On the whole people don't like ‘risk’ (whatever that is exactly). True, taking some risk may be our best course. True, we can't entirely avoid risk. True, some people appear to be thrilled by doing dangerous things. But most people, in most circumstances, would rather take less risk, all other things being equal.

Why? Perhaps surprisingly this simple question has yet to receive a convincing answer. It's obvious that if you see a child playing with a loaded gun, thinking it's a toy, there is a risk of someone getting hurt or killed and that's bad. In general, if there's an outcome we don't like (i.e. find aversive) then we are also averse to the possiblity of that outcome.

What is not so obvious is why we prefer not to accept a gamble with 50:50 odds where if we win we get Ł1,050 but if we lose then we lose Ł1,000. In the long run, on average, we gain money from bets like this, so why do we usually avoid them? This is the puzzle that has generated the controversy. Is there something about the uncertainty, i.e. do we have an attitude to risk per se, or can our preferences be explained in some other way?

In this short article I'll dip into the famous theories and then suggest something new, briefly illustrating its practical value as well as it's theoretical attraction.

The established theories in brief

Very broadly, and at the risk of offending the authors of countless variations, there are two famous theories about why we appear to avoid ‘risk’.

The ‘risk’ theory

One theory says risk is a concept or quantity that is real in our minds and, perhaps instinctively, we are averse to it because, well, we just are. This is over and above our aversion to the possibility of unwelcome outcomes and is a theoretical aversion to the sheer uncertainty involved.

The ‘risk’ theory is correct, at least to the extent that there are now people and organizations that calculate or judge quantities they call ‘risk’ for which an institutional or personal aversion is expressed. However, this is largely a product of the existence of the theory itself. Would it happen if there weren't regulations telling people to do it? Workable tools for governance of risk taking can be built using this approach but as an explanation for naturally occurring behaviour it has problems.

A huge challenge for supporters of the ‘risk’ theory is to define the measure of ‘risk’ that we use and respond to. Various suggestions have been made, including the variance of outcomes, the semi-variance (like the variance but it only considers below average outcomes), and value at risk numbers.

However, pick any one of these and apply it to a personal decision you might make and you'll probably realise that some aspects of the calculation don't match your way of thinking about it. For example, if ‘risk’ is taken to be variance of outcomes then this fails to capture our tendency to focus on bad things that might happen.

Another huge problem with this idea is that it doesn't actually say why we are averse to risk! It just says there is something called risk and we don't like it.

The ‘utility’ theory

The other big theory says that it's not really ‘risk’ that we're averse to at all. The explanation for our apparently ‘risk averse’ behaviour lies in the way we value different possible outcomes.

This is usually illustrated using money. The idea is that a pound sterling is worth more to you when you are poor than when you are rich. The theory is based on an imaginary scale of value called ‘utility’ and in utility terms each extra pound sterling is worth a little less than the previous one.

Put it another way, imagine you owned a big pile of cash and faced a gamble where you could gain a large sum of money or lose an equally large sum. The gain would mean piling extra pounds on top of your already-large stash. However, the loss would mean losing pounds from your stash, including pounds near the bottom of a dwindling pile. The loss would hurt you more than the gain would please you.

In this way the theory of utility offers a real explanation of why we don't like ‘risk’ that can be traced back to the satisfaction of basic human needs.

However, there's a problem. This theory doesn't seem to be a full explanation for actual decision making by people in the face of uncertainty. We seem to react against small losses to a much greater extent than our reaction to large losses would imply. We also seem to have a preference for certainty.

Ideas for altering the theory to account for this inconvenient fact have included these:

Drawing more complicated curves linking money and utility and suggesting that people evaluate gains and losses against their current position rather than against the position of having no wealth. (This is Prospect Theory.)
Resurrecting the concept of ‘risk’ and tweaking the utility curve a little more in recognition of risk aversion to get it to predict human behaviour better than it otherwise would.
Combining a utility curve elicited without uncertainty (renamed ‘value’) with a new concept called relative risk aversion that tries to capture what happens when uncertainty is reintroduced.

The problem with all these is that they offer no reason why the curves should have any particular shape. It's just a way to try to get closer to predicting actual behaviour.

Observations towards a new theory

The ‘risk’ theory and the ‘utility’ theory have something in common. They both involve simplifying our analysis of potential future chains of events by stopping our analysis at some point and applying summary numbers. In effect, they say ‘After that the possibilities seem endless so as a guide for decision making let's just say that [different quantities of money have these values] / [different degrees of risk have these values].’

