Risk and Uncertainty

1 Introduction

Decision making involves making decisions now which will affect future outcomes which are unlikely to be known with certainty.

Risk exists where a decision maker has knowledge that several possible outcomes are possible – usually due to past experience. This past experience enables the decision maker to estimate the probability or the likely occurrence of each potential future outcome.

Uncertainty exists where the future is unknown and where the decision maker has no past experience on which to base predictions.

Whatever the reasons for the uncertainty, the fact that it exists means that there is no ‘rule‘ as to how to make decisions. For the examination you are expected to be aware of, and to apply, several different approaches that might be useful.

2 Risk appetite

‘Risk appetite’ is the term given to describe the amount of risk an organisation is willing to accept in pursuit of value.

Risk appetite is determined by two factors:

• Stakeholders’ attitude to risk
  

• Risk capacity, which is the amount of risk that the organisation can bear.
  

Taking a personal example:

Some people are risk seekers and like to gamble; others are risk averse. So, if betting on a horse race, the risk seekers might be attracted to gamble on the high odds 100 to 1 horse. However, the risk averse person would tend not to consider that sort of gamble. They have different attitudes to risk.

However, let’s say both a risk seeker and a risk averse person have $100,000 in the bank and were being asked to bet $100. Then, even the risk averse person might be tempted to go for 100 to 1 odds. In this situation they have high risk capacity because losing $100 is of little consequence if you have $100,000 in the bank.

But what if each person had only $100 in the bank? There’s a fair chance that neither would bet $100 because the consequences of losing are so serious: they have very low risk capacity.
Overall their appetite for risk (ie their appetite for the gamble) depends on their own attitudes plus the risk capacity.

In terms of performance management and the principal agent relationship between directors and shareholders, the directors of the company should take into account the risk appetite of shareholders when making decisions. Some shareholders might prefer a ‘safe’ company with moderate returns whilst others, with higher risk appetites, might prefer more adventurous companies with the possibility of high returns. The directors, as agents, should be acting in the best interests of their principals and should make decisions that are congruent with shareholder preferences and risk appetites.

Nowadays, stakeholder theory suggests that directors should try to take into account the wishes and preferences of all stakeholders, not just shareholders.

3 Decisions under risk and uncertainty

The approach taken when making decisions will depend on decision-maker’s attitude to risk. Ideally this will reflect the risk attitude of shareholders, but it is almost inevitable that some of the directors’ personal risk preferences will affect their decision-making.

A risk seeker will be interested in the best possible outcome, no matter how small the change that they may occur.

Someone who is risk neutral will be concerned with the most likely or ‘average’ outcome.

A risk avoider makes decisions on the basis of the worst possible outcomes that may occur.

For example:

A company can adopt one of three strategies, A, B or C. Independently the country’s economy could enter a period of recession (probability = 0.3), stay the same (probability = 0.5) or have strong growth (probability = 0.2). The company has estimated its profits under each economic condition for each strategy and the full information is:

Decisions under risk

If a decision is being made under conditions of risk then the probabilities of each outcome occurring are known (or the decision-maker is willing to estimate these). In this case expected values can be used ie weight each outcome with the probability of it occurring.

So,

If Strategy A is adopted, the expected profits are: 0.3 x 1,600 + 0.5 x 1,400 + 0.2 x 1,350 = 1,450
If Strategy B is adopted, the expected profits are: 0.3 x 1,300 + 0.5 x 1,500 + 0.2 x 1,500 = 1,440
If strategy C is adopted, the expected profits are: 0.3 x 500 + 0.5 x 1,100 + 0.2 x 2,000 = 1,100

The decision would then be based on the highest expected value, here 1,450, and Strategy A would be adopted.

Decisions under uncertainty
If a decision is being made under uncertainty then the probabilities of each outcome are not known. Decision-makers have much less information to go on and so they are inevitably going to be more influenced by their attitudes towards risk: their risk appetites. Decisions are much more subjective. There is no absolute ‘right’ decision that can be made in advance: a decision is right if it is the decision that managers and investors (ideally their views will be congruent) feel most comfortable with. Some investors will be risk-seeking, others will be risk-avoiders. All are entitled to their views.

We will look at just two approaches: maximax and maximin. No company will mandate that one or other of these approaches must be adopted. The approaches are simply to illustrate that when information is lacking then decision-makers will make decisions that are in tune with their attitudes to risk and risk appetites.

Maximax
Investors will be drawn to this approach if they are optimists. They are like a gambler who places all their chips on one roulette wheel number. They know it’s risky, but seek the big pay-out.

We will use the data presented above, but remember that the probabilities are no longer known.

So this investor will consider Strategy A and see that the best outcome is 1,600; Strategy B’s best outcome is 1,500; Strategy C’s best outcome is 2,000.

The best of the best outcomes (think maximax) is 2,000 so this investor would go for Strategy C.

Maximin
Investors will be drawn to this approach if they are pessimists and therefore risk avoiders because they are sure that whatever they do fate will not be kind to them.

So this investor will look at Strategy A and see that the worst outcome is 1,350; Strategy B’s worst outcome is 1,300; Strategy C’s worst outcome is 500. The best of these bad results is1,350 so this investor would choose Strategy A.

4 The limitations of expected values

Although we say that someone who is risk neutral would take an expected value approach to decision making, there three two serious limitations of this approach:

• The expected value is not usually ‘expected’.
  

• The expected value gives no indication of the risk.
  

• The estimation of the probabilities is very unreliable
  

Example: mutually exclusive projects ($’000)

Project cost = 3,800

The expected value of the income from both projects is greater than the cost of 3,800 so both appear worthwhile and Project A seems to be preferable as it has a higher expected value.

However neither of the expected values of 5,200 or 5,000 is expected to occur: the only possible results seem to be 2,000, 4,000, 6,500 and 10,000. If Project A were chosen, there is a greater than evens chance that only 2,000 will be earned, creating a loss of 1,800 (ie 2,000 – 3,800). Project B is never expected to produce a loss. Perhaps Project B is preferable?