# Stage 2: Measure and estimate risk exposures

Having identified the categorisations appropriate to the organisation, using this typology or another one that better suits the major risks the organisation faces, the next task is to measure the assorted risks.

There are two main ways of thinking about the possible results of risk exposure. Either you can focus on the ‘expected return’ or on ‘possible outcome versus return’. The expected return method is usually easier to use in a quantitative or comparative way. For example, assume you are faced with choosing between action A and action B, each with the same level of risk. If it is possible to calculate the expected return of the alternatives then it is usually sensible to opt for whichever offers the better expected return.

How do you calculate expected return? This is the sum of the values of the return of each possible outcome multiplied by its probability of occurrence. The formula for this is represented as

where

E(R) = expected return

R_{i} = value of outcome i

P_{i} = probability of outcome i

This is the same definition as that for the mean return in statistics since ‘expected return’ and ‘mean return’ are the same thing.

The expected return method is very much applicable and useful in finance – for instance, in your study of portfolio theory.

An important use for expected return is when considering avoidable risk: that is, risk to which the organisation can choose whether or not to be exposed. The simplest form of the rule is: ‘only take on avoidable risk if the expected return is positive’. Similarly, if you have to decide between choices, the rule should be: ‘choose the option with the highest expected return’.

You should immediately realise that either form of this rule is not yet complete as it does not address the balance between level of risk and level of return. Strictly speaking, satisfying the rule as so far stated is a necessary, but not a sufficient, condition for accepting avoidable risk. Please accept this for the moment as it avoids judgements about ‘acceptable’ return for taking on risk: the simplification will allow us to investigate, in Box 6, another aspect of deciding on exposure to risk.

## Box 6 When simplicity is not enough

You have the chance to play one of two coin-tossing games. Whichever you choose to play, you will only have the chance to toss once. Oh yes, notwithstanding the reputation of your opponent, the coin is fair! The probability of heads therefore equals the probability of tails, 0.5.

**Game A** If the coin lands on heads you will receive €12; if it comes up tails, you pay €10.

**Game B** If the coin lands on heads you will receive €12,500; if it comes up tails, you pay €10,000.

What should you do? First, calculate the expected return of each game.

**Game A**

E(R) = (+ €12 × 0.5) + (– €10 × 0.5) = + €1

**Game B**

E(R) = (+ €12,500 × 0.5) + (– €10,000 × 0.5) = + €1,250

So surely you play Game B? It offers €1,249 more expected return. It even offers a better percentage return, since for Game A

E(R)/Stake = €1/€10 = +10%

and for Game B

E(R)/Stake = €1,250/€10,000 = +12.5%

The simple decision rule is quite clear: play Game B.

But what if you lose on your one toss?

Personally, I could not afford the loss of €10,000 and I doubt if many of you could either. The possible negative outcome is not supportable, so I must decline to play Game B even though the expected return is more favourable.

The simple rule therefore needs to be extended to include checking that the downside possibilities are not ‘catastrophic’ if they actually occur.

Now, I can afford to invest €10 in Game A…

This idea of ‘avoiding catastrophic outcomes’ leads to the second factor we need to include when assessing risk: namely, ‘possible outcome versus return’. This does not contradict the ‘risk versus return’ as epitomised by portfolio theory and the capital asset pricing model (CAPM), but adds to it. ‘Risk versus return’ looks at the situation as a whole and judges whether on average the risk is worth accepting. This new criterion says that for some sorts of risk it is necessary to consider whether some possible outcomes are so insupportable as to outweigh almost any level of average return.

The standard deviation is a way of condensing into a single number information about the average amount of scatter around the mean of a distribution. Since this represents uncertainty about the return received in any particular period, it is truly a measure of risk as we have defined it. For some types of risk, however, it is not practical to calculate a proper statistical measure such as the standard deviation. Additionally, historic measures based on past returns may not capture ‘discontinuities’ that generate insupportable outcomes. For example, stock market declines, such as during 2001–03, may be seen as included in, and allowed for, by standard deviation analysis, but crashes that happen in the space of a few days, such as in 1929, 1987 and, arguably, 2008, reflect such radical and unusual changes as to preclude capture of such a measure.

In either situation, including a ‘catastrophe avoidance’ criterion is not a rival to the standard deviation, but an adjustment to it. Figure 5 illustrates the idea, perhaps rather crudely.

