Challenges in advanced management accounting
Challenges in advanced management accounting

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Challenges in advanced management accounting

4.1.1 Attitudes towards risk

In this course, we have taken the attitude that decision-makers are risk neutral. This means that they select the option which produces the greatest NPV, regardless of how risky the option is. If the same decision was taken many times, selecting the option with the greatest expected value each time would produce the highest value in the long run. However, many decisions taken in business are one-off decisions, not decisions which are repeated many times.

In this context, other attitudes towards risk are often taken. People can be risk averse, meaning that they avoid risk. The technical definition of a risk-averse decision-maker is someone who will sacrifice higher expected value in order to avoid risk. Note that this definition is different from the common definition of simply avoiding risk where it is present. Here is an example to demonstrate what this means.

Imagine you are offered a bet: you win £9,000 if you roll a six on a die, but you pay £1,500 if you roll any other number. Would you take the bet? The expected value of the bet is in your favour:

So the expected value = (£1,250) + £1,500 = £250

A risk-neutral person would accept the bet, since it has a positive expected payoff: the average gain on the bet is £250 per time. However many people would refuse such a bet, and demonstrate that they are risk averse in this case. A risk-averse attitude is common in many people, and in business decision-makers to some extent. People often prefer to stick with what they have – for example, a profitable and low risk business, rather than risk losing this for the (better than average) chance of making more money or expanding the business successfully.

It is also possible to be risk seeking, meaning unsurprisingly that people seek out risk in order to get better returns. The technical definition of a risk-seeking decision-maker is someone who will sacrifice higher expected value in order to take on risk. Note that this is different from the common definition of someone who is simply willing to take risks: a risk-neutral decision-maker will also do this when the expected value is in their favour.

Suppose the bet above is changed slightly so the payoff for a six is only £6,000. The expected value of the bet is now:

Described image
Equation 10

So the expected value is (£1,250) + £1,000 = (£250).

Someone who was risk neutral would now reject the bet, because the expected value is negative and the bet will lose money on average. However a risk-seeking individual would still take the bet despite the expected value being negative, because taking the bet increases the risk they are exposed to.

Obviously, risk-seeking individuals in this definition are unusual. Most people will accept some risk in return for a greater average return, and people vary in how much reward they require for additional risk. However, few people will take on more risk at the same time as making the expected value worse on average – being ‘risk-taking’ is usually meant as a relative term. Almost everyone is risk-averse to some extent, and how ‘risk-taking’ someone is, is a measure of how close to being risk-neutral they are.

The layman definitions fit in better with how most people use these terms (and also how they are used throughout this course). Risk-seeking people are simply people more likely to take on risk than risk-averse people. For example, risk-seeking investors would be more likely to invest in stocks, attracted by the higher potential returns on offer, while risk-averse investors may invest in bonds and gilts, which have little risk attached to them but have lower expected returns.

By investing in riskier investments such as stocks, risk-seeking investors are actually increasing their expected return not decreasing it, because the long-term average return of stocks is historically higher than bonds. So these risk-seeking investors are really just risk-neutral investors (in the technical sense of the term) who are taking the option with the highest expected value and are not deterred by the higher overall risk.

Note that the technical and common definitions of risk-averse investors tend to be more similar. For example, in declining to invest in stocks, investors are both avoiding risk (the common definition), and also reducing their expected return in order to do so (the technical definition).

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