Awakening the Zombie

The headline writer obviously makes the same assumption most investors do that Japan has been a zombie for a long time. As the article points out, Japan has actually been fully competitive in sterling terms with other markets in the last decade and particularly useful in the credit-crisis bear market. What counts is valuation, not economics.

At today’s low valuation Japan should be as useful as other major markets, but has the potential to be the best.

Following on from his article Bull in a China shop, Stuart has been quoted in the following articles explaining why buying into the popular fund now is likely to result in tears.

The Independent – Is China a bargain or a bubble?

Times Online – Fresh issue of shares on China fund (this link will only work if you have subscribed to Times Online)

Motley Fool – Emerging markets to watch

The debate about equity risk, and who can afford to bear it, usually crops up in FTfm in the context of defined benefit pension funds. Last week Pauline Skypala drew attention to an influential academic voice in personal investment planning, Zvi Bodie of Boston University. Championing a “safety first” approach, Professor Bodie believes that if people were told how bad real equity returns can be and for how long, they would choose to replace equity bets with inflation-indexed government bonds. Our experience, with a business model that is indifferent to clients’ choices, does not bear this out.

It looks a reasonable assumption. Imagine your unbiased financial adviser walks you though a set of charts showing the cumulative real returns for between 50 and 110 years of the UK, US, Japanese and European markets. She shows you the grisly 20-year period since the Japanese market peaked at twice its long-term trend, subsequently languishing at about half the trend. But many other 20-year periods from market peaks are also flat or even negative. Even from an extreme low, in the 1974 bear market, she could point to a decade of flat returns, adjusted for the then high inflation, from continental Europe. You hardly need the American Great Depression to complete the picture.

All this history should be embedded in the assumptions about future real return probabilities underpinning investment advice. But this is only half the story. Investors also need to be told what it costs to avoid all forms of equity-related risk.

Prof Bodie is right to point out that individuals have a near perfect hedge for both inflation and economic risks, in inflation-indexed government bonds. Substituting risky assets by the risk-free hedge, it is possible to quantify the cost and benefits of avoiding equity risk, in the shape of a narrower and lower range of probable outcomes. Safety first must deal with “lower” as well as “narrower”.

Clients given both sets of unbiased information make different choices from those assumed by academics. We plan and manage goal-based portfolios for individuals using a process that closely follows Prof Bodie’s ideas about the economics of lifetime financial planning for households, as well as his text-book solution for combining risky portfolios and a risk- free asset. Our real return probability ranges for the risky portfolio, which is globally diversified, are realistic, conditional on where markets appear to be in relation to sustainable trends, specific to every time horizon, and the ranges increase with time. Duration-matched index-linked gilts are our risk free substitute.

Clients’ exposure to inflation-indexed risk free assets happens to be 36 per cent, but that largely reflects the average of their ages and risk preferences. Behind it lies a typical planning process. Conversations start with a safety first bias and then move away from it, in favour of deliberate risk-taking for longer horizons, because clients value the pay-offs. It is not because they are all young or very rich. They mostly have different goals competing for capital that risk-taking can help resolve. Even the wealthiest, who really can afford the high price of avoiding all equity risk, will not pay it because they believe that their capital (like their heirs) should not be lazy or inefficient.

Pauline Skypala, formerly the scourge of the retail investment industry when on the FT Money team, and now FTfm editor, usually focuses on institutional investment but in her Opinion piece last week she referred to a recent interview with Zvi Bodie in a US financial planning journal in which he argues that individuals would choose to hold inflation-indexed bonds in preference to equity-based investments if they were only told the ‘true’ risks of equities and were offered investment services that implemented a ’safety first’ approach.

As this post deals with a fundamental principle of modern planning and portfolio management, it forms a new part of our Research Resource. It accompanies my Feedback response published in FTfm today.

 In this post we

• explain the approach advocated by Prof Bodie and implemented in our Outcomes Driven portfolios
• provide a technical explanation without assuming technical knowledge
• observe what clients actually do when given complete information in an unbiased way. 

It is written for the three categories of people we know read our posts:

• professionals, both pure financial planners and wealth managers, who should feel challenged by this simple and robust alternative to conventional asset allocation techniques
• individual investors, who (with the exception of No Monkey Business clients) are not being offered this powerful alternative
• financial writers.

So No Monkey Business

Because we

• adopt the risk management technique for portfolio construction that Bodie Kane and Marcus (amongst others) set out
• base portfolios on personal outcome targets defined and set by clients with our help but not our direction
• charge flat fees loosely related to wealth levels but not to particular asset values or asset types

therefore we can

• tell clients the truth about risk and what it costs (in resources, outcomes or certainty) to avoid it 
• be economically indifferent to what risk they then choose to embrace or avoid

the consequences of which are

• the process leads where it leads
• if 36% of total holdings are now in inflation-proofed government securities that largely reflects the average age and risk preferences of our clients.

The FTfm article

We thought it would be interesting to share with FTfm readers where it actually leads. The answer appears to be that clients given complete and unbiased information take more risk, not less risk. This is not at all what Zvi Bodie expects or does himself (which he has made common knowledge).

