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The certainty equivalent is a figure representing the amount somebody would accept as a guaranteed payment rather than instead choosing a higher payment that is not guaranteed. The amount will vary depending on how risk-averse the person involved is. The concept can be used both in general statistics and probability, and in a specific context of financial investments.
A simple example of the certainty equivalent would be a parent who offers their child the choice between a weekly allowance of $10 (USD), or to have the allowance be dependent on whether their softball team wins that week's game, with $20 allowance if they win and nothing if they lose. If the team usually plays well, the child may take that option. The parent may then offer to increase the guaranteed option to $15. The child may decide this is now a better choice than taking the risk. In this situation, the child's certainty equivalent is thus $15.
In and of itself, the certainty equivalent is simply a number and of little use to economist or investment analysts. Where it becomes more useful is in plotting a graph where the certainty equivalent is tracked as a variable is changed. The two variables will usually be the amount of money at stake and the potential winnings or return. The graph may be modified depending on how risky the proposition under examination is. Such a graph, and the accompanying analysis, may be useful for a company considering issuing bonds or shares. It will give them some insight into the amount of potential returns it would have to offer to persuade a particular proportion of investors to switch from risk-free savings to risky investments.
One potential problem with the certainty equivalent is that different people have different attitudes to risk. The certainty equivalent will be lower for a risk-averse person as they will settle for a relatively low guaranteed amount rather than take the risk. For somebody less concerned about risk, the certainty equivalent will be higher as it will take a higher guarantee for them to be persuaded to give up the possibility of a higher return.
Exploring this concept can be both a frustrating and illuminating exercise for analysts. This is because it can expose how most people have an illogical attitude to risk. For example, many people regularly play the lottery, even though the combination of the prizes available and the chances of winning mean that statistically they will wind up worse off from playing. At the same time, most people take out insurance policies, even though the combination of the premiums charged, the amount of cover provided, and the likelihood of making a claim means that statistically people taking out insurance will wind up worse off.