**Paul Sweeting reflects on the way we think about, and distinguish between, different types of risk**

*The Actuary*’s August 2020 interview with Mervyn King stated that risk has two meanings: the common one, ‘an unpleasant outcome’, and the financial theory definition, ‘measurable volatility’. This could suggest that those in finance have only one view of risk. For some, the terms ‘risk’ and ‘volatility’ may be interchangeable. Having a rigid view of what is meant by risk is a problem, as King points out. However, for many who consider risk, the reality is even more complicated than this –and this complexity can lead to further problems.

When thinking about risk, a good place to start is the decision-making process. When we make decisions, we weigh up what we want to happen and what could go wrong – even if we’re not doing so consciously. We can think about this process in terms of optimisation: what we want to happen is the objective; what could go wrong is the risk. However, ‘risk’ can mean several different things.

One way of thinking about risk is as uncertainty over a range of outcomes: several things could happen, and you don’t know which will. If only one is the ‘right’ outcome, you can talk about the ‘risk’ of the others happening. For example, if you bet on a horse to win a race, then there is a risk that any of the other horses will win, or that yours does not win. This view sees risk in terms of ‘bad’ outcomes.

**‘Black swan’ events**

Some people make a distinction between risk and uncertainty. One view is that risk implies something that can be measured, while uncertainty implies something that can’t. As King said, the COVID-19 crisis falls into the second category, but the concept of uncertainty is not new: the distinction between risk and uncertainty was made a century ago by Frank Knight. For this reason, this type of uncertainty – where it’s impossible to make any calculations around the likelihood or size of an event – is called Knightian uncertainty. It can also be thought of as an unquantifiable risk. Knightian uncertainty is linked to ‘black swan’ events. One way of thinking about these is as events that could not have been predicted in advance, but are rationalised as being clear with hindsight – so before they happen, they’re in the realms of uncertainty, but afterwards they are regarded as a risk.

The interest in black swan events came about because of the 2008 financial crisis. The reasons behind the crisis are complex, but it was called a black swan event by many because it was impossible to predict – although some believed that the chances of a large market crash were greater than option prices implied. In hindsight, many pointed out that it had been clear there was going to be a crisis, but few had made this argument beforehand.

The fact that you can’t come up with probabilities or impacts doesn’t mean uncertainty should be ignored – far from it. It’s dangerous to assume that if something can’t be measured, it’s not important, or likely enough to worry about. You might not know how likely it is that a particular thing will happen, but you can still consider taking action to protect yourself against it. It’s just that the quantitative trade-offs you might normally consider – between the size of the risk and the cost of mitigating it – can’t be made.

**Risk in finance**

So, a risk is some sort of bad outcome that can be quantified. But given that you can quantify it, and perhaps calculate a probability for this outcome, the risk could be this probability rather than the outcome itself. In terms of a horse race, it could be the probability that the horse you’ve backed doesn’t win. Or it could refer to the consequences rather than to the risk itself – the risk that that you lose your house if your horse doesn’t win.

All of this can be put into a financial setting, but it does highlight other ways of looking at risk. For example, if we’re looking at a loan we’ve made, these concepts translate over quite easily. There is a risk that the loan won’t be paid back; this risk can be quantified as a probability. There is also a risk – which can itself be quantified – that a lender will go bust if too many loans aren’t repaid. This involves looking at how the risks of default across the portfolio of loans are related, which is a big topic in itself.

It’s worth noting that all these definitions of risk relate to discrete outcomes: something either happens or it doesn’t. A horse wins or loses; a loan is repaid or it isn’t. However, in finance we also need to think about continuous risks, such as equity market risk. The amount by which an equity index changes each day can be thought of as continuous, on a sliding scale. Even discrete risks such as loans can be treated as continuous if you have enough of them and you think in terms of the loss from that portfolio.

**Continuous risks**

When you’re looking at continuous variables, the most common measure of risk is volatility – the standard deviation. This is a measure of variability; a higher standard deviation means the underlying investment is more volatile, so the potential size of a loss is higher, but the potential size of a gain is, too. These could be thought of as downside risk and upside risk. If the probability of losing up to a particular amount is about the same as the probability of gaining the same amount – relative to what you expect – then volatility works fairly well as a risk measure, subject to some rather important caveats. However, if those probabilities are different so that you’ve got asymmetry between gains and losses, then you might want to use a measure focused specifically on downside risk. If we want specific measures of downside risk, we need to look at measures that consider only bad outcomes. This brings us to metrics such as value at risk (VaR): the maximum expected loss over a particular time horizon with a particular degree of confidence.

It’s used by banks and insurance companies to determine how much capital they ought to hold. For example, the 95% 10-day VaR can be thought of as the answer to the question ‘how much capital do I need to hold such that the risk of me going bust over the next 10 days is 5%?’ As you can see, the risk can be the risk of insolvency or the answer to the VaR calculation – which is why it’s important to be clear what we mean when we talk about risk.

“One view is that risk implies something which can be measured, while uncertainty implies something which can’t”

What about the caveat I mentioned in relation to volatility? This is quite subtle, and it’s about how a volatility number is used. If you have at least two observations, it’s possible to calculate the volatility of those observations. This is true no matter what distribution the observations have. However, in finance, volatility is often used to calculate risk under the assumption that the observations are normally distributed. If they’re not – for example, if they have fat tails – the level of risk can be severely underestimated.

**On the same page**

Another point King alludes to in his interview with *The Actuary* is the fact that future observations might not have the same distribution as past ones. There are many statistical approaches to capture this feature, but the underlying risk here is that past observations do not exactly define the future. To assume that they do will result in risk being misstated.

It’s also important is to recognise that there is not necessarily a right answer when it comes to what is meant by risk or uncertainty. Some people may define either term differently to any of the descriptions above. What’s crucial is that if there’s a conversation about risk or uncertainty, all those involved are using the same definitions. Failing to do this and talking at cross purposes is itself a risk – and one that can derail attempts to manage risks effectively.

**Paul Sweeting** is chief risk officer at Hassana Investment Company