This is not the article I most wanted to offer the FT. When Professor Blake of Cass Business School wrote a piece in FTfm recommending designing pensions from real spending outcomes back to resources and risk taking, FTfm published our response saying ‘clever us, that’s just what we do’. When Edhec Business School wrote a piece for FTfm saying it was time the private wealth management industry adopted the institutional techniques of asset liability modeling and liability driven investing, Pauline published a piece from us saying ‘clever us, we’ve been doing exactly that for the last five years’. So the article I would have like to write was ‘clever us, we did what Prof Bodie suggested and it works – for us and for our clients’. But we have limited bragging rights with the media so sharing practical insights about where it leads was a smaller ask.

Explaining the method

Like so much of what we do, the core of our portfolio construction approach is no longer innovative, if viewed in the wider context of institutional practice rather than retail investment services.  Its text-book definition is the Two Asset Portfolio, because it divides a portfolio into two independent components: risky and risk free.

Technical background:

The Two Asset Portfolio sits within the general theoretical framework of Modern Portfolio Theory (MPT) – the link opens Wikipedia in a new window – and the concepts captured by the Capital Asset Pricing Model (CAPM), the distinctive feature of which is the Capital Allocation Line. In imaginary space (usually depicted in a graph) defined by return and risk, it is the line which connects a risk free rate with the opportunity set of risky alternatives, such as different equity markets.

It does not, however, require you to assume that all the risky assets lie on the line. They could be distributed quite randomly in risk/return space in which case there are lots of ’optimal’ diversified combinations that share the characteristic of having the highest return per unit of risk, all of which maximum-effiency portfolios then mark out an Efficient Frontier. 

In a Two Portfolio approach, the optimal location on the Efficient Frontier is defined by the highest possible excess risk-adjusted return, which (graphically) is where the Capital Allocation Line anchored on the risk free rate is tangental to the frontier.

This general principle is adaptable to specific definitions of risk and return, which will in turn suggest the appropriate risk free asset. In most applications of MPT today, including the ‘factory model’ of standardised asset allocation, risk is defined as short-period variance in returns in nominal terms (usually monthly or quarterly standard deviation, annualised) and, consistent with that, the risk free asset is usually cash or Treasury bills.  However, if the portfolio utility is better defined by long-period purchasing-power outcomes, because of the nature of the client’s goal and how the client will measure satisfaction, the returns, risk and risk free asset should all be redefined to ensure they fit that definition of the utility.  

The Two Asset approach is often described by the term used in corporate finance: the Separation Theorem, because it treats the risky asset (or venture) as capable of being optimised separately from the identity and risk preferences of its owner. In the context of the ‘factory model’, which for convenience treats all portfolio utilities as identical and uses the same nominal short-period risk and returns, the idea that all clients could hold the same risky component of their overall portfolio is logical. In fact, however, the ’factory model’ treats the risky portfolio as the entire portfolio. This is what firms would be tempted to do if they could only raise fees for managing the risky portfolio and not for cash, hence the conspiracy theory.

We have established that the risk free asset and the optimal risky portfolio are the two separate building blocks. Therefore:

• how they are combined determines the overall risk of the portfolio 
• and becomes the way of personalising the risk exposures and managing them.

The theoretical solution for working out the right combination is indifference. It refers to being ‘equally satisfied’ by the prospect of earning exactly the known risk free return or the range of probable returns provided by the risky portfolio. You would be indifferent between the certain return and the uncertain returns. 

But we like the implication too that it is a choice that the professional advising you is indifferent to:

• we have no interest in what you choose
• and only you can choose.

Planning in plain English

The trick when translating a choice described by algebra into one clients understand is this:

• keep with numbers
• but apply them to outcomes, not returns
• and make them outcomes that they can relate to and are relevant (or maybe even vital) to them. 

With retirement planning this is usually dead easy (thanks, Prof Blake): it is sustainable real rates of annual gross ‘income’ or drawdown, where the probabilistic range of outcomes reflects both inflation and capital market uncertainty and how they each develop with longer time horizons. At some blended tax rate (depending on how the asset are held and taxed), gross draw translates into sustainable spending. ‘Sustainable’ means all of three things: it does not need to alter with changes in stock market levels but can be increased with inflation and the capital will not run our before the job is done.

Not only do clients understand this language but they can also control the conversation and take it on. They can elaborate their target outcomes, such as wanting more early in retirement, then less but allowing for more again at the end. They can talk about conflicts, such as between their own spending and benefiting children or charities. They can resolve them in terms they understand, such as gifting (or reserving) only as much capital as would leave sufficient to meet tolerable worst-case spending outcomes at a chosen level of risk taking.

The meaning of ‘risk free’

This solves the problem of a shared language but it requires one other thing, a unique risk free asset (thanks, Prof Bodie): inflation-indexed bonds. This is because most goals that individuals plan for have ‘natural’ outcomes, as the clients think about them (not as advisers do, note), that are defined by purchasing power at some future date.

