Wrong. For most investors, the job is relatively straightforward with just a little basic maths.
Let’s start with the basic big question: how should you divide your wealth between risky assets such as equities and a safe one such as gilts? (I’ll start simply and introduce complications later.)
The riskiness of your wealth will depend upon how much you invest in each asset, the volatility of each asset and the covariance (how much the assets are likely to move together). There’s a formula for this. The variance of a portfolio of gilts and equities is equal to:
(P^2equities x Vequities) + (P^2gilts x Vgilt) + (2 x Pequities x Pgilts x Covariance)
Where P is the proportion of our wealth in each asset, ^2 is the square function and V is the variance of the asset. The covariance is the correlation between two assets, multiplied by their standard deviations.
Now, variances aren’t the easiest things to understand, so we take the square root of them to give us a standard deviation.
My first chart shows the solution to this equation for varying weights on equities on the basis that these have an annualised standard deviation of 20 percentage points, that gilts have an annualised standard deviation of five percentage points, and that the correlation (and therefore covariance) between them is zero. I reckon these are reasonable round number working assumptions.
A standard deviation sounds fancy. But it’s simple. Just remember: one in six. A standard deviation of 10 means there’s a one in six chance of returns being 10 percentage points or more below average, and a one in six chance of them being 10 percentage points or more above average. And, therefore, a two-thirds chance of them being within 10 percentage points of average.
Take for example a portfolio split 50:50 between gilts and equities. It has a standard deviation of 10.3 percentage points, so there’s a one-in-six chance of annual returns being 10.3 percentage points or more below average.
What’s average? If we assume equities will return five per cent a year after inflation and gilts nothing – again, working round numbers – then average returns will be 2.5 per cent a year. So there’s a one in six chance of annual returns of minus 7.8 per cent or worse.
If this chance seems too high for you, then you should hold fewer equities and more safer assets. For example, my chart tells us that a 75:25 split between gilts and equities has a standard deviation of 6.25 percentage points, implying a one in six chance of a loss of five per cent or more. Or – what is the same thing – a five-sixths chance of something better than a five per cent loss.
What about losses of different sizes? Here’s the beauty of standard deviations. We can translate units of standard deviations into probabilities by using the assumption that returns are normally distributed – that is, as a bell curve – and then using simple statistical tables.
So, for example, what’s the chance of an annual loss of 15 per cent or more on a 50:50 gilt-equity portfolio? It’s a 1.7 standard deviation event, which statistical tables tell us is a 4.5 per cent chance.
My second chart uses our ability to move between standard deviations and probabilities to show the probability of losing 10 per cent or more in a 12-month period for different combinations of gilts and equities. For 100 per cent equity portfolios, this risk is more than one in five. For portfolios with less than a quarter in equities, it is under 4 per cent.
We have, then, described the odds you face. Where you put yourself on this line is a matter of choice. For example, a two-thirds gilt, one-third equity portfolio offers an expected return of 1.65 per cent and 5.8 per cent chance of losing 10 per cent or more. But a two-thirds equity, one-third gilt portfolio offers an expected return of 3.3 per cent but a 16 per cent chance of a loss of 10 per cent or more.
So far, I’ve discussed annual returns. What if you’re a long-term investor interested in longer-term risks?
No problem. We can tweak the maths. The trick here is the square root of N rule; the standard deviation of returns over N years is equal to the annual standard deviation multiplied by the square root of N. (This assumes that returns in one year are uncorrelated with those the next, which is near enough true for our purposes). So, for example, the standard deviation of five-year returns is 2.24 (the square root of five) times the annual standard deviation.
Let's take our 50:50 equity-gilt portfolio. It has a five-year standard deviation of 23.1 per cent - 10.3 multiplied by the square root of five. With an expected annual return of 2.5 per cent, or 13.1 per cent over five years, this implies that the chance of a loss over five years is a 0.57 standard deviation event (13.1 divided by 23.1), which is a 28 per cent chance. And there’s a one-in-six chance of a loss of 10 per cent or more.
If these strike you as high chances, they should. Equity volatility is so high that even over long periods, there’s a good chance of a fall.
So far, so straightforward. Now for some complications.
Our first complication is that I’ve assumed a zero correlation between gilts and equity returns. But this isn’t certain. Correlations between them have varied a lot – from positive to negative – down the years. If the two become positively correlated, gilt-equity portfolios will be riskier than I’ve assumed because there’s a bigger danger than both will fall together.
This is one case for holding cash. It protects you from this danger, as it would hold its value (in nominal terms) if gilts and equities fall together. It might also be a case for holding gold, as it too might not fall when gilts and equities both do.