At some point this is a good thing and ultimately we usually do need to stop the analysis of future events at some point. Workable tools for governance of risk taking in organizations can be developed using this idea.

However, if we pursue our analysis a little further than usual some interesting observations can be made and what emerges is a new theory of apparently ‘risk averse’ behaviour that extends and improves on the utility theory. It offers solid reasons for our behaviour.

These observations are useful because they can improve our decision making, planning, and business design. They are also theoretically satisfying because they have a good chance of accounting for more behaviour under uncertainty than has been achieved in the past.

Three crucial observations

There are (at least) three factors that influence our decision making in the face of uncertainty and explain most (perhaps all) our apparent ‘risk aversion’:

Decreasing incremental value with quantity: Just as utility theory says, more of something we want typically makes us happier, but the more we have the less difference one more unit makes. Not everything works like this, but most things do. Once our basic needs are satisfied ‘more’ just doesn't matter as much, and this applies to food, drink, children, copies of a favourite book, and even money.
Disruption is costly, and more so when rushed: Adjusting our lifestyles, business models, or strategies is disruptive and can be stressful and costly. For example, if you come into some money and decide to buy a better house then that will lead to stress, expenses, and perhaps quite a lot of painting and decorating. (Conceivably there are a few people who have too little to do and welcome the activity, but most of us are too busy most of the time.) If you lose a lot of money and have to sell your house and get a small flat then that too is disruptive. This disruption combines with the pleasure or pain of being in improved or worsened accommodation as a result. Typically, the costs are greater if we have to change things in a hurry, and this is more likely following a sudden, large loss.
Foreknowledge can be useful: One of the advantages of knowing what will happen in the future is that we can (sometimes) act differently. For example, we don't have to cover possibilities we know will not happen. We can prepare in a more focused way for what we know will happen. Consequently, we prefer to know in advance and our preference grows with the scope for worthwhile early action, even if that action is no more than planning.

I do not know if these observations combined can account for all apparent ‘risk aversion’ (or even just the rational part of it) but clearly they can account for more than the utility theory alone. It's also not known how often my generalisations are correct. For example, I suggest that rushed change is usually more disruptive and costly than change we can do gradually, as easy opportunities arise. How true is this? Do people respond to it habitually? It would be interesting to find out.

However, we can still apply this theory to decisions we take, and benefit from it, by simply asking if any of these observations appear to be true in our case.

An approach to analysis

One great advantage of thinking in this way is that it helps us focus on the practical circumstances that should influence our decision making and planning. Those circumstances are things we can sometimes change. For example, we may be able to deal with more uncertainty when investing in business ventures if we have more money on hand, more of it as a buffer, are able to adjust our strategies more cheaply, and can improve our forecasting so as to cut the uncertainty.

So, instead of trying to discover by navel gazing something that is imagined to be a given – our ‘risk appetite’ for example – we can turn to facts and put our inventive minds to finding ways to gain an advantage.

We can focus on the following key events and the periods of time between them:

The point at which we are making the valuation, usually ‘now’.
The period in between making the valuation and discovering the uncertain outcome, during which we may make some kind of preparations.
The point at which we discover the previously uncertain outcome.
The period between discovering the outcome and it having an effect on us.
The period during which we make a transition in our lifestyle or business model.
The period during which we experience the new lifestyle or business model.

The value of knowing in advance

This first example is to illustrate the value of knowing more about the outcome.

Imagine you have to make a long car journey to a business meeting. You don't want to be late for the meeting, but the problem is that you are not sure how long it will take to make the journey. Traffic is variable and a breakdown on a motorway could cause a huge delay, while many other minor problems are possible. In addition, you are not even sure how long the journey takes ‘on average’. Imagine you are 95% sure it will take between 1 and 2 hours. When do you set out?

In this situation, if there was nothing to prevent me, I would allow 2 hours and take some work to do if I arrive early. This is far from ideal because it means getting up earlier than usual and, most likely, some not very productive time in a noisy reception area.

If I knew for certain the day before the meeting exactly how long my journey would take then there probably would be no need to get up early and I would probably have time to answer some emails before setting out. If I discovered the exact journey time just before setting out that would be less useful because, by that stage, there would be less I could do to take advantage of that knowledge.

In terms of subjective ‘utility’ points, suppose a 1 hour journey arriving on time was worth 10 points to me and a 2 hour journey arriving on time was worth 2 points, then a 50% chance of a 1 hour journey combined with a 50% chance of a 2 hour journey would not be the average of these, which is 6 points. Instead, it would be something much lower, like 4 points, reflecting the need to cover the possibility of a long journey by getting up early and leaving a safety margin.