Dealing with real outcomes at different horizons immediately tells us advisers that we have to deal with two risks, arguably equally momentous: capital markets and inflation. As noted in our technical explanation, most applications of portfolio theory, including the ‘factory model’, ignore the different effects of inflation at non-standardised horizons.

In the special case of drawing down capital for lifetime spending, the uncertain duration of the plan is a third source of risk, because we do not  know how long we will live. 

Why ILGs, not bonds

Because index linked gilts have a fixed duration and are inflation-proofed, and because they bear only the principal risk of the British government, they can be described as ‘risk free’ in terms of both inflation risk and equity risks (in a previous Insight we explained how most risky assets share the same sources of risk as equities and are derivatives of equity, as loosely implied by ’business risk’).

Non-indexed bonds, whether corporate or government issue, cannot perform this risk free role. Though bonds are the conventional ‘balancing’ asset in what we call the standard ‘factory model’ of diversified, multi-purpose portfolios, they only serve to transfer the risk exposure from business risks (which are actually positively linked to general inflation) to naked inflation bets. In the same way that a ‘level’ annuity without inflation protection is a gamble on the predictability of inflation, fixed income is not only not risk free, it is a big bet. It is also a bad bet.

In our opinion, conventional bonds do not even belong in the risky portfolio, once risk is being managed by dilution or substitution, because the weak diversification value of bonds is then redundant. The reduction in real outcome uncertainty relative to equities is small (unless you want to assume the historical instability and unpredictability of the inflation process is not relevant) and the reduction in expected return is very large. A bizarre product of traditional planning is that individual investors for most of their life hold conventional bonds and at the same time mortgage debt but without ever making any connection between the two. 

The power of the method

Our application of the Two Asset Portfolio follows  Zvi Bodie’s idea of a ‘ladder’ of stepped, horizon-matched ILGs combined with an optimal combination of global equity markets (using trackers - why blow all the good work on risk and cost control done so far?) where risk tolerance or indifference is directly exhibited by the way clients choose between different ‘model runs’ illustrating different combinations of 

1. resources assigned to the goal 
2. ranges of real outcomes at different dates 
3. the thing that makes them balance at any required level of confidence: a level of risk tolerance.  

The power of the method lies in the fact that clients do not need to know what #3 means, or what it looks like when dropped into risk/return space so it cuts the Capital Allocation Line (pretty though that is). They only need to know what changing #3 does to #1 and #2, as in its effects on the certainty of achieving the target outcomes for a given level of resources (present capital plus future contributions). These effects they see. They can see as many runs as they want till they get to a solution for each goal, and between competing goals, that gets the job done in the way most satisfactory for them.

The evidence about equity risk

Using a financial model, clients will only be confident about the numbers you show them if they can see where they come from. Here, Pauline Skypala and Zvi Bodie are both right that the industry does not seem to want you to know how bad real outcomes can be, even with long expected holding periods. They have used every trick in the book to disguise risk. Although this partly carried over from an early tradition of paternalism, I do not believe this excuse holds any more and therefore lean towards conspiracy (otherwise No Monkey Business would have been a dishonest title for my book).

The Feedback article describes a process we use of walking new clients through a set of charts that show the cumulative real returns of the major equity indices for up to a century of data. We point out the long periods of flat or even negative returns, which are the real product of equities dealing badly with the inflation or business environment and investors making bad decisions about discounting the continuation of bad times. This is the flip side of the long bull market phases that selective memory (and advertising) might otherwise bias towards.

Here is one example, for the US market, used in a recent post discussing the valuation of the S&P.

Fig 1 Real total returns and fitted trend: S&P 500 (semilog)

The trend for the entire data history from 1925 (the unbroken orange line) is 7% pa. This is the ‘engine’ driving the funding of future financial goals using equity investments. But this underlying driver is literally overwhelmed over short periods by the scale of the deviations from it. Note how frequently real returns are flat for decades at a time. If you bought at the height of the ‘nifty fifty’ growth-stock boom in the 1960s you had to wait over 20 years to get you money back, when inflation is taken into account. Talk of a double dip if market falls again now is not quite accurate. If we look at the period since the dot com bubble burst in 1999, another dip will be the third in a long ‘correction’. We are already over 10 years in.

You hardly need our gruesome charts for Japan to see that equity returns can be negative or flat in real terms for very long periods and that you will almost certainly experience extreme disappointment in a lifetime of investing. Welcome to the world of true risk. 

Feedback: what clients actually choose

Zvi Bodie’s point is appealing: why would anyone run these kind of risks? The answer is simple: if they cannot afford, or do not like, the alternative.

Emphasising the risk is itself a bias unless we are also careful to explain and illustrate the cost of avoiding risk. It is the high cost of avoiding risk, in possible outcomes permanently given up or inefficient use of capital, that leads our clients to opt for a higher level of risk taking than is assumed by academics.

