Let us lay two choices in here. The first one has a guaranteed return, but you should accept it now. The second choice offers a higher but uncertain return because we can never predict the future. What would you choose between the two? Risk-averse people would most likely choose the first option, and we call it a certainty equivalent. It is a guaranteed amount of money that you can think about as an amount similar to the attractiveness of a risky asset.

The choices we make have consequences.

With the choices that we laid earlier, we realized that if an entity offers investments with risks, it comes with a price. What do we mean? While higher-risk investments provide more returns than those with low risks, they should pay a risk premium on top of that. The risk premium is like compensation to investors that gave their “yes’ despite the possibility that they may never get the money they invested in back. It means that the more risk that investment has, the more premium the entities should pay on top of the average return.

Let us cite a scenario.

You can choose between Bond A, which offers a 2% interest, and Bond B, which offers 9% interest. Let us say that you decided to go with Bond A over Bond B because you are risk-averse. It means that the certainty equivalent and the payoff differential are equal. Since you are risk-averse, it would take a lot for you to say yes to Bond B. When we say a lot, we mean that the possible returns should be more than 9% of the entity’s bonds.

In this scenario, it makes to think that certainty equivalent can become a measurement when we want to determine how much entities need to pay investors to get them to agree to a riskier option. So, for every investor, it will be different because everyone has different risk tolerance. In fact, there is also a similar term in gambling, and it also means the same. Gambling also has a certainty equivalent. It is the amount that an entity needs to pay so that the other person will become indifferent between that and a given gamble.

Time for an example

The certain equivalent is relative to that of an investment’s cash flow, and it is the risky cash flow that someone believes is the equivalent to a different cash flow. This cash flow is more, but it also poses more risks. The formula that we can use to find the certainty equivalent cash flow is as follows:

Certainty Equivalent Cash Flow = Expected Cash Flow/ (1+ Risk Premium)

Here is a detailed explanation of the different calculations:

• Risk premium. The calculation is like the risk-adjusted rate of return with the risk-free rate deducted.
• Expected cash flow. We calculate it by taking the probability-weighted dollar value of every expected cash flow, and then we add them up. 

Let us wrap it up from here.

Certainty equivalent stands for the amount that an investor will want to accept now than the possibility of more money in the future because there are many risks. This amount will always be different because everyone has different risk tolerance. This idea is closely related to a risk premium that refers to the amount an entity should pay an investor to agree and take a risky investment.