This brings me to a second complication: what exactly is a safe asset?
If you are only interested in your wealth at a particular future date, the answer’s simple – an index-linked gilt which matures on that date. This – and this alone – gives you certainty about your future real purchasing power.
Most of us, however, care about our wealth over many future dates, not just one. This complicates things. Bonds and bond funds expose us to price rises and (unless they are inflation-proofed) to inflation risk - the danger that the value of our money will be eroded by rising prices. Cash also exposes us to inflation risk and also to reinvestment risk; if bond yields or cash rates turn out to be lower than expected, you’ll have to reinvest maturing savings accounts at disappointingly low returns.
For many of us, there is no safe asset. We must simply choose which risk we prefer.
A further complication is that I’ve assumed equity volatility of 20 per cent a year. But in fact, volatility varies over time. During the financial crisis it was higher than this, whilst recently it has been lower.
However, I’m not sure we should worry much about this. For one thing, low volatility should imply low expected returns and high volatility high expected returns. For the average investor these should cancel out; the unpleasantness of extra volatility is offset by better expected returns. And for another thing, time-varying volatility matters only if we can predict its changes. This is a job better left to the professionals; the fact that they are betting other people’s money rather than their own on their ability to do so tells you all you need to know.
There’s another assumption I’ve made which isn’t entirely correct – that returns are normally distributed. This is roughly the case for smallish falls but not for big ones. Big falls – not just in shares but in other assets such as commodities – are more likely than a normal distribution implies. Xavier Gabaix at Stern School of Business in New York has quantified this. He’s shown that extreme returns - those of more than two standard deviations - follow a statistical pattern. It's the cubic power law.
To see this, let’s ask: how likely is a 10 standard deviation fall in equities? This is a 12 per cent fall in a day or 28 per cent in a week; the square root of N rule tells us this.
To get the answer, we take half of 10 – because we’re interested in the bad half of the probability distribution – and raise it to the power of three (this is the cubic bit). This gives us 125. The cubic power law tells us that such a fall is 125 times less likely than a two standard deviation event. We know the latter is a 2.27 per cent chance. So it follows that a 10 standard deviation chance is a 0.018 per cent chance. This implies that we should see a 12 per cent fall in a day about once every 5,494 days, or once every 21 years.
This works for individual shares, for commodities, and for any standard deviation greater than two. (Below two, the normal distribution is roughly right).
Exactly why a cubic power law works is another matter. It just happens as a matter of fact rather than theory to fit the facts. But it has an important implication. Some of us are loss averse, in that big losses hurt proportionately more than small ones. The (say) 1 per cent chance of a 20 per cent loss might have the same expected value as the 20 per cent chance of a 1 per cent loss, but for some it is a nastier prospect. If you’re one of these, you should be wary of equities and commodities because of their extra risk of a bad loss.
So far, I’ve assumed that how much risk you take, once we’ve calculated the odds, is a matter of taste. It is, ultimately. However, there’s another complication here. What matters for risk management is your total portfolio – all your assets and all your liabilities. These can put you in a better or worse position to take risk. For example, you are better able to adjust to equity losses if you can:
■ Reduce your bequests without feeling bad;
■ Postpone retirement;
■ Are young, and so can benefit from time diversification, the tendency for bad returns to be followed by better ones;
■ Can trade down your house and so can release home equity to offset share losses;
■ Have low outgoings, or (less likely) can reduce your spending without much pain.
So far, I’ve considered portfolios of just two assets. But of course, there are many others such as commodities, second or third homes, foreign currency or collectibles such as wine or antiques. We can consider these by using a generalized for of our first equation. The variance of a portfolio is equal to:
(1/N x average variance) +((N-1/N) x average covariance)
Taking the square root of this gives us the standard deviation of a multi-asset or multi-equity portfolio.
In general, adding different assets to a portfolio reduces its riskiness because doing so increases the weight of the covariance terms and reduces the weight of the variance terms, and covariances are usually smaller than variances.
There are, though, two big caveats here. One is that in the long-term covariances between different assets will be higher than short-term ones, and will be higher in really bad times than in normal ones. This is because asset prices depend upon the health of the economy and so should rise over time with GDP even if short-term noise causes them to move in different directions.
Secondly, volatility is not the only risk. For example, housing and some collectibles such as classic cars carry liquidity risk; you might not be able to sell them quickly at a decent price, especially in bad times.
Which raises a crucial point. There are many types of risk and different ways to manage them. Some of these risks affect some more than others. The box gives an inventory of them.