I did not have room in the FT article to illustrate this but I show below an example we have used in retirement seminars. It uses numbers (real or purchasing-power pounds) to show the cost in resources applied or in consumption enjoyed of replacing all equity bets with index linked gilts (’taking bets off the table’) and the further cost of removing the longevity risk by buying an index linked annuity (’leaving the casino’). The resources assigned are £2m; the resources have to last for 35 years at least and the client values higher spending early in retirement. The three alternatives are:

1. Sustainable draw with optimised risk taking: you could start at £125,000 pa with a 50% chance it will need to taper down to £105,000, and a 99% chance of not breaching a worst-case floor draw tapering from £125,000 to £57,000 in the client’s late 80s if markets are consistently bad.
2. Allocating 100% to ILGs throughout the plan: to match the worst-case outcome above takes capital of £2.2m and to match the better possible outcomes at 50% confidence (the median with optimised risk taking) takes £3.2m – a ‘resource cost’ of £1m.
3. Avoiding all risks including longevity: £2m buys a real income of £64,000 pa – an ‘outcome cost’ of £61,000 pa in the early years and £41,000 pa at the end.

The point is, the numbers speak for themselves. Given complete information about both the scale of the risk and the cost of insuring or avoiding them, as factors in this realistic practical example of half or twice, you are likely to stay at the table.

Incidentally, the multiple of two that describes the value of an inflation-proofed annuity applies also to the value of final salary scheme pensions. This is what it would cost you to replace what is effectively a large ILG ladder on your personal balance sheet. It means that one of the hardest decisions high-earners often face is whether to bear the risk that their pension scheme and its sponsor will both collapse under the intolerable burden of meeting its over-generous promises, with the consequence that a pension of £150,000 a year drops to the ‘insured’ level of £30,000. Up to the insured level, it is a risk free asset but above it there is a very small chance of catastrophe. Some advisers believe that even the insured level, being underwritten only by scheme levies to build up a protection fund, could be reneged on if the fund is overwhelmed by system-wide failures.

Are our clients representative?

This is not a controlled experiment: most of our clients are in the top 1% by wealth and income. Other investors and other advisers might assume they can afford to embrace more risk. This misses an important point. People take bets instead of laying them off because they value the payoffs. They think about the possible payoffs in terms of consequences. For goals such as retirement spending, the resources may be higher but so are the levels of spending at which the consequences look unpleasant or even intolerable. It is all relative. Rich people as well as poor people make rational gambles. It is mainly when you drop below the typical IFA target customer that the gambles are not constrained by own resources and are framed largely in terms of externalities, such as social security. 

In my Feedback piece I also suggested that the wealthiest, who could actually afford to live off the cash streams, capital or interest, from their ILGs (like their Victorian forebears who ‘clipped coupons’ on their Consols and never thought to work), choose to to take risk instead. A common motivation we see is that ‘capital should work hard’, because they worked hard to get it. Less common but just as important is that playing the game is its own reward, so satisfaction or success is measured as replacing (through return on investments) the money consumed. 

Is it more expensive?

In another important respect our clients may not look representative because they can afford the economic cost associated with planning goal-based portfolios where resources, risks and outcomes are the product of interaction with sophisticated technology (which is expensive to develop or license) and where confidence in the process calls for education and explanation as well as illustration (which is time consuming).

Our answer to this has always been simple: pay for it with the savings you make by opting out of the industry’s deeply conflicted factory model and its dependence on active management. These pile up the costs but have no economic worth.

The ILGs cost between £9.50 and £12 to buy and nothing to hold; the equity ETFs or tracker funds cost between 0.2% and 0.5% pa to hold.  At our average ILG holding of 36% (reflecting the sum of all customised combinations) for Defined Outcome portfolios, we cut typical implementation costs to 0.24%. This compares with published charges from industry giants like Towry Law of 1.6% (on which may be loaded asset-based fees for new contributions and tax wrappers). Many smaller IFAs will apply total costs of 2% or more, by loading up portfolios with expensive active products they cannot discount, and private banks load them up with their own products where they have no incentive to discount. Savings of 1.36% to 1.76% pa pay for an awful lot of unbiased, high-quality advice and education.

This example demonstrates that there is very high umbrella of inefficient charges resulting from traditional industry structures and investment processes. There is no reason why modern, technically-proficient firms should not compete successfully under this umbrella, offering better solutions at a lower price at a decent profit for themselves.

Equity risk as a mirror of business
Market economies, like religions, are adaptive systems responding to the shifting needs and attitudes of society from one period to another. What they retain is their essential dependence on businesses, great and small, as the driver of the performance of the economy through time. Governments can make transfer payments between individual citizens and can help soften the collective blow of changes in the tides of economic performance. But these will make relatively little difference to the impact of these shifting tides in business conditions on individuals’ financial welfare.

With the benefit of a long historical perspective it is possible to see that market economies have in fact adapted very successfully, hence the fundamental nature of equity risk is much more stable and predictable than we might intuitively expect. Nonetheless, it is clear that the shifting fortunes of business through time mean that different generations may well experience substantially different economic outcomes. Investment returns are an important manifestation of those outcome differences. It may seem unfair and undesirable but it is part of the essential nature of equity risk.

