What a Certainty Equivalent Is, What It Tells You, How to Use It

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Updated February 22, 2021

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What Is the Certainty Equivalent?

The certainty equivalent is a guaranteed return that someone would accept now, rather than taking a chance on a higher, but un🔜certain, return in the future. Put another way, the certainty equivalent is the guaranteed amount of cash that a perso🔜n would consider as having the same amount of desirability as a risky asset.

The certainty equivalent represents the amount of guaranteed money an investor would accept now instead of taking a risk of getting more money at a future date.
The certainty equivalent varies between investors based on their risk tolerance, and a retiree would have a higher certainty equivalent because they're less willing to risk their retirement funds.
The certainty equivalent is closely related to the concept of risk premium or the amount of additional return an investor requires to choose a risky investment over a safer investment.

What Does the Certainty Equivalent Tell You?

Investments must pay a risk premium to compensate investors for the possibility that they may not get their m🎶oney back and the higher the risk, the higher prem☂ium an investor expects over the average return.

If an investor has a choice between a U.S. government bond paying 3% interest and a corporate bond paying 8% interest and he chooses the government b༺ond, the payoff differential is the certainty equivalent. The corporation would need to offer this particular investor a potential return of more than 8% on its bonds to convince him to buy.

A company seeking investors can use the certainty equivalent as a basis for determining how much more it needs to pay to convince investors to consider the riskier🥃 option. The certainty equivalent varies because each investor has a unique risk tolerance.

The term is also used in gambling, to represent the amount of payoff someone would require to be indifferent between it and a given gamble. This is called the gamble's certainty equivalent.

Example of How to Use the Certainty Equivalent

The idea of certainty equivalent can be applied to cash flow from an investment. The certainty equivalent cash flow is the 澳洲幸运5开奖号码历史查询:risk-free cash flow that an investor o🔯r manager considers e🐈qual to a different expected cash flow which is higher, but also riskier. The formula for calculating the certainty equivalent cash flow is as follows:

$\text{Certainty Equivalent Cash Flow} = \frac{\text{Expected Cash Flow}}{\left(1\ +\ \text{Risk Premium} \right )}$

The risk premium is calculated as the risk-adjusted rate of return minus the risk-free rate. The expected cash flow is calc꧒ul🔯ated by taking the probability-weighted dollar value of each expected cash flow and adding them up.

For example, imagine that an investor has the choice to accept a guaranteed $10 million c🐬ash inflow or an option with the following expectations:

A 30% chance of receiving $7.5 million
A 50% chance of receiving $15.5 million
A 20% chance of receiving $4 million

Based on these probabilities, the♔ expected cash flow of this scenario is:

$\begin{aligned} \text{Expected Cash Flow} &= 0.3\times\$7.5\text{ Million}\\&\quad + 0.5\times \$15.5\text{ Million}\\&\quad + 0.2\times\$4\text{ Million}\\ &=\$10.8 \text{ Million} \end{aligned}$

Assume the risk-adjusted 澳洲幸运5开奖号码历史查询:rate of return used to discount this option is 12% and the risk-free rate is 3%. Thus, the risk premium is (12% - 3%), or 9%. Using the ♐above equation, the certainty equivalent cash flow is:

$\begin{aligned} \text{Certainty Equivalent Cash Flow} &= \frac{\$10.8 \text{ Million}}{\left(1 + 0.09 \right )} \\ &=\$9.908 \text{ Million} \end{aligned}$

Based on this, if the investor pref𝄹ers to avoid risk, he should accept any gu💙aranteed option worth more than $9.908 million.

澳洲幸运5开奖号码历史查询

What Is the Certainty Equivalent?

What Does the Certainty Equivalent Tell You?

Example of How to Use the Certainty Equivalent

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