# Certainty Equivalent

## What Is the Certainty Equivalent?

The certainty equivalent is a guaranteed return that somebody would acknowledge now, as opposed to taking a risk on a higher, however unsure, return from here on out. Put another way, the certainty equivalent is the guaranteed amount of cash that a person would consider as having a similar amount of attractiveness as a risky asset.

- The certainty equivalent addresses the amount of guaranteed money an investor would acknowledge now as opposed to facing a challenge of getting more money sometime not too far off.
- The certainty equivalent differs between investors in light of their risk tolerance, and a retired person would have a higher certainty equivalent since they're less able to risk their retirement funds.
- The certainty equivalent is closely connected with the concept of risk premium or the amount of unexpected return an investor expects to pick a risky investment over a more secure investment.

## What Does the Certainty Equivalent Tell You?

Investments must pay a risk premium to repay investors for the possibility that they may not get their money back and the higher the risk, the higher premium an investor anticipates over the average return.

In the event that an investor has a decision between a U.S. government bond paying 3% interest and a corporate bond paying 8% interest and he picks the government bond, the payoff differential is the certainty equivalent. The corporation would have to offer this specific investor a possible return of over 8% on its bonds to persuade him to buy.

A company seeking investors can involve the certainty equivalent as a basis for determining the amount more it needs to pay to persuade investors to think about the riskier option. The certainty equivalent shifts in light of the fact that every investor has a unique risk tolerance.

The term is likewise utilized in gambling, to address the amount of payoff somebody would expect to be impassive among it and a given bet. This is called the bet's certainty equivalent.

## Illustration of How to Use the Certainty Equivalent

The possibility of certainty equivalent can be applied to cash flow from an investment. The certainty equivalent cash flow is the risk-free cash flow that an investor or manager considers equivalent to an alternate expected cash flow which is higher, yet additionally riskier. The formula for working out the certainty equivalent cash flow is as per the following:

$\text = \frac{\text}{\left(1\ +\ \text \right )}$

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

For instance, envision that an investor has the decision to acknowledge a guaranteed $10 million cash inflow or an option with the accompanying expectations:

- A 30% chance of getting $7.5 million
- A half chance of getting $15.5 million
- A 20% chance of getting $4 million

In light of these probabilities, the expected cash flow of this scenario is:

$\begin \text &= 0.3\times$7.5\text\&\quad + 0.5\times $15.5\text\&\quad + 0.2\times$4\text\ &=$10.8 \text \end$

Accept the risk-adjusted rate of return used to discount this option is 12% and the risk-free rate is 3%. Accordingly, the risk premium is (12% - 3%), or 9%. Utilizing the above equation, the certainty equivalent cash flow is:

$\begin \text &= \frac{$10.8 \text}{\left(1 + 0.09 \right )} \ &=$9.908 \text \end$

In light of this, assuming the investor likes to stay away from risk, he ought to acknowledge any guaranteed option worth more than $9.908 million.