For the purposes of this Insight, it is much more sensible to think of equity risk as the measure of business uncertainty, across these shifting tides, than it is to focus on some much narrower statistical definition of risk such as volatility, or dispersion of short-term returns. Because these tides are themselves best observed in real terms, undistorted by inflation, it is uncertainty of real outcomes that is the measure of equity risk we want to encourage. Contrary to the view the financial services industry seeks mischievously to inculcate in its customers, equity risk does not reduce with time and this is an important piece of conventional thinking to unlearn.

In practice, it is difficult, if not impossible, for individuals to live their lives free from equity risk even when they actively seek to avoid its most obvious form, when holding equity investments. It is ubiquitous and unavoidable, through employment, accrued pension rights, asset holdings, liabilities and contractual investments.

Since equity is the source of wealth creation, we will later ask why, knowing the cost of trying to avoid equity risk, people should even want to, instead of leading their lives in some deliberate and sensible accommodation with risk.

Equity risk overwhelms diversification
When investors hold financial assets directly, under advice or via a discretionary manager, they are likely to follow a fundamental portfolio principle of diversification: spreading risk. Our high-level view of equity risk poses no problem for one aspect of diversification, which is the avoidance of unrewarded specific risks, but it does pose a problem for a second aspect, which is spreading the exposures across a number of different types of asset.

Specific risk refers to the idiosyncratic risks of individual assets, such as shares in a particular company, and contrasts with undiversifiable ‘systematic’ risk of a market or asset class as a whole. Academic evidence suggests that the system risks, which tie in closely with our high-level notion of tides in business conditions, are rewarded by ‘risk premiums’ whereas undiversified exposure to specific risk is not rewarded. The investment industry can adopt this distinction very easily by using diversified vehicles that reflect the market system, such as actively-managed or index-tracking collective funds, or by designing portfolios of individual securities within a market that are well diversified.

Entrepreneurs will protest that individual business risks are rewarded and that diversifying away all the exposures to specific risks is the wrong principle. There is no need for dispute here as they are essentially two very different ways of investing. Problems tend to arise when investors do not clearly select between the two approaches or when they fail to identify their true preferences, or belief systems, and invest out of character, such as imagining they are entrepreneurial when in fact they are system players. It is also perfectly possible that the same investor will apply both approaches, perhaps for different purposes and with different sources of capital.

The distinction between assets classes
The principle of diversification of capital between a range of different types of assets or strategies is to reduce the statistical measure of risk, volatility or dispersion of short-term returns, on the basis that it should be possible to do so without reducing expected returns. In a world abhorring free lunches, diversification between asset classes can look like the only free lunch available.

The numerical characteristic on which this depends is correlation: the way different asset types move together. If those movements are not perfectly correlated, there is scope to smooth the return path of the combined portfolio.

Our high-level view of equity risk overwhelms the differences between these asset classes, in terms of the underlying risks that characterise them, and reveals them to be essentially different versions of, or derivatives of, equity risk.

To illustrate this, we take as a starting point a diversified portfolio benchmark of the Association of Private Client Investment Managers (APCIMS). To reflect the increasing use of structured products and private equity at the top end of the private wealth management market we have arbitrarily reassigned 5% to each from the equity share of the benchmark.

The three conventional slices of the pie, equity, property and fixed income, are distinguished here from the additions to diversification, hedge funds, private equity and structured products, whose slices have been lifted out.

If we apply the thinking of underlying business risk to each of these portfolio building blocks, we can summarise as follows:

• Commercial property is a subset of corporate balance sheets and cash flows, since the rental income streams are entirely dependent on the capacity of businesses to pay and honour their covenants in all other respects.
• Fixed income has three risk components, nominal interest rates, inflation and credit quality, each of which is a reflection of the high-level business context. If within a structure of diversification we were to avoid unrewarded bets, consistent with first principles, then we would not want to take on inflation risk but might retain credit risk. It is self-evident that the market’s changing perceptions of the chance of default are a first and foremost a judgement on equity capital surviving bankruptcy.
• After the chastening of the credit crunch, high-brow opinions about private equity are shifting towards the more prosaic academic view that returns are a function of public equity conditions with the addition of leverage. Both buying and selling prices are set largely by public equity-market conditions. Proponents may also argue that the private phase allows transformation in the underlying performance of the business that would not be possible in the public market but this flies in the face of the history of change in public companies.
• Structured products are not necessarily equity-based but we think the vast majority are. The structure only alters equity risk to the extent of introducing asymmetry in the payoffs, as in any option strategy. On a theoretical basis, rolling over equity options is self-defeating, like all forms of portfolio insurance, as the mean cost is a function of volatility which itself is related to the mean risk premium for bearing equity risk.
• Hedge funds encompass a wide range of strategies but equity risk still dominates, particularly when private clients obtain their exposure through funds of funds.

On this analysis, the 45% that is diversified away from pure equity volatility is not avoiding equity risk as we have defined it. Virtually all the portfolio is at the mercy of the shifting tides of business conditions and this is what long-period portfolio outcomes, in real terms, will tend to reflect.

What do we know about equity risk?

