Alongside such hardy annual harbingers of Christmas as the John Lewis advert and the return of Noddy Holder to the airwaves, I am also seeing an increasing volume of “year ahead” outlook notes from investment banks and fund managers.

Some are surprisingly specific in their predictions. One in particular suggests the possibility of a “melt-up” for equity markets (specifically the US) early in 2020, followed by a violent correction and then a strong recovery to leave the index barely changed on the year. Such a prediction requires near perfect insight into the economic cycle, the US presidential election and human behavior, and while I take my hat off to them for trying, I can’t help feeling that the strategist in question is on a hiding to nothing.

The call for the prediction of the S&P 500 reaching as high as 3,400 by the end of next year, or as low as 2,600 (now 3,110), is almost entirely predicated on the outcome of the US election and how that will affect the market valuation

Another approach is to set out a range of outcomes based upon different scenarios. One such note sees the S&P 500 as high as 3,400 by the end of next year, or as low as 2,600 (now 3,110). The call in this case is almost entirely predicated on the outcome of the US election and how that will affect the market valuation. Further uncertainty is introduced with a long list of possible influences, including the US/China trade war, market illiquidity, corporate leverage and anti-trust investigations, giving the strategist plenty of hiding places.

I am actually more comfortable with the latter approach, because market returns become essentially more random in nature the shorter one’s investment (or prediction) horizon. It’s one reason why you won’t find me making year-end predictions for the level of the FTSE 100 Index, for example. But growth trends and a tendency towards mean reversion in terms of, say, relative valuations between asset classes, can be more informative over longer periods.

The Swiss mathematician Jacob Bernouilli is credited with being the first person to prove the relationship between probable outcomes and the frequency of events. He noted that calling the toss of a coin just once produces a binary outcome – you’re either 100% right or wrong depending on whether it comes up heads or tails. The more times you toss the coin, the smaller the probability that the cumulative percentage of heads or tails will diverge from 50%. This is known as the Law of Large Numbers.

Jacob Bernouilli's theorem underpins the basic concept underlying a vast of amount of money which is run in “quant” strategies today.

It might be a stretch to describe Bernoulli as the first quantitative hedge fund manager, but his theorem underpins the basic concept underlying a vast of amount of money which is run in “quant” strategies today. Unfortunately even these are not guaranteed to provide smooth positive returns owing to the existence of “fat tails”, events that fall outside the normal distribution curve. These were popularised as “Black Swans” by Nassim Nicholas Taleb.

In the real world we are beginning to appreciate their increasing presence thanks to the effects of climate change and the incidence of, for example, “thousand year floods” that occur three times in a decade. Given that the managing and pricing of risk by insurance companies is based upon the actuarial application of the probabilities of particular outcomes, you can see how this could have severe implications both for the financial health of the insurance industry and the ability of householders to obtain affordable cover.

On a somewhat longer time horizon, we are currently working through our annual exercise to estimate – I’m deliberately not using the word “forecast” – seven-year forward returns across a range of asset classes. These are then bundled together at a portfolio level.

Although such an exercise might seem equally as futile as trying to predict the short-term level of the FTSE100, it does serve to provide an idea of the returns a client might reasonably expect to generate over such a period. That can be important in setting realistic expectations as to what needs to be saved or can safely be spent. It can also determine how far along the risk curve clients need to go in order to achieve their required or desired returns.

One huge caveat about such return forecasts is that although we produce an annualised number, we also know that returns tend to be non-linear, and so are punctuated with big falls and rises along the way. This has become a very hot topic for those in the “decumulation” (sorry, horrible word, I know) phase of the investment cycle because of the risks posed by a severe fall in the value of a portfolio in the early years of decumulation, known as “sequence risk”. I rarely give a plug to other services that we provide, but some of my colleagues have recently devised a new Targeted Drawdown Strategy that can help to mitigate such risks.

Our process of estimating future seven-year returns has been in place for six years now, and so we are beginning to get an idea if it is any good. In December 2013, the projections were as follows. For a Medium Risk Income portfolio: 4.8% annualised; Medium Risk Balanced: 5.9%; Medium Risk Growth: 6.3%. After almost six years, the actual returns (based on our Strategic Asset Allocation benchmark, so not accounting for any excess returns produced by asset allocation and stock-picking) are respectively 7.02%, 7.57% and 8.13%.

Three key observations. First is that the returns are running better than we expected, much of which will have been generated by the persistent upwards re-rating of equity valuations. Second, the dispersion of returns between the models is lower than expected, with bond yields having fallen far further than we thought possible thanks to low interest rates and Quantitative Easing. Finally, and linked to the last point, volatility has been much lower than expected (despite the odd ructions along the way), realising at 5.76%, 6.47% and 7.26% vs estimates of 8.2%, 11.1% and 12.4%. This, in risk-adjusted terms, means that the last six years have been phenomenally good. Given the current starting points, it is difficult to see the next six years being so kind.