Expected Utility Calculator

With our expected utility calculator, we aim to help you assess the probable outcomes of different scenarios. If you wish to understand more about this topic, please check out our risk calculator and expected value calculator.

In this article, we will cover the following:

• What expected utility is;
• How to calculate expected utility; and
• The importance of expected utility in decision-making.

We will also present examples to help you to understand the calculation process of expected utility better.

Expected utility is a metric that is commonly used to help make rational decisions when facing a situation with uncertain outcomes. Thus, expected utility theory is a model that you can use to quantify the desirability of different choices based on their potential benefits or drawbacks.

Utility is defined as the value of the outcome to the person in question. Hence, the utility value assigned to each outcome is subjective and can vary from one individual to another, reflecting personal preferences, risk tolerance, and individual circumstances.

When coupled with probability, which is the likelihood of each outcome happening, the expected utility provides a way to make consistent and rational choices.

To understand how to calculate expected utility theory, let’s look at the below example with two possible investment outcomes:

• Investment A:
  • Probability: 40%
  • Monetary value: $10,000
• Investment B:
  • Probability: 60%
  • Monetary value: $20,000

You can calculate the expected utility using the following steps:

1. Assess the probability and monetary value of event 1.

   The first step is to determine the probability of event 1 along with its monetary value. In our example, Investment A has a 40% chance of happening, and its monetary value is $10,000.

   To facilitate this calculation, you can also check out our probability calculator.

2. Evaluate the probability and monetary value of event 2.

   Next, you should compute the probability of Investment B and its the payoff attached to it. In this instance, investment B has a 60% probability and a monetary value of $20,000.

3. Compute the expected utility.

   Now, you can calculate the expected utility using the expected utility formula below:

   expected utility = (probability of event 1 × (monetary value 1 ^ 0.5)) + (probability of event 2 × (monetary value 2 ^ 0.5))

   For the given example:

   expected utility = (0.4 × ($10,000 ^ 0.5)) + (0.6 × ($20,000 ^ 0.5)) = 124.85

Now that we have understood the calculation of expected utility, let's look at how the expected utility can guide strategic decisions:

• Optimizing portfolio management

  Expected utility is an instrumental metric used in finance. It is used to balance portfolios by assessing the risk-reward trade-off of various investments. Investors often have different risk tolerances, profiles, and preferences; hence, it is sometimes more important to assess a portfolio based on its expected utility instead of just looking at the returns.

• Guiding business investments

  Companies often face investment decisions with uncertain returns. Expected utility allows them to choose investments that best align with their financial strategies and risk tolerance levels, potentially avoiding choices that, while lucrative, could jeopardize the company's financial stability if risks materialize.

• Negotiations and contracts

  Expected utility is also commonly used in negotiations. Within a negotiation, different terms offer different utility to each party. Understanding the expected utility of different contract terms can help negotiators prioritize which terms to push for and which to compromise on based on the relative value and likelihood of each outcome.