This effect has also been studied under the title ‘value of information’ and more recently as ‘real options’.

Considerations here include work done to prepare for the outcome that actually occurs, the benefit of that work, and the work wasted preparing for outcomes that in fact do not occur.

If there is nothing that can be done to prepare then knowing about the outcome in advance provides no advantage. Or, put it the other way, uncertainty over the outcome is no disadvantage.

The cost of transition

For various reasons there may be a delay between the consequence being known and having to take any action as a result of it. With a large reserve it may even be that no action is required because some other consequence later compensates for the first consequence.

If you have a large money reserve and lose money in a one off bet then one way to handle that might be to continue with the same lifestyle and see what happens. Another would be to trim the lifestyle slightly (i.e. make a transition) so that it can last as long as the previous one.

A loss or gain, if it is to make a difference to our lifestyle for any period, requires adjustments. These adjustments are the transition.

For example, a better paid new job might fund a new kitchen, but you cannot enjoy that new kitchen until a lot of choosing, shopping, and talking to tradesmen has happened, and then you have to live without a usable kitchen for a few days while the work is done. Then you have to check it and get fixes done. Then, and only then, can you start to enjoy your new kitchen. Losing that job could lead to more lifestyle adjustments.

Here is an example for a company:

Imagine a company has three good years and decides it can afford to establish itself in a neighbouring country. This expansion is a transition, taking it from one ongong business model to a new one.

The new business unit is loss making initially but they hope it will become profitable in a couple more years. Unfortunately, at this point the global economy deteriorates cutting profits in the home operation and increasing losses in the new foreign business. The board realises it cannot afford to keep supporting the foreign operation and decides to sell or close it. They know this is damage limitation and that a good price is unlikely, but still urgent action is needed and they end up closing the business after four months of futile attempts to make a sale. This is another transition, back to the old business model, made all the more expensive and painful by the time pressure and poor economic conditions.

As in this example, transitions under time pressure may be more stressful and may be more costly. For example, if you have to sell your car under time pressure you may get less for it. If you can buy a new house with no time pressure you have more chance of getting a bargain.

Downward transitions following losses are more likely to be under time pressure than upward transitions. However, reserves can reduce this difference.

The cost of transition provides a rational basis for judging gains and losses relative to one's current position. It also offers a rational reason for downward transitions being more of a problem than upward transitions. This perhaps explains some of the findings that Prospect Theory seeks to explain. However, I do not think it explains the exaggerated aversion to small losses that actual behaviour in laboratory studies usually shows. That behaviour remains irrational.

It would be interesting to see some research using realistic scenarios, distinguishing between one-off losses and losses to regular income, and studying the effects of having reserves as a buffer.

The end result

What we end up with, excluding preparation and transition effects, is another important part of the value overall.

Typically, we see diminishing marginal value in more of a particular resource. Having one copy of my book is great, but having two copies is not twice as great. Money is a resource that typically shows this characteristic. Also food, water, shelter, and sex.

However, diminishing marginal value is not the only regime we can face. There are also situations where, unless we have at least a certain amount of something, any amount is useless.

When we think about companies having enough money to stay in businesses, or animals having enough calories to survive winter, it can be difficult to know just how much is needed. If a company flips rapidly into financial difficulty this is more dangerous than sliding slowly, provided the situation is recognised, because there is time to adapt to unfolding difficulties when things move more slowly.

Sometimes competition creates situations where being the one winner brings huge rewards. A tiny difference in speed can make the difference between being an Olympic gold medallist and being only a silver medallist, or between being the champion and being the runner up. In Formula 1 motor racing the points in the 2010 season were adjusted to provide an extra bounty for winning races, creating a greater incentive to race aggressively and take other chances in hope of one of the top places.

Further practical examples

The following examples illustrate the above theory applied to some further real decisions.

Good questions to ask in business meetings

In most business meetings that consider plans and decisions there are alternative courses of action whose consequences are somewhat uncertain. Things might work out very well, very badly, or somewhere in between.

Good questions to ask include:

‘Money is not a perfect guide to value. How much would we have to lose to be ruined?’ ‘What if that loss was over a period of time rather than all on one day?’ ‘If this plan doubled our profits how much more valuable would that be to us compared to other gains and losses were are considering?’ ‘What would happen next?’ ‘What could we do with that result?’
‘How badly does it have to go to force us to change something painful (e.g. shed staff, abandon a market, move premises)?’ ‘Can we change our plans, practices, or contracts so that change is less painful?’ ‘If we did that, would it help us compete in an uncertain market?’ ‘What are our cash and near-cash reserves like and what do we forecast?’ ‘What other ventures of ours could draw on our reserves?’
‘If we knew more, earlier, what could we do differently and how much difference could that make?’ ‘How could we know more, earlier?’ ‘If we look at things as a pool of investments rather than one by one, does the future look more predictable?’ ‘And how could we use that predictability?’

