This is rarely the way ILGs are actually used in private client portfolios, even when managed by highly-qualified professionals. This is a testimony to the ubiquitous hold of money illusion but also to the intellectual arrogance of most professional money managers in the face of investment uncertainty. Arrogance is a form of behaviour conducive to higher fee generation when clients believe market risks can be successfully exploited for gain by skilled agents. But humility is more likely to be conducive to higher return generation when market risk is not easily exploitable or costs of trying are high. Both money illusion and skill illusion explain why so little use is made of ILGs as unique ‘power assets’, as distinct from just another asset class to throw into the diversification pot.  

Risk free or just another bet?

This debate, which rarely reaches the wide audience it deserves, burst into the open in the columns of the FT this month. The American finance professor Jeremy Siegel is well known as the author of ‘Stocks for the Long Run’, a book (now in its 4th edition) which has helped establish in both professionals’ and the public’s mind the essential characteristics of different asset classes that make them useful for investment objectives. Professor Siegel wrote a guest column for the FT titled ‘Inflation-linked bonds face a headwind of many risks’ in which he nodded towards the special benefit of ILGs, particularly in pension plans, but also listed reasons why they were over-priced (both in the UK and their equivalents in the USA) with real yields of barely 1% (’levels that would have been unimaginable just a few years ago’). He concluded by warning of large losses on the horizon for holders of such bonds as economic activity and inflation both picked up. Equities, he felt, offered ‘much better long term protection against inflation than today’s low-yielding inflation-linked bonds’.

Outrage from the ‘power asset’ camp! It provoked a  letter signed by another American finance professor, Zvi Bodie, three frequently-published consulting actuaries familiar to UK pension funds and ex-corporate finance head turned pension consultant, John Ralfe. They argued: ‘The conservative pension saver, especially those with little or no other capital, should avoid the worst outcomes in retirement by holding inflation-protected bonds, even if it means giving up the possibility of the best outcomes by holding equities.’

They also argued that the risk of equities is typically misrepresented by the investment industry, which (either out of mischief or ignorance) understates the risks and overstates the likely payoffs when investing in equities.

Much as I welcome the argument, as it helps to banish popular illusions about risk and the management of risk, I have to say there are fallacies on both sides of this debate, as well represented in these two FT pieces. The faults lie partly in the assumptions that lie behind the maths and partly in a disconnect with personal risk preferences in the real world.  In this Insight we will try to find the firm ground between these two camps and show how it can be used as a foundation for individual portfolio choices.

I am not particularly concerned with a less meaningful aspect of the debate which is that there will always be arbitrageurs in the market and investors with a particular opinion about future inflation who will trade between ILGs and conventional gilts as if both were risky assets. On a short term view, when the position taken is not matched to or defined by the maturity of the bond or the duration of the investor’s objective, they clearly both are bets, not hedges. If this is largely what Professor Siegel was referring to, he is right.

Assuming a non-random equity ’system’

The sort of historical evidence in support of equity investing made famous by Professor Siegel is broadly supportive of the view that equity returns are a fairly intuitive output of adaptive capitalist systems. They do broadly what you would expect as an economist, if you only knew that stock markets recorded the performance of publicly-traded companies in some form of ‘market economy’. However, it is important to distinguish between nominal returns, which are distorted by each country’s and each period’s inflation experience, and real returns, deflated by a national retail price index. Inflation is one of the externalities we expect market systems to adapt to, more or less well.

Interpreting behaviour from real returns, without separating between income and capital, it makes surprisingly little difference if the market economy is Anglo-Saxon, Swedish or Japanese. There is in fact (yet) no theory of why millions of individual decisions by real investors based on idiosyncratic views of personal welfare leads to either similar trends in equity ‘total’ returns (both income and capital) or why the very large deviations from trends that emerge in all the data histories are both bounded and also similar between countries, regions, different stages of economic development and different periods of history. There are many sources of differences, including how they behave together, at the same time, but these may contain less useful information (or none at all) compared with the similarities.

The absence of a theoretical explanation of sustainable trends and of reversion to the trend is a concern for many and a particular concern for academics. But even if there was a theoretical explanation, it would rely on the same data as the only practical basis of experiment. If you have little choice but to participate in the system, you might as well leave proof to others and work out for yourself what view of the world and the system you are willing to hang your hat on. I decided a long time ago that, with respect to real total returns from equities over long periods, it was not a random world.