As soon as we define this in terms of real returns from markets as systems we know we can use historical return data for published, representative indices for different equity markets to understand and quantify equity risk. A corollary of viewing the market as a system is that we should measure ‘total’ returns, income and capital (so that income distributions are treated as being reinvested), since the consumption of income is an individual choice, often arbitrary, not a system feature.

We show below a series for the UK equity market from 1900 that is based on the annual Barclays Gilt Equity Book, which provides back-filled data prior to the formation firstly of the 30-share industrial index and later the launch of the All Share Index. This is similar to the UK data assembled by Dimson, Marsh and Staunton for their ground-breaking book, The Triumph of the Optimists, which examined a century of returns from equity investing around the world. The UK market data benefits from genuine continuity, whereas many European markets and Japan suffered bouts of hyperinflation that distort the history of real returns. Post-war reconstruction can also effectively mean that the returns were enjoyed by different investors before and after that hiatus. The UK and US equity markets are the two major markets that are unusual in avoiding all such distortions. In all cases, money returns are converted to real returns using a recognised, contemporaneous measure of retail prices in each country.

UK Long Term Real Return Trend

The index itself is calculated by compounding short-period, deflated total returns. It is presented in log scale to ensure that the changing rates of change are always proportional (contrasted with non-log series for financial assets that tend to show exponential growth towards the top right-hand corner of a chart).

The visible features are i) a trend and ii) cycles around the trend. Cycles are different from random deviations from a trend because successive observations are themselves serially-correlated. The trend is a measure of systematic ‘reward’ for bearing equity risk and the cyclical deviations are a measure of either or both of the underlying business cycle and a tendency for market sentiment to follow a herding principle.

Two trends have been fitted to the data: one (grey) for the observations that could have been made without hindsight up to any point of time and the other (yellow) a single trend fitted to the entire series. Differences between them speak of the broad shifts in business conditions we like to focus on. The slope of the whole-period trend for the UK is 6.2% per annum. This represents the ‘typical’ systematic reward for bearing UK equity risk.

However, because the deviations from the trend are clearly very large (after cumulating in a cyclical fashion perhaps over many years), the typical rate is never going to serve as a good forecast of the future rate over some shorter period than another century. These deviations are a key component of equity risk, pointing to a wide degree of uncertainty about future real levels. Uncertainty about where we will end up is not the only measure of equity risk since we may also be unsure about both the validity of the observed trend and the starting position in relation to the trend. These sources of uncertainty are directly related to the amount of data we have to work with, although we will never know how much data is required to be truly representative.

Mean reversion
The feature implied when a trend appears valid over a long time series is ‘mean reversion’. Since a purely random series may also show an upwards drift, it is not enough to assume mean reversion is actually at work. But there are statistical tests (summarised in No Monkey Business: what Investors need to know and why) that confirm the likelihood the process is genuinely mean reverting.

From a theoretical point of view, this is entirely consistent with other widely-accepted evidence of mean reversion in economic components of equity returns that are based on some equilibrium theory. Examples are the competition between returns to labour and capital, which tend to make swings in the balance of advantage self-correcting, marginal returns on capital in business and rates of dividend distribution compared with retention for investment. If these fundamental business drivers are mean-reverting it follows that deflated measures of corporate financial performance, such as earnings per share, will be mean-reverting and that the market valuation process based on such observations, such as price-earnings ratios, will then in turn be mean-reverting.

The size and duration of deviations from trend evident in this UK series nonetheless imply that the mean reversion process is quite weak in explaining short-period returns. The profile of these deviations is also itself highly variable, because of the unpredictability of the large shifts in business conditions that prompted this Insight.

In the UK’s history we can single out 1973/4 as a truly exceptional bear market, coming from a peak ratio of trend of 126% in 1972 to an eventual ratio at the bottom of the bear market of 36%. Yet within 12 months of the low, the ratio had recovered to 67% and was back on trend by 1984, less than a decade later.

This V-shaped recovery contrasts dramatically with recent experience in Japan. The same chart for Japan, using data from 1957 (which we treat as undistorted by the post-war recapitalisation of the Japanese equity base), shows a bear market commencing in 1989 at a peak ratio of 187% which reached a ratio of 67% in three years. For the next 10 years, mean reversion failed to occur and the ratio eventually drifted down to 39% (very close to the UK’s bear market low point).

Japan Long Term real Return Trend

Although Japan is widely viewed as enduring an exceptional period of economic adjustment, not shared by other countries, this is simply not the case. This sort of massive adjustment process, impacting dramatically on achievable equity returns, has also occurred in Europe and the USA. Reflecting the poor recent performance, the observed trend for Japanese real returns has been drifting off and at 5.3% pa is substantially below other markets.

Europe ex UK Real Return Trend

Japan’s ‘lost decade’ was mirrored in the period of ‘Eurosclerosis’ that marked the 1980s. Partly an inability to adjust to high inflation, Continental Europe also struggled to adjust its post-war industrial model to much slower domestic growth and increased global competition. During its lost decade, both real profits and dividends declined dramatically before the pendulum of mean reversion in underlying economic performance started to swing back, and with it stock market returns. Its whole-history trend is 6.9% pa so it has clearly made up for this blip.