Using savings to cut disruption

Should you upgrade your lifestyle every time your financial prospects improve and downgrade it every time they worsen? Even if you had a super-steady job this would be an exhausting way to live. You would be constantly shopping for a new car, better house, improved kitchen appliances, and better private schooling for your children. You would endlessly be cancelling holidays in order to book alternatives more suited to your latest wealth assessment.

What most financially aware people do instead is use savings as a buffer that makes lifestyle changes a matter of choice rather than urgent necessity. We want to build that buffer then spend most of our time in a settled, steady way of life, perhaps upgrading cautiously when easy opportunities arise.

If you think about these factors as you make big lifestyle decisions it should help you see the value of savings and reach a better decision than you would if you considered only the situation after making the lifestyle change.

Business flexibility

A volatile and unpredictable business environment calls for a flexible business. It should be possible to reallocate resources, change priorities and methods, and generally respond to events using smooth graduations of response controlled by frequently rehearsed decision mechanisms.

If, instead, the business is designed around a particular level of demand, a fixed set of products, special accommodation of a certain size, and any change is costly and requires a lot of management attention, then that business will behave in a more ‘risk averse’ way.

Value of forecasting

The value of forecasting to a business depends on how predictable its future is and on how much it can do to influence or prepare for that future. Most businesses do not make forecasts decades in advance because it's hard and because there's not much they could do that would take decades to implement. Such long term forecasting is not worthwhile.

However, some businesses have actions they can take that are important and require years of advance notice. Think of companies that prospect for oil, develop nuclear power stations, or make fine whisky. For them, far future gazing is much more likely to be worthwhile.

Theoretical development

This idea of extending the original utility theory to recognise more of the practical impacts of uncertain possibilities is a theoretically important one and could be developed in various ways.

One direction would be to try to build quantitative models that describe decision making, and a distinctive feature of this approach would be the use of more than one curve. The information needed for decision making could not be captured in a single utility curve. Consider just two of the effects.

The factor, ‘Decreasing incremental value with quantity’, is just the familiar utility curve idea and we would expect a person's curve to remain the same even if their actual current level of wealth changed.

However, the factor, ‘Disruption is costly, and more so when rushed’, creates a penalty for changing lifestyle (for better or worse). It implies a curve that shifts as a person's current wealth level changes, as in Prospect Theory.

Furthermore, the impact of the third factor, ‘Foreknowledge can be useful’, depends on whether anything different can be done with foreknowledge, not on the level of uncertainty alone.

Empirical studies are needed to explore each of the three factors, and theoretical work may reveal yet more factors to be considered.

The initial study I performed, ‘What circumstances are relevant to decision making under uncertainty?’, shows only that most people recognise the importance of these factors to rational decision making. This should encourage us to think that a theory developed along these lines will make a lot of sense to most people.

Advantages for modelling

The main advantage of thinking things through in this way is to move from wondering how you feel about alternative outcomes to thinking about practical specifics. It gives people specific things to think about.

However, there are also some potential advantages where quantitative modelling is attempted. For a given decision it may be possible to construct or elicit a single utility curve that captures all the effects and is enough to make a decision. However, this curve will have to be constructed or elicited again for similar but slightly different decisions.

For example, if you start from a different level of current wealth then a new curve is needed. In contrast, with the cost of transitions captured separately no new work is needed. Or consider the impact of learning more about the probabilities of alternative outcomes in situations where it is possible to exploit this knowledge by better preparation. Because the uncertainty has changed the preparation can change and that means the single utility curve would also have to change. With the preparation effects modelled separately it is only that part of the thinking that would have to be revised.

Finally

A short summary of the advice I have for people making decisions under uncertainty is this: Never make the mistake of thinking that your ‘attitude to risk’ is a product of your personality. It's not. It's a product of your circumstances and you can get your calculations wrong. Consider the value of different future positions, the cost of making changes (or being forced to make them), and the value of knowing the future in advance. Be specific, and practical, and you will reach a better understanding of what different potential future outcomes would mean to you.

(This has been a brief presentation of what seems to me a breakthrough in thinking about ‘risk averse’ behaviour. I hope to flesh it out further in the near future and please get in touch with me if you have something to contribute.)

Made in England

Working In Uncertainty

The real reasons we avoid risk

Contents