If the system were random

This preamble is important because many of the critics of the representation of equity risk believe it is in fact a random world. These letter writers, for instance, argue that ‘the proper measure of equity risk is the cost of buying insurance against underperformance versus the risk-free return – a “put option” on a stock market index. If risk reduces over time the cost of equity put options against any shortfall should reduce. But the cost increases the longer the option period, reflecting increasing not decreasing risk. The theoretical price, based on a standard option pricing model and actual prices charged by banks, is about 25 per cent for 10 years and 30 per cent for 20 years.’

The mathematical truth in this statement, that risk expands, not shrinks, with time conceals an assumption that it expands at the rate of a random time series (the square root of time) rather than at the slower rate of a mean-reverting series. The ‘theoretical price’ of the risk derived from option markets is not a proff of anything because it extrapolates from short-period nominal return behaviour which is (probably) random. There is no market in 25 year equity options and, if there were, arbitrage from the physical equity market would cause it to reflect the same assumptions of mean reversion widely made by participants in that market.

ILGs and mean-reverting equity returns

Hanging your hat on a sustainable but uncertain trend in long-term real returns also means that you will assume that the mean expected equity return will rise faster than any risk free rate, such as the 1% real yield of ILGs. The insight that risk rises with time means the band of probable outcomes around the trend increases slightly for every year the investment is expected to be held. (This will still translate into a declining standard deviation of short-period returns the longer the expected holding period, which was the source of the widespread error that risk falls with time, as it does not compound each single-period standard deviation over the relevant length of time.)

The concept of a rising and expanding range of possible real wealth outcomes around a known risk free rate with a lower slope is expressed in the diagram below. The principle to which the letter refers, of both lifting the floor or worst-case outcome but at the cost of a lower slope for wealth generation, is illustrated here by substituting half the equity portfolio by a risk free ILG. Depending on the values assumed, there is a point at which the distribution of outcomes lies entirely above the risk free rate. At any point, you can adjust the level of substitution of equity risk by ILGs to achieve a tolerable worst-case outcome. You would find the same general principles explained in Professor Bodie’s widely-used text book ‘Investments’.

Choosing between risk free and equity bets

The FT letter writers express the opinion that ‘conservative’ investors, worried about the consequences for living standards of a bad outcome, should not make an equity bet at all but accept the certain but very low real return and outcome of ILGs. This is a massive over-simplification. If it has a paternalistic purpose, it is thoroughly misguided.

The question investors at any level of wealth, whatever their instincts about risk, need to ask is ’how much risk should I take, given the consequences of bad outcomes and the floor below which these become personally intolerable, and what will that cost me in resources?’

If, like other reluctant participants in the capitalist system, I want a certain standard of living but do not want to bear much risk to obtain it, I think I would like to know whether I could in fact afford to avoid risk. If the implications of building more certainty into my life was a mediocre living standard, either by making spending sacrifices whist still earning or in retirement (or even both), I might accept a bit of a capitalist gamble to lift most of my probable outcomes above the mediocre.

If, on the other hand, I were extremely wealthy and had no children, and was not hard-wired to keep creating wealth (as many enthusiastic participants in the capitalist system are), I can imagine I might decide to stop taking risk, or would only take enough to secure improvements in my spending power that I was likely to value. I have no need to gamble and no satisfaction from gambling. I can leave the table and live on gilt coupons (index linked, of course).

These practical examples of risk taking preferences, in a real-world context with particular personal consequences, illustrate an important role of ILGs in both financial planning and investment management as the market benchmark of the cost of avoiding risk, in both resources and outcomes.

Choices at retirement

The benchmark for avoiding all risk at retirement is the income provided by an index linked annuity, as this deals with longevity risk as well as capital market and inflation risks. Using a retirement plan as an example:

• On the basis of current real yields, a capital sum of £1,000,000 will produce an annuity income before tax (for a 60 year old male with two-thirds spouse benefit) of £25,250pa. This illustration ignores the practicality that, if it were in a pension plan, you would apply the tax free cash to a purchased life annuity which unfortunately does not come with full indexation. Being an annuity the real payments will be level each year, even though you might prefer higher spending targets early in retirement and less later, but with equivalent real outcome certainty.
• With controlled risk taking, in current equity market conditions, the same sum might generate a profile of preferred spending starting with a gross equivalent draw of  of £40,000 pa at the start of retirement. Depending on the payoffs from risk taking and how quickly or slowly they emerge, the starting rate might increase to a mean expected rate of £90,000 pa in real terms, sustainable to age 95. On worst-case real investment returns, the rate of draw might taper, in line with the time preferences, from age 75 to about £26,000, so never less than the level real annuity.   
• At retirement, it would be illogical to hold ILGs and draw down from them instead of buying an inflation-indexed annuity. More of the resource would need to be assigned to funding the extra years of life beyond the actuarial expectancy of the pool of lives in the annuity fund – the illustrations above assume 35 years instead of about 27 years.  To match the same worst-case gross draw as above holding only maturity-matched ILGs would require £400,000 more capital and to match the median draw would require a further £600,000.

No free lunch

An important insight of the FT letter writers is that equity investing is typically presented as a free lunch. They say: ‘The higher expected return of equities over inflation-protected bonds is simply a reward for the risk of holding equities; it is not a “free lunch” or a “loyalty bonus” for long-term investors.’

Provided the trade off between resources, certainty of outcome and risk taking is properly explained and quantified, there is no illusion involved in making a case for equity investing. On the contrary, it avoids the illusion that avoiding risk is cost free and affordable. In the example above, the actual rate of sustainable draw is consistent with 99% confidence of not breaching the floor, there is no spending of payoffs from risk taking before they have been earned and the cost of avoiding different forms of risk is explicit.

ILGs perform an invaluable and indispensible role both in communicating the principles and quantifying the trade offs. They should feature in every financial plan and every portfolio review. But they should also be the main method of risk control in the portfolio itself.

I single it out because outsmarting the smarts with simple thinking is very No Monkey Business. In fact, the same data has regularly featured in No Monkey Business posts since 2006 (about a year behind Paulson) as an obvious parallel with the Nationwide deflated index of UK average house prices which I regularly monitored on the No Monkey Business blog from about 2002. Just don’t ask me where my $4b is.

What drew me to the study of the trend and deviations from trend in real house prices was that it was itself a parallel application of an important insight about equity returns: historical time series for ‘real total returns’ (ie cumulative indexed performance with income reinvested, deflated by a consumer price index) contain valuable predictive information for investors, and more so than conventional valuation measures like price/earnings multiples and dividend yields. This was one of the big but simple ideas set out in my book in 2002. Since 1999 it has been the basis of horizon-specific probabilistic return projections in a model we now use to manage Defined Outcome portfolios.  

Such an apparently naive solution to a complex problem is deeply offensive to most investment professionals as it implies redundancy for much of their industry. I naturally therefore warmed to the naivete of the Sunday Times account, as typified by this extract.

'Everybody said home prices never had declined on a nationwide basis except during the Great Depression,” Paulson later recalled. He sent Pellegrini scurrying back to his cubicle to determine how overheated the property market was.Tracking interest rates over the decades, Pellegrini concluded that they had little impact on house prices. But as he reviewed academic and government literature and figures, Pellegrini grew frustrated. He couldn’t quantify how excessive housing prices were or show when a bubble might have started. He couldn’t even prove the price surge was distinct from historic moves.Grasping for new ideas, Pellegrini added a “trend line” to the housing data; this illustrated how much prices had surged lately. That’s when Pellegrini took a step back to view things over a longer period, ordering up data on home prices all the way back to 1975. Suddenly, the answer was as plain as the paper in front of him: housing prices had climbed a puny 1.4% annually between 1975 and 2000 after inflation was taken into consideration. But they had soared by more than 7% a year in the following five years, until 2005. The upshot: US home prices would have to drop by almost 40% to return to their historic trend line. Not only had prices climbed like never before, but Pellegrini’s figures showed that each time housing had dropped in the past, it fell through the trend line, suggesting that an eventual drop was likely to be brutal. Pellegrini sat upright, staring at his trend line, amazed at how simple and clear it was.The next morning, he raced in to show Paulson. “This is unbelievable,” said Paulson, unable to take his eyes off the chart. “This is our bubble. Now we can prove it.” Pellegrini just grinned, unable to mask his pride.'

