Everybody's complaining about our post-truth society and fake news. Implicit in such complaints is the idea that truth is a binary thing - that claims are either true or false. In many cases, though, this is not the case. Many things can be true, but useless or even downright misleading. Instead, there is a zone of imprecision, an area where statements are more or less reasonable. It is this domain that investors must live in, and make themselves comfortable with.
Let's take an example: what is the correlation between bonds and equities? This question is the basis of asset allocation. The more negative is the correlation, the more likely are bond prices to rise if shares fall. This would mean bonds are a hedge against equities, which would mean we could hold lots of shares in the knowledge that we have insurance against them falling - just as we can drive faster if we have car insurance. A positive correlation, on the other hand, would mean that shares are riskier, as we have no such hedge.
So which is it? We can make a precise statement: Since January 1986 the correlation between monthly returns on the All-Share index and on the FTSE UK all government bonds index has been 0.15.
But this is like a plumber telling you he'll call at 10.27am. It's precise, but not necessary true, at least in a sense investors can use. History tells us that sometimes equities and gilts have been negatively correlated, and sometimes positively so. The investor who acts on the precise correlation of 0.15 could take on more risk than he's bargained for if the correlation between the two assets turns out to be higher than this in coming months.
Herein lies the problem with optimal portfolios. As the finance writer William Bernstein has said, we can only build a truly optimal portfolio if we know future returns, variances and correlations. But we don't know these, and cannot know them. We can have precise numbers about their past values, but these might not tell us about their future ones.
You might think this is obvious. If it had been, we'd not have had the financial crisis. One reason why banks held so many mortgage derivatives in the mid-2000s was that portfolio optimisers told them to do so. Precise numbers said that such instruments offered higher returns than government bonds while offering great security. Those precise numbers, however, turned out to be a bad guide to the future, and losses on those derivatives drove some banks to the wall. An acknowledgment of imprecision would have served banks' shareholders and the public much better than precise numbers.
Conversely, the statement "bonds and equities might move in the same direction or might not" might seem trivial and imprecise. But it's true. And it's useful, as it warns us not to rely on a precise number and not to think we can optimise our portfolios.
As banks learned in 2007, precision can be worse than useless. It can give us what the Nobel laureate Daniel Kahneman has called an "illusion of certainty" and so cause us to become overconfident.
Some experiments at Princeton University by Alexander Todorov and colleagues have shown this. They asked people to forecast the results of basketball games and found that subjects who were given more information about the teams made worse predictions than those who were less informed, although they were also more confident in those wrong predictions. More precise information, then, can be worse than useless.
Let's take another example. The efficient market hypothesis says that share prices immediately embody all available information and so you can't beat the market unless you take extra risk. Is this true?
Precisely speaking, no. We know that momentum and defensive stocks on average beat the market and don't seem riskier than others in most senses.
But it doesn't follow that the theory is wholly false. Quite the opposite. The Financial Conduct Authority said recently that "funds which are available to retail investors underperform their benchmarks after costs", thereby confirming lots of other research. One of the main implications of efficient market theory - that you shouldn't spend money on fund managers - is thus vindicated. The theory isn't precisely correct. But it's true enough to be useful.
If we ditch efficient market theory because it isn't precisely right, we lose a useful guide to action.
I've just said that defensive and momentum stocks beat the market, but what do I mean by defensives and momentum? I've defined these precisely in my no-thought portfolios: momentum stocks are the 20 biggest risers in the past 12 months among stocks with a market capitalisation of over £500m, and defensives are the 20 with the lowest betas, based on monthly returns in the past five years.
I use such precision, however, only because I need it to operationalise and test the theories that defensive and momentum investing works. But my confidence that they do so does not rest upon a precise definition of defensives or momentum, nor on the precise results of any single particular test. Instead, it rests upon a large body of evidence which shows that defensive and momentum investing works in different markets under different definitions and in different times. It's the general body of evidence that matters, not any particular precise result.
There's yet another sense in which imprecision matters - in economic forecasting. When economists say that (for example) inflation will end this year at 3 per cent they don't mean it will be precisely 3 per cent - or at least, they shouldn't mean this. Instead, they mean that they believe that the centralish point of their range of probabilities is for inflation to rise to a rate significantly but not alarmingly above the Bank of England's 2 per cent target.
Similarly, when I use lead indicators to forecast equity returns, I do so only for the sake of completeness - and to show that I've done the work. I really only mean to say that my least worst centralish estimate is for returns to be around average.