Scenario A shows the value of a project for the whole range of possible outcomes: it is not a true ‘distribution’ in the proper statistical sense, but is meant to represent qualitatively the same sort of idea. The project is more likely than not to end up with a positive value, as implied by E(R) > 0. Furthermore, all the possibilities give relatively modest values, some positive, some negative, none extreme.

Scenario B, on the other hand, is expected to give a higher value than Scenario A, but there is a small chance of it ending up horribly negative – a catastrophic outcome. While the expected return is better, we should also include in our consideration such an unpleasant possibility.

It is worth noting that the expected return system can encompass the possible outcome versus return method. If you look at each of the terms in the E(R) summation, as well as the final result, then you can analyse the individual outcomes as required for this second method of assessing risk. Here you consider each potential outcome and what would be the profit or loss should it actually occur. If one or more outcomes have an unacceptably large negative return, that is, a catastrophic result, then this information should be taken into account.

A benefit of this ‘summing over outcomes method’ is that it forces us to think through the consequences of each possibility. Sometimes this is more important than calculating expected value. Also, it is much easier to apply this system where the assessment must be essentially qualitative, either in respect of the values or of the probabilities. However, this method has one significant disadvantage: if it does not result in comparable measures, it makes assessing between options much more difficult, or, at the very least, less precise.

## Activity 3 Stop and reflect

The net present value (NPV) rule of ‘accept capital investment projects with a positive NPV’ seems to be an example of the naïve version of our risk rule: that is, it does not consider the level of return. Is this true?

### Discussion

No – providing the cost of capital has been correctly risk weighted. Assuming that this has been done, then a zero net present value means that the project is exactly ‘fair’. In the terms of this discussion, the expected return is just enough to justify the risk. If, however, the calculation has been done with an organisation’s ‘standard’ or non-risk-weighted discount rate, the NPV rule has potentially been impoverished as a decision tool, especially if the proposed project is much riskier or much safer than the average for the business.

## Risk mapping

Risk mapping needs to show key areas of risk for the organisation in terms of danger and size of exposure. The aim is to provide the organisation’s policymakers with data to enable informed strategic decision making about the allocation of the organisation’s risk capacity. Where possible, the mapping might include benchmarks for some types of risk. This is likely to be feasible for market-oriented risks (for example, foreign currency, interest rate, commodity price and so on) as there is more chance of there being a published benchmark.

Box 7 shows the operational-research technique of decision-tree analysis, which can be useful for showing the links between choices and the risk implications of making those choices. Even if you do not go through the whole process of estimation and ‘roll back’, just drawing the tree will often clarify cause and effect.

### Box 7 The concept of a decision tree

The principle in this operational-research technique is to draw a graph of decision points and outcomes for a project or process, which forms the ‘tree’ and its branches. In the full method, a monetary value and probability are assigned to each outcome and then the tree is ‘rolled back’ to work out the pathway through the project that offers the highest ‘expected monetary value’ (EMV). An example is shown in Figure 6 for a television company deciding whether to produce a new series.

Often, just going through the process of drawing the tree is useful in itself. In particular, it helps clarify where our choices branch away from each other: in other words, if we choose to do X we have ‘burned our boats’ (meaning that there is no chance to go back and change or reverse an earlier decision – the phrase relates to the action taken by Julius Caesar’s Roman army which, in 49 BC, burned its boats having crossed the River Rubicon in pursuit of the enemy) with respect to choices W, Y and Z. Clearly, the points at which we cut ourselves off from possible courses of action are significant when thinking about the risks of a project. At times, this graphical approach can be a direct help in itself by showing us where, for example, re-ordering of the project could serve to delay irreversible decisions – often an immediate aid to risk reduction. Adding in the values and probabilities is, in effect, providing the input for the calculation of an expected return, but in a way which also takes into account the chronological sequence of events. Sometimes this adds little to our decision making, but often with more complicated projects (or strategic plans, if considering a whole organisation) it does improve the manager’s knowledge to a worthwhile degree – and that ought, on average, to lead to better choices being made.

So what should be the output from this second stage of the risk management process? Against each category chosen in Stage 1 there should be an analysis, probably containing both numeric and qualitative information, assessed in whatever way is appropriate for the particular type of risk. During this stage instruments that can be used to shift or trade risks are also identified. The next step is to assess the effects of exposures.