The standard source material for real house prices, deflated by general inflation as measured by the CPI, was the S&P Case-Shiller Index. Pellegrini refers to data going back to 1975 but there is in fact earlier data which I came across a little later in the form of index creator Professor Robert Shiller’s submission to a Congressional commitee. In September 2006 I posted an item on the No Monkey Business blog called US house prices: you thought we had a problem which included a chart of over one century of real prices for single-family homes.

It was important that the data be real. Real prices are perhaps better decribed as relative house prices, because they measure prices relative to general price inflation. But even real price series were rarely publicised because of people’s obsession with changes in the price level, treating house price inflation as the key information rather than the level of relative prices itself. This was a widespread problem in the US just as it was in the UK. I still berate newspaper editors for repeating this error.

As I pointed out in my article, fitting a regression trend to the long time series data was not helpful because there were several distinct phases of price behaviour, including just two since the end of WWII, up to and after about 2000: no real growth followed by a growth explosion. In my article, I contrasted the absence of any overall trend in US real house prices prior to 2000 with the trend in post-war real prices in the UK, which has been fairly persistent at about 2% per annum, in line with growth in personal incomes.  The 0% trend in the US for some 50 years means that relative to personal incomes US housing had become progressively more affordable. I agreed with Prof Shiller’s interpretation that this was due to easy access to new development land, an endowment we clearly do not enjoy in our planning-constrained small island.

More important, the only plausible explanation for the change in price dynamics after 2000 was the change in credit availability. The fact that people wanted to believe in endless rapid growth, a new twist to the American dream, was a necesssary condition but it also required bankers and mortgage investors to throw caution to the wind or the boom would have simply run out of fuel. And it was the massive stock of derivatives created on the back of securitised mortgages, two symptoms of the credit-induced madness that overtook the housing market, that gave Paulson & Co the instruments, in the form of credit default swaps (insurance contracts that would pay out if the underlying securities fell in price), which had the inherent leverage to turn £147m into $20b.  That was convenient but it was also smart and gutsy.

Is he right?

In this increasingly popular view, the actions by governments to pump money into the stalling financial system are seen as giving stocks a reprieve before they reached the sort of valuation levels that properly discounted the post-credit crunch realities facing economies and businesses. Hence the anxiety now as the patient looks to be coming off life support. 

John Authers’ preferred measures of value, using replacement value of assets (Tobins q) and a trailing 10-year average of earnings, supports the story that US equity investors, like the banks, got lucky and were bailed out before reality had sunk in to share prices.

I don’t think we can agree with that. Our own measure of value suggests that the last move down in the S&P at the start of 2009 took the market to an extreme level with only a few historical precedents in any major equity markets, all equally important as long-term buying opportunities.

Whilst we attach a great deal of importance to our measure of value as a basis for forecasting long holding-period return probabilities that can be used in asset allocation, it still does not mean there is a negligeable chance that the S&P will fall through the earlier low. Though it would be unprecedented for the US market, it happened in the UK in 1974 and in Japan in the 90s and again in 2003. What can happen in one place can happen in another.

There are also several historical examples where extremely high predicted value has persisted for a decade or more, Japan being one but Continental Europe in the late 70s and early 80s is a less familiar one, being disguised at the time by high inflation.

Though the FT piece was about the market most likely to influence the general direction of global equities, it is worth noting more parochially that on our measure the FTSE All Share Index is the least undervalued of all the major markets and did indeed recover well before reaching a historically exceptional valuation.

Lateral thinking about equity valuation

We agree with John Authers that Tobin’s q and trailing 10-year earnings will dampen the effects of extreme cyclicality in current fundamental inputs to valuation, particularly reported earnings. As an accompanying chart in his column showed, reported earnings in real terms reached a low point last seen in the 1930s although clearly this is not what has happened to ‘earnings power’ for American business.  The q ratio dampens variance simply because replacement value of assets is very stable, so the significant information comes from price change. Averaging earnings over several years will also dampen the valuation variance but is transparently arbitrary and may also leave price variance as the important information. These may therefore be better than conventional price/earnings ratios when earnings are disturbed but they are still not rigorous indicators of extreme valuation, high or low.

As market historians, Chris Drew and I have since the late 1990s adopted a lateral approach to equity market valuation, formalised in a return-generating model called Lambda. We ignore fundamental inputs, because of the measurement problems, in favour of tracking the path of achieved real total returns from each market and comparing it with its own long-term trend, using ’best fit’ regressions. The model has not been invalidated by subsequent return behaviour and has indeed handled several episodes of extreme valuation very well.

