Risk Attitude with a Utility Function

[Kevin Skovron]

Risk Attitude with a Utility Function

[Anonymous]

Volume 1, pg 14, fig IA1.1 and Ex IA1.1

Does an investment of 220m euros have a 50/50 chance of making/protecting, or losing 500m euros?

In essence am i to take this as a client is willing to use e220m to hedge a e500m portfolio?

At 0 we have 0, the horizontal arrow points left from dotted line because that is where both zeros intersect?

Which leads us to the drop down arrow presumably to -220 as would the horizontal arrow would lead us to -220 on the Y axis
Thank You.

[Anonymous]

Kesko,

I do not completely understand your question, but figure 1.A.1.1 does not mean that an investment of Euro 220m has a 50-50 chance of making or losing 500m.

All it means is that the firm is faced with a situation where it could either win 500m, or lose 500m. The loss of 500m is worth a lot more to the firm in terms of utility, in fact in the given example it has a utility of -820. (Note that -820 does not mean 820m Euros, it only means 820 utility units.) A gain of 500m has a utility of 280, which means the total expected utility from the situation is -270. A utility of -270 corresponds to Euro -220m – which is the certainty equivalent. Therefore this is what the company would be willing to pay to get out of this situation (ie where it could win or lose 500m with equal probability.)

Hope this helps.

Mukul

[Author]

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