Given an opportunity to participate or to forgo to participate in an event for which the outcome, and therefore his or her receipt of a reward, is uncertain, the certainty equivalent is the maximum sum of money a person would pay to participate or the minimum sum of money a person would accept to not participate in the opportunity. The difference between the certainty equivalent and the expected value is called the risk premium. Certainty equivalents are used in evaluating attitudes toward risk.
I am awaremy question is going to vague:Has anyone has a worked example for the above?
how much is the maximum would you be willing to give up in case something adverse happened? Or how much is the maximum you would be willing to accept if something good happened -> if you were 100% certain on an event happening or not - how much money would you assign to it -> that is the certainty equivalent.
now you have a probable chance of event occurring - Prob of occurrence * Value of the event = Expected value.
Difference between these two = risk premium.
that is all the snippet is trying to say.
there is no mathematical example that is present - especially since someone who is risk averse would not be willing to pay out or accept a large sum (so his certainty equivalent would be low). While someone who is risk seeking would love to “raise the odds” - and accept / bet a ridiculous large sum of money - his certainty equivalent would be high.
-> Given an opportunity to participate or to forgo to participate in an event for which the outcome, and therefore his or her receipt of a reward, is uncertain, tThe certainty equivalent is the maximum sum of money a person would pay to participate or the minimum sum of money a person would accept to not participate in the opportunityan event with uncertain outcome.
The certainty equivalent is: -
the maximum money a person would pay to participate in the uncertain event (e.g.: how much are you willing to pay to participate in a lottery?) or…
the minimum money a person would pay so that they can avoid that uncertain event (e.g.: how much are you willing to pay to insure yourself against a possible loss?)
Crude example 1: - Take a lottery with a single payoff of USD100 and an odd of 0.01 of winning (you either win USD100 or USD0). The expected value of the lottery is USD100 x 0.01 = USD1. However, Alice is willing to pay a maximum of USD3 to participate in the lottery. The risk premium is USD3 - USD1 = USD2. Crude example 2: - Bob owns an asset worth GBP500,000. There is a probability of 0.0001 where Bob’s asset may be destroyed (say through some calamity). The expected value of this contingent event is -GBP500,000 x 0.001 = -GBP500. However, Bob may insure his asset through an… insurance service. He is willing to pay GBP600 to purchase the insurance. Therefore, the certainty equivalent is -GBP600 - (-GBP500) = -GBP100. Note that Bob is effectively accepting a certain “loss” of GBP600 to avoid a possible loss of GBP500,000.
Taking “Crude example 2” for Bob.
If Bob is willing to pay a maximum of GBP500, the certainty equivalent would be -GBP500-(-GBP500)=GBP0 which would imply that Bob is “risk neutral” (indifferent between purchasing or not purchasing insurance)
If Bob is willing to pay more than GBP500, the certainty equivalent will be >GBP0 which would imply that Bob is “risk averse” (will likely pay a little more to avoid the risk of losing GBP500,000.
If Bob is willing to pay less than GBP500, Bob is willing to accept the risk of suffering a possible loss of GBP500,000 (or at least, will not buy any insurance for above GBP500). In that event, Bob is said to be “risk loving”.
I am not sure if CFAI uses the term “risk loving” though and my examples are really, really crude (I literally pulled those examples out of nowhere) so use those examples only to understand the general concept.