On this measure, the recent low for the S&P was as low as the previous extremes of the early 30s and 40s as well as 1974 which was revisited (in real but not money terms) in 1982.

Fig 1 shows the S&P continuously-compounded logarithmic returns with gross dividends reinvested and deflated by the CPI from 1925, as an index. The whole-history regression trend (colour) is 6.8% pa but the hindsight-free trend using data up to each point in the series (colour) was above or below this as a function of the particular period. In my book I showed a Wilshire series for US equities for nearly two centuries that revealed a similar trend in both centuries, in spite of massive contextual differences. Data for other major equity markets also suggests about 5-7% pa as a trend, with much narrower dispersion of the differences than economic context and culture might suggest. Global evidence suggests regression trends are not just a statistical accident but an economically sustainable quantity that is a core element of the equity return process. We believe there are strong theoretical underpinnings for this, based on both economics and risk aversion.

Fig 1 Trend and deviations from trend in real equity returns: S&P 500

This idea of sustainable real equity returns over long holding periods is really important. It conflates into a single measure two crucial influences on returns: i) fundamentals (like earnings and dividends) and ii) investor behaviour changes (like risk aversion, sentiment and momentum following). Historically, even over long holding periods, the second set of uncertainty sources has usually dominated the first, which makes the traditional focus on fundamental inputs look odd. If jointly the two sources of uncertainty lead to bounded deviations from trend, as a further core element of the return process, we do not need to disaggregate them to model either returns or risk.

Fig 2 expresses the level of the real total returns index as a ratio of its own trend, or detrended, which we call the Market Value Ratio. We use this as a basis for adjusting upwards or downwards the mean expected returns extrapolated naively from the trend alone. Low price denotes high value and high future returns and vice versa. By making some assumption (itself based on historical analysis) of the time-dependent reversion to trend, we can estimate real return probabilities for every holding period as often as we gather new historical return data. The actual frequency is monthly.

Fig 2 Market Value Ratio: S&P 500

What can we do with value?

Fig 2 makes the point of this post that the S&P low in March last year was extreme. This observation was sufficient to justify exceptionally high expected future returns, provided long holding periods could be assumed. For investors with naturally long horizons, this amounts to a lot. It is why we added with confidence to clients’ total equity exposures up to the low point, while others were selling, and reduced them either side of this recent year end. See Is your manager doing a good job? (22nd January). 

Observing extremely low value by March 2009 may even have been enough to warrant assigning a very low probability to further downside risk over short horizons, which would also amount to a lot if, it could be relied on.  We do not believe it can. We prefer to treat short holding-period returns as a ‘random walk’. That was not the basis of our decision to buy.

An aside for more numerate readers: short-run returns, whether deflated or not, also have the highly inconvenient statistical characteristic of fat tails, or extreme outliers that would not be predicted if assuming a normal distribution. Long holding-period real returns, on the other hand, appear to be normally distributed. 

We sympathise with John Authers who is obliged (as a good journalist rather than a good story teller) to remind us that even a ’true’ valuation of the market tells us very little about the chance of the market falling or rising or staying the same over the next few years. This might read as ’sitting on the fence’ but it is more insightful to see that good valuation measures simply have restricted uses.

For us, as financial planners and even as portfolio managers, using them to project long holding-period real outcomes is actually more important than using them to try to time markets. Imagine yourself in 20 or 30 years time looking back and deciding you got the outcomes you wanted and planned for. Is it most likely you will credit the many market timing decisions that made up the path your money took or rather making the right long term decisions? We have no doubt and we don’t think our clients do either.

The information contained in the returns themselves and in the underlying asset allocations is about our investment process itself. So an analysis of our performance is an analysis of our process in action.

The process itself addresses a much trickier question: how do you manage money when the lesson properly learnt from both theory and practice in financial markets is that a manager cannot know what is going to happen in the short term, and their opinion is of limited value to their client? How does a battle-hardened agnostic place their bets and why?

The process is an outcomes-driven approach to goal-based investment portfolios, which we term ‘Defined Outcome Portfolios’. The approach is detailed here on the website.

The key characteristic of this approach is that some bets are avoided or hedged and others tightly and dynamically managed, within a specified ‘risk budget’. The risk budget is expressed in terms of a range of tolerable outcomes, in real terms (after inflation), at the times the money is needed.