If you think there are a lot of them, you’d be right. Risk is everywhere, and in different forms. If anyone claims there is a risk-free way of making big money, he is a charlatan.
You might think all these risks and all the complications I’ve mentioned make effective risk management impossible.
Yes. A completely optimal and efficient way of managing risk might be impossible. But a few equations and general principles can organize our thinking about risk sufficiently for us to make roughly reasonable decisions. Maynard Keynes famously said that it is better to be roughly right than precisely wrong. And in 2008 banks showed us that the costs of being precisely wrong can be enormous. Retail investors can at least do better than that.
VARIETIES OF RISK
* Low risk; ***** high risk
Inflation risk
Likelihood: * (near-term/); unknown (long-term)
What it is: The danger that prices will rise quickly, raising our future cost of living.
Who should worry? Everyone, but especially people on flat rate annuities. Wage-earners shouldn’t worry so much because over the long run wages should rise as prices do, which means our earning power is a hedge against inflation risk.
What to do: Hold index-linked bonds or national savings.
Distribution risk
Likelihood: **
What it is: The risk that incomes will shift from profits to wages over time, which means that even a growing economy could see share prices fall.
Who should worry? Investors who don’t have wage earnings.
What to do: Hold assets other than UK equities, and perhaps emerging market ones: it is unlikely that the distribution of incomes would shift to wages in all economies.
Reinvestment risk
Likelihood: **
What it is: The risk that interest rates will stay low, causing you to earn low returns when your bonds or fixed-term savings mature.
Who should worry? Longer-term investors.
What to do: Hold bonds whose maturity matches your time horizon – so if you’re most worried about your wealth in 10 years’ time (say because you’re hoping to retire then) hold 10-year bonds.
Exchange rate risk
Likelihood: ***
What it is The danger that sterling will fall, thus raising the prices of imported goods and overseas assets.
Who should worry? The same people who should worry about inflation. Also, anyone hoping to retire overseas or to buy an overseas holiday home.
What to do: Hold the currency you are planning to need in future. Otherwise, hold some index-linked assets.
Correlation risk
Likelihood: *****
What it is: The danger that previously uncorrelated assets will fall together, so that what you thought to be a well-diversified portfolio proves to be riskier than you imagined.
Who should worry? Everyone.
What to do: Hold cash.
Stagnation risk
Likelihood: **
What it is: The danger that the UK suffers a Japanese-style lost decade, in which the economy and stock market stagnate.
Who should worry? Everyone, but especially younger investors as these would suffer worse job prospects as well as lower equity returns, and because a 'buy on dips' strategy won’t work.
What to do: Hold bonds – index-linked or nominal – as these would benefit from disappointing growth. Hold emerging market equities, as some of these are less vulnerable to stagnation and might benefit from low interest rates in the west.
Longevity risk
Likelihood: varies from person to person
What it is: The danger that you will outlive your wealth.
Who should worry? Those in good health.
What to do: Buy annuities, as these pay out for as long as you live.
Liquidity risk
Likelihood: ****
What it is: The danger that you will be unable to sell some assets quickly at a decent price: this afflicts houses, alternative investments such as classic cars and art; and some private equity funds which have lock-in periods.
Who should worry? Anyone who might need to raise cash quickly.
What to do: Ensure that you never have to be a forced seller, by holding liquid assets such as cash.
Style/behavioural risk
Likelihood: ****
What it is: The danger that hitherto good stock-picking strategies – such as defensives, momentum or quality stocks – will fall out of favour.
Who should worry? Stock-pickers.
What to do: Either don’t rely upon single strategies and hold a tracker fund. Or, have the discipline and long-term horizons to stick with the strategy during bad times.
Cyclical risk
Likelihood: * (near-term) ***** (eventually)
What it is: The danger of recession, in which we lose not just because share prices fall, but because house prices do and our jobs and private businesses face risk of closure.
Who should worry? Anyone who isn’t retired. Or retired people dependent upon variable interest rate income.
What to do: Avoid cyclical stocks, especially if your job or business is at risk from recession. Hold bonds, as these do well in recessions.
Projection bias risk
Likelihood: Varies from person to person.
What it is: The danger that we imagine that we will not be bothered if a particular risk materialized, only to discover that we are upset when it actually does.
Who should worry? Everyone, but especially those who believe they are not worried.
What to do: Don’t try to fool yourself. If you think “this risk doesn’t worry me”, ask yourself why. A legitimate answer would be that you have the resources to bear it; for example, if you’re retired and have a fixed income, you can bear recession risk. Less legitimate answers would be that you don’t believe the risk will materialize, or that it doesn’t seem so bad.