The US history of real returns (based on the S&P 500 Index) also provides examples of long-duration deviations from trend. Because of the data length (and quality) we can be more confident the observed trend of 6.8% pa is representative.

US Real Return Trend

Contrary to popular opinion, the Depression era was not marked by the failure of equity returns to mean revert. Though unemployment ravaged the nation, aggravated by the dust bowl that was impervious to economic initiatives, industrial output was pushed up within three years of the 1929 Crash and real stock prices followed. It is impossible to separate the initial effects of the New Deal from the impact of world war and many observers believe it was the latter, not the former, that eventually underpinned America’s economic revival.

On the other hand, America’s adjustment to the testing economic conditions of the late 1970s led to a much slower recovery in real share prices, albeit from a less extreme ratio in 1974, than the UK. It took 20 years for the market to get back on trend.

Positive deviations that persisted for a long time are just as important in determining actual returns and in shaping the views of contemporary investors about equity risk. Many current UK investors are likely to have been influenced by the persistence of above-trend real returns from about 1990 until this recent bear market began. Likewise, the overvaluation of US stocks that peaked in the late 1960s (particularly growth stocks that were in the front-line of globalisation) may well have reflected complacency about the persistent above-trend returns from the mid-1950s.

Quantifying equity risk

These data histories provide us with a measure of the realistic scale and duration of the shifting tides that lead to substantial differences in achievable returns from equities and other asset classes. They also provide us with a basis for making mean expected returns a function of starting conditions, provided we believe the process really is mean reverting.

Given the similarities between the return processes (and even the observed trends) in these four market groups, it is sensible to assume that the equity return process, as s system, operates very similarly in different countries, overwhelming cultural differences and even persistent differences in economic power and performance. Mean reversion makes for a flatter world than intuition (or a little economic knowledge) might imply.

It is therefore sensible to assume that:

• Anything that has occurred in one place can occur in another
• Anything that has occurred in the past can occur on the future
• Things will occur on a scale and with a frequency in your own lifetime that ensure that your own outcomes will be subject to the uncertainty of large-scale changes in business conditions
• Any complete range of possible outcomes must allow for multi-asset class diversification to be overwhelmed by the dominance of this form of equity risk.
• Using a long-term asset model (‘Lambda’) We believe that we can quantify the full range of outcome uncertainty at any future horizon based on our interpretation of current conditions. Even when we believe the data is representative, the uncertainty is still going to be greater than many professional investors and advisers glibly suggest to their clients. However, in markets with less data or less reliable data, notably Europe (ex UK) and Japan, we will expand the range of uncertain future outcomes even further to allow for this possible source of error.

A further adjustment we need to make in quantifying uncertain future outcomes is for currency risk when projecting returns in foreign markets. In a real-return modelling framework, foreign markets are as capable of generating real returns in one currency as another, on the basis that differences in their inflation rates will tend over time to be offset by nominal exchange rate changes (another equilibrium theory known as Purchasing Power Parity). The risk associated with currency is therefore the movements in the exchange rate not explained by actual observed inflation differences. This is easy to measure. Combining the two sources of risk, equity and currency, needs to reflect the fact that they appear to be independent of each other.

Equity risk and time
What emerges very clearly from our quantification of equity risk is that it is completely at odds with the popular industry canard that equity risk declines with time, or that uncertainty about returns reduces the longer the forecasting (or assumed holding) period. The only measure of equity risk that declines is the annualised standard deviation or measure of dispersion. Mathematically, this is a function of the square root of time for a random series, and some greater rate of reduction in the case of a mean-reverting time series. As soon as you compound the annualised rates over the actual forecasting period, it becomes clear that equity risk continues to expand with time. This phenomenon was expressed by a leading actuary many years ago as the ‘expanding funnel of doubt’ and it is a phrase we find salutary to repeat in our conversations with clients.

How can it be that the investment industry can so blatantly misrepresent such an important attribute of equity risk in its marketing literature and in its communications with clients? We are at a loss to know whether the explanation is ignorance or cynical mischief-making. The cynical view assumes that the industry has a bias to understating risk so as to encourage investors to buy high-margin products, because the margins typically follow the underlying investment risk. Indeed, there may even be a twisted logic to the tactic since it becomes irrational to invest in products with high charges unless they have some scope for high returns, however small the chance of clearing the cost hurdle and earning those returns. Unfortunately, this is not a conscious rationale investors are invited to engage in.

We show below an example of the expanding funnel of doubt for a foreign equity market with a fairly long data history, an observed trend of 6.6% pa and a starting ratio of 50% – so reasonably close to current conditions in several major markets. Costs are assumed to be minimised by using trackers rather than active funds. The range of possible outcomes is with 99% confidence, which is theoretically as confident as any modeller can be and allows for the very small chance that the entire model assumption about systematic equity returns is either wrong or for some reason breaks down globally.

At 15 years, the probability of earning a zero real rate of return is 1%. The model assumptions about the strength of mean reversion are such that most of the return difference from starting conditions should have been reflected in 15 years.
What better ways to manage equity risk?
If diversification between different classes is not a good way to control the outcome uncertainty that can dramatically impact individuals’ financial position, is there a better way?