With such an approach, the outcomes at shorter horizons are the wrong ones to make bets about. To the extent they are fully matched by risk free assets, matched to the duration of that time horizon, a key insight is that clients can afford to be indifferent to the volatility of these assets. If the volatility has no impact, their short-term performance is also of little import. The volatility is zero for cash but index linked gilts, though risk free in real terms at maturity (because of the government guarantee of inflation uplift), are nonetheless quite volatile in the period prior to maturity. But the volatility has no impact on outcomes, by definition.

Only the volatility of risky assets has a bearing on the probable plan outcomes and therefore the chances of the client achieving their minimum objective. These are the bets, as opposed to the hedges.

This transforms the relevance of the volatile short term return path of the ‘current’ portfolio. It makes a nonsense of comparisons of achieved short-period returns with other managers. Our clients are out of the performance race and in a journey, of their own planning.

Private clients are largely unaware of how to use performance information where planned goal outcomes are partially protected by hedging. They are not alone, however. The advent of ‘liability driven investment’ in the institutional market, which is the closest parallel, has also forced trustees to rethink the significance of reported performance, both for their own asset manager and for comparisons between managers.

Returns
In an earlier post, part way through the market fall, we took two clients as examples. Since all clients have a different combination of explicit time horizons, outcome profiles and risk tolerance, we have to use samples, not a universe. We have updated these two examples in this article.

They both have Defined Outcome portfolios funding retirement spending. One is still ‘in accumulation’, with about 5 years before drawdown starts. The second is already in drawdown, meeting current retirement spending.

The examples were chosen to have similar risk tolerance so that the asset allocation differences, as output by their own models, are explained by the time horizons (although changing profiles for spending outcomes at different stages of retirement also make a difference).

The returns are money-weighted returns. Because the cash flows, mainly new savings or draw, typically arise at month end, there is essentially no difference in the cash-flow adjusted returns whether money-weighted or time-weighted.

The period is from December 2007 through August 2009, as this roughly corresponds to the start of the bear market and the subsequent recovery.

The accumulation portfolio achieved a return over the whole period of -11.3%. The drawdown portfolio achieved a return of -4.1%. The paths of each, indexed to 100 at 31/12/2007, are shown below in Fig 1.

Fig 1: Index returns of two Defined Outcome portfolios

Asset allocation
The building blocks of a Defined Outcome portfolio are divided into two:

• Risk free assets (matched to the nature and duration of the time horizon, such as £x real spending in year y)
• Risky assets (in the form of a mix of equity markets across the world, as represented by broad indices with all but ‘systematic’ risk diversified away).

The two are combined to ensure that the projected outcomes of a dynamically-managed ‘plan’ (not just the current portfolio), counting down to fixed dates, are always consistent with the agreed tolerable outcomes.

The return paths of the building blocks (source: Lipper Hindsight) are shown in Fig 2 below, indexed to 100 at 28/09/2007

• The cash return is a one month deposit rate (the risk free asset for durations below about three years)
• The index linked gilt return is derived from the over 5 years FTSE index (as representative of the ‘medium-dated’ maturities where we typically combine risky and risk free)
• The equity returns are for index-tracking funds provided by Legal & General (as representative of the returns that could have been earned from tracking the risky asset building blocks, after the fund expenses attributable to institutional units).

Fig 2: Indexed total returns of the portfolio building blocks

Attribution
Because the asset allocations output from each model run for each client are implemented using index-tracking funds and individual index linked gilts, the portfolio return and its variability are almost entirely explained by the allocations.

The accumulation portfolio started with an equity allocation of 100% and the drawdown portfolio 65%. The risk free return has been relatively flat due to both low interest rates on cash and moderate volatility and net change in index linked gilt yields over the period.

Considering the difference in equity exposure at the outset, the gap at its widest point between the two portfolios is surprisingly small. The largest drop for the accumulation portfolio reached 28%. This also appears relatively small compared with the returns apparently experienced by most UK-based equity investors, including those investing purely in the UK, which was down 38% at that same point.

As Fig 2 hints at, a large part of the answer is geographical diversification. We tend to hold more in European, Japanese and US markets than most investors. This follows logically from the intention of diversification and is likely to be an output of any portfolio optimisation process that seeks to maximize expected return per unit of risk. However, most investors constrain exposures to foreign markets to suboptimal levels. Diversification benefits reflect the distribution of weights to each market not just the number of markets held.