Most people, when forming expectations, do so imprecisely. We have a hunch or gut feel about our job security or whether we'll get a decent pay rise or some big orders - usually nothing more precise than that. If there can be knowledge of the future, it's often what Michael Polanyi called tacit knowledge - an inarticulable vague sense. Such tacit knowledge, aggregated over millions of people, can produce quite decent forecasts.
But is knowledge of the future really possible? Back in the 1920s, Frank Knight at the University of Chicago distinguished between risk and uncertainty. Risk, he said, is quantifiable, as when we say there's a one in 13 chance of drawing a king from a pack of cards. Uncertainty, however, cannot be quantified.
Some of our ideas about the future can be roughly quantified, so we can speak of risk. If you're prepared to assume that the future will resemble the past, we can roughly quantify the chance of a fall in the market. For example, Bank of England data show that since 1899 UK share prices have risen by an average of 4.3 per cent per year in nominal terms, with a standard deviation of 20 percentage points. If we assume returns are normally distributed - which is near enough for smallish moves - this implies there's around a 40 per cent chance of the market falling in any year. Again, we shouldn't take this as a precise number, but perhaps as a decent Fermi estimate.
Other questions, however, can't be even roughly quantified. Will robots take our jobs? Will secular stagnation continue? Will Donald Trump's protectionism trigger a damaging world trade war? We can't meaningfully attach numbers to these. We face genuine Knightian uncertainty.
One especial way in which such uncertainty matters for stockpickers is in considering the danger of companies failing. We know that many companies do eventually die. But what's the chance of any particular one doing so? Economists at Volterra Consulting have shown that it varies in the same way that the extinction probability varies for biological species. Usually, the death rate is low, but this is punctuated by periods of more frequent deaths. This warns us that we can't attach reliable numbers to the probability of a particular firm collapsing in (say) the next few years.
My point here is a simple one. Investors must live with fuzziness, imprecision and uncertainty. Precise numbers can be misleading, and even worse than useless because they can inspire overconfidence. Maynard Keynes never actually said that it's better to be roughly right than precisely wrong. But he should have done.
In saying this, I'm echoing the philosopher Alasdair MacIntyre. He's written: "Facts, like telescopes and wigs for gentlemen, were a seventeenth century invention." His point is that it is dangerous to think of facts as being independent of judgment. Facts only make sense within particular cognitive frameworks, and good frameworks warn us that 'facts' aren't always reliable.
So, how can investors cope with this? One way is to recognise that we'll never invest perfectly. Optimisation is impossible, and we'll always miss out on some profitable opportunities. The best we can do is make do - what the late Nobel laureate Herbert Simon called "satisficing".
Although it's impossible to optimise, we can at least avoid the obvious mistakes. This means:
■ Minimise tax (legally). Make full use of individual savings accounts (Isas), self-invested personal pensions (Sipps) and capital gains tax allowances. People who invest for income often fail to do this. They forget that we can create our own dividends simply by selling some shares - and often do so more tax-efficiently.
■ Minimise funds' charges. Ask of any actively managed fund: what is this giving me that I can't get from a tracker or investment trust? Often, the answer's nothing. Remember that fees compound horribly over time.
■ Don't bet against momentum. Run your winners and cut your losses. And be wary of stocks that have fallen a lot even if they look cheap: even the cheapest stock can still fall 100 per cent.
■ Be wary of 'growth' stocks, especially the more speculative ones. We know that growth stocks underperform value over the long run. And Aim stocks have done especially badly.
Another thing we can do is to make sure we're comfortable with our portfolios. One way to do this is to conduct informal stress tests. For example, ask yourself: how would I feel if shares were to drop (say) 20 per cent in the next 12 months? Don't deny that they can: to do so is to assume knowledge we cannot have. And beware of the projection bias - our habit of projecting our current tastes into the future. The fact that you're comfortable with shares when they're close to record highs does not mean you'll remain relaxed if they slump. If such a drop would trouble you - if it would cause you to cut your spending or delay retirement - then you might be holding too many equities. Consider shifting into safer assets.
Also ask: what worries me? If it's a fall in house prices, consider owning foreign currency, as this often rises when house prices fall. If it's inflation, hold index-linked assets. If it's falling share prices, hold more cash.
If all this seems obvious, good. The point is that you don't need fancy maths to manage risk. Common sense, combined with the humility to recognise that we don't know much, is sufficient.
A world in which 'facts' are misleading and in which fuzziness and imprecision are crucial might seem uncomfortable to some - to the sort of person (often a journalist) who makes a fetish of numbers without asking what they mean and how accurate they are. But it's the world we live in. The late Thomas Mayer wrote a book called Truth Versus Precision in Economics. Investors should be more aware of that trade-off. As Professor Mayer wrote: "We over-invest in information and underinvest in knowledge and wisdom."