Clearly there is but though consistent with modern investment theory (and some institutional practice) it is inconsistent with the dominant retail investment business format.

The solution is dilution of equity risk, by holding offsetting positions in risk free assets. For this purpose, it is vital to define the individual’s purpose for the money as this will determine whether the risk free asset is one that needs to include inflation protection. For any goal whose target outcomes are defined in terms of purchasing power (such as retirement spending), the only risk free asset is index linked gilts, since these carry a guarantee of full (and largely untaxed) compensation for future inflation whatever it turns out to be. For very short horizons, it may be practical to bear some inflation risk, however, and treat cash as risk free.

The array of possible alternatives to equity risk looks very different when defined in terms of each of nominal return volatility (which we also call ‘path risk’) and long-horizon real outcome uncertainty, which we have identified as more important for personal wealth.

The y axis plots the uncertainty of real outcomes and so has cash as relatively risky, whereas on the x axis cash has no path volatility and is essentially risk free. The outcome risk arises because the nominal interest rate paid mostly consists of the market’s assumed required compensation for future inflation. If markets were both good at anticipating future inflation and also able (subject to monetary policy goals) to secure the required compensation, there would be little error in real outcomes from holding cash. In practice, both inflation forecasts and monetary policy influences have given rise to large differences in inflation compensation from cash, ranging from very generous to negative real rates. These errors can compound over long periods, hence introducing an expanding funnel of doubt for cash too.

It is conventional fixed interest whose location, and portfolio role, most changes when expressed in terms of cumulative outcome uncertainty. This is another version of the inflation guess but with the important difference that with fixed income there are far fewer opportunities to adjust the guess. At least with cash, the market can make new forecasts in response to new evidence about inflation, possibly as frequently as daily. With fixed income, you have one guess at the point of purchase and then only small opportunities to reset the guess as a function of the yields at which interest is reinvested. If interest is being spent, the accuracy of the forecast will not even benefit from these other opportunities.

The location of real outcome risk reflects the UK’s particularly bad experience of inflation forecasting and its impact on fixed income, with deeply negative real yields in the 1970s followed by over-compensation in the 1980s. Because the inflation process is so hard to understand and model, it is pointless taking on this sort of bet.

It is also entirely unnecessary since index linked gilts, perfectly matched to your personal time horizon (or series of horizons), get the job done perfectly. Though there may be quite high path volatility prior to redemption, particularly for longer-dated index linked gilts, the investor is in practice indifferent to that movement since the cash flows are perfectly matched.

In the schematic below we illustrate the principle of using index linked gilts to narrow the funnel of doubt by diluting the equity exposure. It is clear that dilution also lowers the slope of the funnel.

The cost of avoiding risk
The expected real return given up when equity risk is diluted needs to be quantified if individuals are to determine their personal risk preferences. In a quantifiable modelling framework like Lambda, each of the key parameters, i) target outcomes ii) time horizons iii) resources required and iv) level of risk taking, can be expressed numerically and illustrated graphically. Running different iterations can quickly demonstrate the trade-offs required, such as between the additional resources required if taking more risk, assuming an unchanged level of confidence in the outcome.

In the example below, we show a retirement spending goal in which the client’s stream of cash flows for spending are organised by three-year time slices. Each is separately funded to produce outcomes within the agreed bands, represented by the candlesticks. In this example, the resources required with optimised risk taking, to meet a schedule of gradually tapering spending targets, are £2m. The approach to risk is dynamic so that the mix between risky and risk free will change both as market conditions change and as the plan gets shorter. These dynamics are reflected in the amount of time-slice risk, as if for a plan rather than for a portfolio.

On a worst-case basis, the sustainable rate of draw from the portfolio will be £125,000 pa tapering to £57,000 pa. But if the mean expected returns are achieved, the initial rate of real spending will barely need to taper, ending at £105,000 pa in real terms. There is a 50% chance spending can be higher than this, or surplus assigned to other goals.

To avoid all equity risk and fund these cash streams entirely using index linked gilts would require assets of £2.2m to match the worst-case outcome and as much as £3.2m to match the mean expected outcome with risk taking.

Clearly, there is a high cost for not staying at the table in this casino. But the client can also at some stage leave the casino itself, by purchasing an index linked annuity. However, applying all of the available £2m to an annuity now will generate a sustainable real income of just £64,000, nearly half the initial rate of draw and barely above the worst-case tapered draw late in the plan. At a much later stage, on the other hand, maximising spending may be better achieved with an annuity than continued risk taking, particularly if a client assigns a low value to leaving capital at death as a bequest.

Knowing these costs of avoiding even pure, direct equity risk, it is not at all clear that most investors would want to.

It is because this process is entirely customised that the existing industry formats would struggle to adopt it. It is important that the process be highly quantitative, and delivered with slick technology, to offset the cost implications of mass customisation. But it also requires other changes in business approach, not least the fixing of flat rates of fee for a portfolio service, to ensure that the manager is completely indifferent to the risk-taking preferences exhibited by the client.