Short-term correlations between different equity markets are highly unstable (and indeed increased dramatically during the bear market). But differences in achieved returns do emerge, implying differences in future returns. With fairly similar long-term real return trends apparent in the historical data, mean reversion operates both between and within markets. Larger international exposure allows this to be exploited more efficiently.

As it turned out, much of the benefit from geographical diversification in this particular period came from currency movements. Sterling fell as asset prices were at their weakest and strengthened as equities themselves rallied.

Currency movements are not normally well correlated with market movements so most of the time these two sources of risk will not combine to increase portfolio risk significantly. What happened here, with currency dampening portfolio volatility, cannot be predicted in advance or relied on.

Asset allocation changes
Fig 3 shows the asset allocation changes for a drawdown model starting with the December 2007 quarter and ending in the two months to August 2009. The actual model runs are monthly but we have conflated the changes to quarterly, to simplify the rebalancing narrative.

The resources at the outset in this model run were £1.8m which puts the changes shown below into context. The range of monthly change in allocations at the highest level, between risk free and risky, is from 4% to 8% of the total portfolio. This is clearly a gradualist approach.

Fig 3: Changes in net equity exposure

The narrative here, even if at the time it needed some explanation and illustration,  is entirely consistent with the portfolio process and so held no surprises for the client.

• Two quarters of additions to equity exposure relative to index linked gilts as the bear market began, as expected equity returns to each planning horizon were then higher than before and higher relative to index linked gilt yields for the same horizon – hence hedges can be marginally lifted
• A small net pull-back in the next quarter as equities rallied and index linked gilts fell, lifting their real yields
• As the US housing bubble started to go wrong and the credit crisis got worse, dragging risk free yields down with it, the next three quarters saw net additions to equities
• From March 2009 the model called for net sales of equities as prices rallied and risk free rates also moved higher.

The net change over the whole period is an addition to equities of £0.25m, equivalent to 14% of the starting portfolio value. Considering the net fall in equities over the whole period, and the relatively small net fall in risk free rates, a constant risk tolerance should be expected to lead to reductions in hedging and an increase in risky exposures. Investors (or their advisers) who instead altered their risk tolerance in response to what they thought was happening in the world would have shown the opposite response, selling risky assets as they declined in price, or might have been frozen into inactivity.

The net changes filter out the rebalancing arising between different equity markets which is also shown in the table. The gross change over the whole period is 42%. In practice, some of the smaller changes indicated by monthly model runs may not be implemented, as the likely improvements in risk-adjusted return are too small relative to the costs of transactions (even when these are minimized by using exchange traded funds on an execution-only stockbroker dealing platform). Many small changes should reverse themselves from month to month. There is an element of judgement in filtering these small changes.

The main changes in country weights are as follows:

• Reductions in Japan, which had started the period at 36% of the risky allocations – high exposure in Japan is a key test of a globally-diversified approach to long-term return return opportunities
• Roughly half of the net addition to equities was in the UK, which is a natural response to increasing real return ranges in all markets, as plan outcomes can then be met with less uncertainty in the home market.

The portfolio model run for August had the following new target allocations.

Fig 4: Closing model allocations

These allocations are entirely logical given the client’s planned profile of the drawdown over the life of the plan; the client’s tolerance of uncertainty in the draw; and our projected return probabilities for the portfolio building blocks, as generated by a new model run in August 2009.

• The 16% cash allocation is matching about three years of spending targets (as an estimated pre-tax equivalent portfolio draw).
• From years 4 to about 8 the outcome targets are fully matched by a schedule of maturing index linked gilts with the same duration as the spending
• The next 6 years are partially matched by index linked gilts but equities are also held against these spending targets
• Only durations later than 15 years are fully backed by equities.

The proportion of the total plan resources that is sensitive to volatility in the portfolio value is represented by the allocations to equities from years 8 to about 15. They are sensitive because the return-generating element of the model does not assume that a fall in equity prices will be offset fully by higher real equity returns within the time frame required for that horizon. There just is not enough time to be that sure. This portfolio proportion, for which short-term performance has an impact on probable outcomes, is about 28%!

