Chapter 2: Utility Theory

[Bernadette Pieterse]

On p14 the alternative definition of certainty equivalent states that:
cx<0
Why would the certainty equivalent of the gamble alone be negative?

Thanks

 

[Natan Brittz]

This is for a risk averse investor with a fair gamble (e.g. equal probability of receiving +1 or -1). A risk averse investor will prefer not to take a fair gamble and will even pay a small premium to avoid the gamble. Therefore cx<0 which is equivalent to paying a small premium to avoid the gamble. This is just the investor accepting less then the expected value (0 in this case) to not take on the gamble's risk.

 

[Calm]

Why would the certainty equivalent of the gamble alone be negative?

Thanks

Because the investor is risk-averse in this instance. So they will pay up to cx to avoid the gamble. But if the investor is risk-loving then cx can indeed become positive i.e. if offered a value of less than cx upfront, they would still gamble.