*Relevant to Papers F2, F5, P4 and P5*

**This article introduces the concepts of risk and uncertainty together with the use of probabilities in calculating both expected values and measures of dispersion**

Clearly, risk permeates most aspects of corporate decision-making (and life in general), and few can predict with any precision what the future holds in store.

Risk can take myriad forms – ranging from the specific risks faced by individual companies (such as financial risk, or the risk of a strike among the workforce), through the current risks faced by particular industry sectors (such as banking, car manufacturing, or construction), to more general economic risks resulting from interest rate or currency fluctuations, and, ultimately, the looming risk of recession. Risk often has negative connotations, in terms of potential loss, but the potential for greater than expected returns also often exists.

Clearly, risk is almost always a major variable in real-world corporate decision-making, and managers ignore its vagaries at their peril. Similarly, trainee accountants require an ability to identify the presence of risk and incorporate appropriate adjustments into the problem-solving and decision-making scenarios encountered in the exam hall. While it is unlikely that the precise probabilities and perfect information, which feature in exam questions can be transferred to real-world scenarios, a knowledge of the relevance and applicability of such concepts is necessary.

In this first article, the concepts of risk and uncertainty will be introduced together with the use of probabilities in calculating both expected values and measures of dispersion. In addition, the attitude to risk of the decision-maker will be examined by considering various decision-making criteria, and the usefulness of decision trees will also be discussed. In the second article, more advanced aspects of risk assessment will be addressed, namely the value of additional information when making decisions, further probability concepts, the use of data tables, and the concept of value-at-risk.

The basic definition of risk is that the final outcome of a decision, such as an investment, may differ from that which was expected when the decision was taken. We tend to distinguish between risk and uncertainty in terms of the availability of probabilities. Risk is when the probabilities of the possible outcomes are known (such as when tossing a coin or throwing a dice); uncertainty is where the randomness of outcomes cannot be expressed in terms of specific probabilities. However, it has been suggested that in the real world, it is generally not possible to allocate probabilities to potential outcomes, and therefore the concept of risk is largely redundant. In the artificial scenarios of exam questions, potential outcomes and probabilities will generally be provided, therefore a knowledge of the basic concepts of probability and their use will be expected.

PROBABILITY

PROBABILITY

The term ‘probability’ refers to the likelihood or chance that a certain event will occur, with potential values ranging from 0 (the event will not occur) to 1 (the event will definitely occur). For example, the probability of a tail occurring when tossing a coin is 0.5, and the probability when rolling a dice that it will show a four is 1/6 (0.166). The total of all the probabilities from all the possible outcomes must equal 1, ie some outcome must occur.

A real world example could be that of a company forecasting potential future sales from the introduction of a new product in year one (**Table 1**).

**Table 1: Probability of new product sales**