The earlier horizons (35% of current resources) are indifferent to volatility because they are fully matched. The later years, beyond 15 years, (the balance of 37%) are far enough off for mean reversion to have offset much of the fall in current value, leaving outcome probabilities little moved by the fall.

Even though there is a middle segment of the plan that is sensitive to volatility, any plan that was fully funded to meet the drawdown targets with a high level of certainty should still meet its original planning targets. This is based on the simulations of the plan, which tested randomly-generated paths for equity markets and exchange rates as well as their interaction with a pre-defined rate of draw in real sterling amounts per annum.

In practice, the progress of the portfolio is likely to feed back to the client’s comfort level in spending. Should this arise because of really bad equity markets globally, implying widespread economic stress, it would not be surprising if the client chose to trim their spending objectives anyway, even if the model stress tests suggested it was not strictly necessary.

FT Money editor Matthew Vincent reports new research by Paul Marson (ex chief investment officer of Goldman Sachs Wealth Management) for Lombard Odier showing that there was no connection between emerging countries’ economic growth rates between 1976 and 2005 and the total return (capital returns including reinvested income) earned investing in representative indices for the different countries.

In “The Triumph of the Optimists”, recording a century of investment returns from 16 different countries, academics Elroy Dimson, Paul Marsh and Mike Staunton also debunk the myth that differences in economic growth in more developed economies explain differences in returns. In “No Monkey Business”, I used similar historical evidence to show that real return trends for developed markets in the post-war period are remarkably similar in spite of very different experiences of both inflation and real economic performance. I also compared two centuries of real (after-inflation) total returns for a Wilshire index for US companies in which the growth trend is essentially the same during its emergence as an economic power and after. I showed how the only period of superior returns from emerging markets came with their emergence as an investment strategy. not their economic performance. The two are not at all the same.

The growth illusion at the country level is an extension of another popular belief that high-growth companies make better investments. What gives the lie to this is the inconvenient evidence that over the last six decades value investing has generally outperformed growth investing. This is not to say that there were not periods in which the discipline of value made an investor look very pedestrian or out of touch.

Can this counter-intuitive finding about growth be easily explained to lay investors so that they might better protect themselves from wealth-reducing biases? It certainly helps if you have any business experience but it is not so difficult to understand.

Paul Marson is on the nail in pointing to the reason: financing: ‘Companies financing from externally gained funds will dilute their shareholders’. This must be true unless high-growth companies, and by extension high-growth countries, are able to sustain higher returns on equity and by a large enough margin to ensure that they are self-financing. This rarely happens.

It is rare because superior growth usually involves heavy investment that depresses returns in the short term and it is also rare because competition works quite effectively to suppress excess profit margins. Companies can appear to resist the dilution effect of raising new equity if shares are priced by investors at very high levels but this then acts as a trap for shareholders as sooner or later this overvaluation will correct. Technology stocks at the end of the 90s spring to mind but so should the ‘funny money game’ in the 70s in which many acquisitive congomerates and asset strippers were first darlings of the stock markets and then blew up.

The growth you should be interested in is the sustainable growth in company earnings per share, which reflects profitability advantages rather than economic performance or sales growth. These will almost certainly look very different from popular perceptions. But this is not the only form of self-defence you need. As Matthew Vincent reminds FT readers, you also have to focus on valuation – the price you are being asked to pay for earnings growth potential.

The reason for the value discipline, at the country level as well as the stock level, is that changes in valuations are much greater than growth differences. Investors quite simply keep ‘getting it wrong’.

The trap was very effectively set at the end of the height of the last growth stock boom in the late 1960s, prior to which growth appeared to have the edge on value investing. It was a potent mixture of a widely-held belief system and massive capital flows, as it coincided with the democratisation of equity investing via mutual funds. At its peak, high growth was particularly prized because the US was by then looking like it was in the slow lane compared with the emerging ‘economic miracles’ in post-war Europe and Japan.

The most obvious way to participate, when international equity investing was much less well developed, was to buy the US multinational companies that were able to escape the constraints of an anaemic home market by embarking on a global land grab. It was too obvious and investors ended up grossly overpaying for the actual earnings growth. Whereas the story itself was, in large measure, true, the valuations were fanciful. The impact was that investors first suffered a bursting of the bubble and then had to wait over a decade or more for earnings to catch up with share prices.

There are many parallels today in popular beliefs about investing in Asia, also a very good story.