Investment risk

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# 2 Quantifying risk

## 2.1 Looking at each of the possible alternative outcomes

Investment risk is synonymous with uncertainty of outcome, so it is logical to try to quantify risk by looking at the relative uncertainty, or probability, of each of the possible alternative outcomes.

Suppose that we are interested in investing in the shares of Company X, and want to know:

• What is the mean or average expected total return for the next year?

• What is the degree of risk or uncertainty in this mean figure?

We might begin by collecting and tabulating data about total returns on the same company's shares for each of the past 50 years. In order to make this example easy to follow, we shall keep the data very simple, but the same principles apply to the more complex patterns of data derived from real-life studies. The simplified table might look like Table 1.

### Table 1 Frequency distribution of the actual total returns on a one-year investment in shares of Company X in each of the last 50 years

Total return (% per annum) Frequency of occurrence Probability
4% 10 0.2
6% 15 0.3
8% 15 0.3
10% 10 0.2
Totals 50 1.0

What can we say about next year's total return on an investment in shares of Company X? If the fundamental factors determining the share's performance are unchanged – and that is a very big ‘if’ indeed – we can convert these long-run frequencies of past returns into probabilities concerning the future. The big question – whether the future is an extension of the past – is one to which we shall return later.

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