Expected Utility Calculator

Name: Expected Utility Calculator
Author: Laxman Kumawat

Calculate expected value and expected utility from outcomes, probabilities, and risk aversion.

Last Updated: May 2026

Risk

Inputs

OutcomesProbabilitiesPercent probabilities that should sum to 100.

Risk aversion coefficient

Expected Value

$12,500.00

Certainty Equivalent

$12,189.79

Risk Premium

$310.21

Probability Total

100.00%

Calculation Details

Item	Value
Outcome 1	$8,000.00 at 25.00%
Outcome 2	$12,000.00 at 50.00%
Outcome 3	$18,000.00 at 25.00%

Investment Planning Notice

Results support education and scenario analysis. They do not provide personalized investment, tax, accounting, or legal advice.

Reviewed For Methodology, Labels, And Sources

Every CalculatorWallah calculator is published with visible update labeling, linked source references, and review of formula clarity on trust-sensitive topics. Use results as planning support, then verify institution-, policy-, or jurisdiction-specific rules where they apply.

Reviewed By

Laxman Kumawat, Finance & Engineering Calculator Owner, reviews methodology, labels, assumptions, and trust-sensitive publishing decisions for this topic area.

Review editor profile

Topic Ownership

Financial calculators, Engineering calculators, Electrical and HVAC planning calculators, Investment, salary, loan, and technical design-estimate workflows

See ownership standards

Methodology & Updates

Page updated May 2026. Finance and engineering calculators are reviewed when formulas, rate assumptions, or technical references change, and during broader category refreshes.

Sources & methodology About the review process

How to Use the Expected Utility Calculator

Step 1: Set Outcomes
Start with outcomes such as 8000, 12000, 18000 so the expected utility calculation has the correct base.
Step 2: Complete the scenario inputs
Add probabilities, and risk aversion coefficient using the same period and quote convention as your source data.
Step 3: Review Expected utility
Read the expected utility result first, then check the supporting values to confirm the formula used the expected inputs.
Step 4: Compare against a benchmark
Compare the result with a benchmark portfolio, peer manager, risk-free rate, or the same strategy over another period.

How This Expected Utility Calculator Works

Expected Utility Calculator applies Σ probability × utility(outcome) to the values entered in the form. Percentage inputs are converted to decimals during calculation, while currency, count, and list inputs keep their displayed units.

Risk metrics require consistent return periods and matching risk measures. Annual returns should be paired with annual volatility or tracking error. The result should be read with the example inputs and formula reference below so the metric is tied to the exact scenario being modeled.

What You Need to Know

Worked Example Setup

The default setup follows the page scenario: Calculate expected value and expected utility from outcomes, probabilities, and risk aversion. Start with these values to check the formula, then replace each input with your own source data.

Input	Example value	How to treat it
Outcomes	8000, 12000, 18000	Use the outcomes from the same scenario as the other inputs.
Probabilities	25, 50, 25	Percent probabilities that should sum to 100.
Risk aversion coefficient	0.00005	Use the risk aversion coefficient from the same scenario as the other inputs.

Formula Reference

Metric	Formula	Use
Expected utility	Σ probability × utility(outcome)	Uses exponential utility for risk adjustment

Formula Terms Explained

The formula is only useful when each term comes from the same scenario. The table below maps the fields in the calculator to the values used in the worked example.

Formula term	Example value	How the calculator uses it
Outcomes	8000, 12000, 18000	Parsed as an ordered list so each value keeps its position in the calculation.
Probabilities	25, 50, 25	Parsed as an ordered list so each value keeps its position in the calculation.
Risk aversion coefficient	0.00005	Used directly as the risk aversion coefficient term in the scenario.

Worked Example Walkthrough

Step	Example detail
1. Start with the example inputs	Outcomes: 8000, 12000, 18000; Probabilities: 25, 50, 25; Risk aversion coefficient: 0.00005
2. Normalize the inputs	The default inputs are used in their displayed units.
3. Preserve list order	Outcomes: 8000, 12000, 18000; Probabilities: 25, 50, 25 are read in order from first period to last period.
4. Apply the formula	Expected utility = Σ probability × utility(outcome)
5. Interpret the output	Read the expected utility result with the supporting rows from the calculator widget before comparing it with a benchmark.

When to Use Expected Utility Calculator

Use case	How it helps
Portfolio review	Check whether return compensated for the risk taken.
Manager comparison	Compare active return, beta exposure, or downside risk across strategies.
Loss planning	Estimate drawdown or value-at-risk context before sizing a position.

Interpreting Expected utility

The output evaluates return after adjusting for volatility, downside risk, benchmark behavior, beta, or potential loss.

A better risk-adjusted result means the return was more efficient for the type of risk measured, not that the strategy is risk-free.

Compare the result with a benchmark portfolio, peer manager, risk-free rate, or the same strategy over another period. Risk ratios can be distorted by short histories, stale prices, non-normal returns, or one unusually strong period.

Common Mistakes

Mistake	Why it matters
Mixed time bases	Monthly volatility and annual return must be converted before comparison.
Overreading one ratio	Sharpe, Sortino, Treynor, and information ratio measure different risks.
Ignoring tail behavior	Normal approximations can understate rare losses.

Before You Use the Result

Review point	What to confirm
Same-period inputs	Expected utility is easier to trust when every input uses the same time period, currency, and quote convention.
Benchmark selected	Compare the result with a benchmark portfolio, peer manager, risk-free rate, or the same strategy over another period.
Risk and cost review	Check taxes, fees, liquidity, downside risk, and data quality before treating the output as an investment decision.
Known limitation	Risk ratios can be distorted by short histories, stale prices, non-normal returns, or one unusually strong period.

Keep the research moving with Sharpe Ratio Calculator, Sortino Ratio Calculator, Treynor Ratio Calculator, and Information Ratio Calculator.

Frequently Asked Questions

Expected utility uses Σ probability × utility(outcome). Risk metrics require consistent return periods and matching risk measures. Annual returns should be paired with annual volatility or tracking error.

Expected Utility Calculator uses outcomes, probabilities, and risk aversion coefficient. Keep those inputs on the same time basis and quote convention before reading the result.

The output evaluates return after adjusting for volatility, downside risk, benchmark behavior, beta, or potential loss. A better risk-adjusted result means the return was more efficient for the type of risk measured, not that the strategy is risk-free.

Treat the output as decision support. Real investment choices should also account for taxes, liquidity, risk, timing, fees, and professional advice where appropriate.

Compare the result with a benchmark portfolio, peer manager, risk-free rate, or the same strategy over another period.

Risk ratios can be distorted by short histories, stale prices, non-normal returns, or one unusually strong period.