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The final frontier

Over the last couple of weeks, I have started to look at the benefits to be gained in an investment portfolio diversifying between low correlated assets with the ultimate aim of devising a combination of investments which aim towards the “efficient frontier”.

Although the term efficient frontier is a technical term used by statistical investment analysts, at the end of the day, it simply describes the formulation of a portfolio which combines the maximum possible medium to long-term returns within an individual client&#39s acceptable level of risk.

The efficient frontier

It is beyond the scope of this article to examine this concept in the detail I believe it deserves to truly do it justice.

It is worth noting here, at least in outline, that the ultimate aim of correlation strategy is to identify and profit from the efficient frontier, being the ideal percentage mix of assets within a portfolio. A quick example should help to illustrate this strategy.

If we look at a portfolio consisting entirely of UK equities, we can identify that the high returns achieved over the last couple of decades have been achieved during a time of relatively high volatility. This is certainly to be expected due to the general relationship between risk and reward that we have already discussed.

If we next look at the performance over the same period of long-dated fixed-interest gilts, we can identify returns well above those produced by most other assets (except equities) but again with a high degree of volatility (only marginally lower, in fact, than the volatility of equities).

It might be expected that a combination of these two high-return, high-volatility assets in a portfolio would have produced returns and volatility somewhere between the two individual asset returns.

While this is true of the overall returns, it is not true of volatility. As these two assets have displayed a low correlation between themselves, most recently at least, the overall volatility of the portfolio will be lower than the individual volatility of either of them – the fundamental aim and concept behind correlation.

But, in what proportions should each of the two assets be held to maximise returns and/or minimise volatility?

The answer to this question is known as the efficient frontier. Identification of the efficient frontier is a partly scientific and partly subjective process and in any event is based primarily on historical returns rather than likely future returns although arguably the former is a guide to the latter.

What the efficient frontier denotes, however, is the combination of assets (the frontier) which gives the optimum combination of low volatility and high returns.

Stray beyond this frontier that the strategy dictates, that is, combine the assets in proportions beyond those indicated by the frontier, and the investor will suffer lower returns and higher volatility – clearly an unfavourable result.

Efficient frontier strategy is complex but worthwhile studying for those seeking a more detailed scientific approach to portfolio planning than this article can hope to achieve but be aware that it can only ever be one of a number of indicators of an appropriate balance of assets within a portfolio.

Throughout this series of articles on investment portfolio planning, I will from time to time return to this concept, giving examples of combinations of assets which aim towards this efficient frontier.

Diversification, correlation strategy and the efficient frontier I acknowledge that the strategies outlined above represent only a small cross-section, numerically at least, of portfolio planning strategies put forward by a large number of at least so-called investment specialists.

These strategies range from the ultra-scientific (requiring tremendous mathematical ability but little common sense) to the neo-bizarre (many resembling horse-racing gambling systems).

The strategies outlined and so far discussed are among the most widely recognised, respected and tested strategies in portfolio planning but they can only form a part of any overall attempt at formulating appropriate portfolios for individual investor profiles.

Volatility as a mathematical tool

All investment portfolios are, or at least should be, derived with the interaction of risk and expected returns taken into account both for each constituent part of the portfolio and for the portfolio as a whole.

The concept of investment risk is well understood by financial advisers and, it appears, almost always highlighted and explained to clients.

However, the principle of investment risk is most usually defined as the chances that, over a period of time, the average rate of return will exceed a stipulated percentage – usually termed the critical yield – in order that a particular strategy might work in the client&#39s favour.

So, for example, a pension income-drawdown illustration might show that a client&#39s invested fund needs to achieve an average annual rate of return of, say, 8.5 per cent if drawdown is to prove financially profitable over conventional annuity purchase.

A lower average annual rate of return than 8.5 per cent will, it is thereby surmised, result in the client being financially disadvantaged while a higher rate than 8.5 per cent will result in financial gain.

In isolation, though, the average rate of return can only reveal half of the investment risk (and reward) picture – volatility is the other half of the picture.


Volatility can be explained in outline by taking an exaggerated example within pension drawdown.

Fred, aged 60, retires with a personal pension fund of £100,000 after taking tax-free cash and transfers this fund to a drawdown contract, taking the maximum permitted income of £10,000 a year.

Unfortunately for Fred, in the first year, his investment fund falls by 50 per cent and so, after taking his £10,000 income withdrawal, he has only £40,000 remaining in his fund after just 12 months.

In the second year, his investment fund unfortunately falls in value by a further 40 per cent, leaving him with only £14,000 at the end of year two after taking into account his £10,000 withdrawal.

In year three, Fred sees his fund fall by a further 20 per cent which, after taking into account his £10,000 withdrawal, leaves him with only a little over £1,000 at the end of this third year. At this point, his contract is of course due its first triennial review.

Continuing this extreme scenario, we will now assume investment performance to improve somewhat over the following years although not nearly enough to permit Fred to take anywhere near the level of income he enjoyed for the first three years (or, indeed, he would have been enjoying had he chosen conventional annuity purchase). Then, in the year of his 71st birthday, his investment fund grows in value by a stagger-ing 500 per cent.

But, by this time, Fred had only 2p remaining (not, we have to stress, a scientifically calculated value for this example) in his fund at the start of the year and this consequently grows to 12p although still does not, of course, permit withdrawal of any meaningful level of income.

In the following year (Fred is now 72), investment performance once more enjoys staggering growth – this time of 400 per cent – but, when applied to the remaining fund of only 12p, still only gives him a fund of 60p in total and again no possibility of withdrawal of income.

This phenomenal growth continues until he reaches the age of 75 but, because of the low base, his total accumulated fund is a meagre £14.78 (again, a made up number simply for illustration purposes) with which to buy a conventional annuity.

So, what has gone wrong and could this situation have been anticipated at outset? Next week, we look at the measures of volatility and start to combine these with the concept of correlation and efficient frontier.

Keith Popplewell is managing director of Professional Briefing.


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