdown contract term, more than counterbalancing the losses during the early years.

Nevertheless, in spite of the apparently high average investment return, it is indisputable that the drawdown strategy has failed in this instance. Fred has been able to enjoy only an extremely small level of income withdrawal (even without taking charges into account) throughout the last 10 years of the 15-year contract term and now retains only a negligible fund with which to buy a conventional annuity.

So what has gone wrong? Clearly, the losses in the early years, especially when coupled with a high level of withdrawals, make it impossible for gains in the later years – even dramatic gains – to compensate.

The difference between average rates of return and volatility Average rates of return give, quite simply, a snapshot summary of the overall fund performance over a given period of time. Volatility, in contrast, shows for the same investment fund how bad or good the performance may have been from time to time.

Risk and reward

It is a well understood principle of investment that risk and reward almost
invariably go hand in hand. The greater the desired reward (rate of investment growth), the greater the level of risk the investor must accept.

For example, over a longer term, the returns on equities have far outstripped the returns from Government bonds which, in turn, have far exceeded the returns from cash deposits.

Looking to the future, there is little doubt that an investor has a greater chance of suffering a loss of a significant part of his capital by investing in equities as opposed to investing in gilts (at least over the short term) and a greater chance of a loss in a gilt investment than by putting money on deposit.

The greater potential investment reward from equities is only possible by accepting a greater level of risk, particularly in the shorter term. In short, equity values are generally more volatile than gilt prices which, in turn, are generally more volatile than returns on deposits. But how can we measure the volatility of investment returns?

Standard deviations

Standard deviations seek to give an indication of just how far away from an average rate of return the actual investment return might deviate over any given period, with the standard deviation being measured over an historical period of years.

The measurement of one standard deviation shows how far the investment performance has deviated from the average over about 70 per cent of the period in question.

Fund A

If we are looking at the investment performance of Fund A over the last 20 years to find that the average annual gain has been calculated as 9 per cent, we might 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.

So, in 14 years out of the 20 years under review, (that is, 70 per cent of the time), the annual rate of return to an investor has neither fallen below 5 per cent (that is, the average of 9 per cent less the standard deviation of four) nor been higher than 13 per cent (that is, 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 will have suffered or the highest rate from which he benefited during the other 30 per cent of the time (as the definition of one standard deviation only covers 70 per cent of the time). We will return to this.

Would an investor consider that 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&#39s make a comparison with another example investment fund.

Fund B

Fund B has grown over the last 20 years by an average of 11 per cent per annum 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, again, 14 years out of 20, the investor could have suffered a loss of up to 5 per cent of his fund (that is, 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 inv-estments, 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 brings with it, in some years, 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 clearly that the higher the standard deviation of an investment the higher has been its volatility, noting again that the standard dev-iations are usually calculated on an historical basis and may not necessarily be an accurate guide to future performance.

Preferred investment strategy

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 higher volatile funds in the expectation over the longer period of higher average rates of return while other investors want desperately to avoid fluctuating returns.

Next week, I will continue this discussion about volatility and I will explain in more detail the principle behind two and three standard deviations.

In the meantime, if the concept of standard devia tions is either new or relatively new to you, perhaps you would like to examine the fund performance statistics of some of the major inv-estment providers, as sum-marised either in their own literature or the statistic pages in the weekend Financial Times.

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