Compare gambles using expected utility with a risk-aversion setting.
Please do not make financial decisions based on these results.
What is the Expected Utility Calculator?
Compare gambles using expected utility with a risk-aversion setting. To use the Expected Utility Calculator, enter probability of win, win outcome wealth, loss outcome wealth, risk aversion; it returns expected utility, expected wealth, certainty equivalent, and shows them instantly as you type.
Where the Expected Utility Calculator fits
Compare gambles using expected utility with a risk-aversion setting. The main figure it returns is the Expected utility, worked out from the values you enter.
It belongs with the other investment tools. If you are comparing options or checking a result from another angle, try the Expected Return Calculator, Continuous Compound Interest Calculator or the Investment Fee Calculator.
How to use the Expected Utility Calculator
- Fill in the fields. You will need Probability of win (%), Win outcome wealth ($), Loss outcome wealth ($), Risk aversion (ρ, not 1). Use a rate of return you consider realistic; small changes compound into large differences. Fields marked optional can stay at zero.
- Read the result. The highlighted box gives the Expected utility, and the cards below show Expected wealth, Certainty equivalent. Tables and charts break it down further.
- Test other scenarios. Results update as you type. Change one value at a time to see what drives the answer, and press Reset to go back to the defaults.
Formula and how it works
Example with real numbers
Here is the Expected Utility Calculator using the default values shown in the calculator above:
Inputs
| Probability of win (%) | 50 |
|---|---|
| Win outcome wealth ($) | 150,000 |
| Loss outcome wealth ($) | 60,000 |
| Risk aversion (ρ, not 1) | 2 |
Results
| Expected utility | -0 |
|---|---|
| Expected wealth | $105,000.00 |
| Certainty equivalent | $85,714.29 |
With these inputs the calculator returns Expected utility: -0. Change any value in the calculator to see how the result moves.
What if you change one input?
Sensitivity check: raising Probability of win (%) from 50 to 60 (about 20% higher) and leaving everything else as in the example above changes the results like this:
| Result | Example | After the change | Change |
|---|---|---|---|
| Expected utility | -0 | -0 | +8.6% |
| Expected wealth | $105,000.00 | $114,000.00 | +8.6% |
| Certainty equivalent | $85,714.29 | $93,750.00 | +9.4% |
The input that moves the result most is the one to check twice. Change it in the calculator above to test your own case.
What the results tell you
The results panel of the Expected Utility Calculator reports Expected utility, expected wealth and certainty equivalent. Compare these figures while changing one input at a time, and use the related calculators below to look at the same situation from another angle.
Method and limits. This calculator applies the formula in the section above to your inputs, in your browser; nothing you enter is stored on our servers. Investment returns are not guaranteed. The result shows what the numbers you enter would produce, not what the market will do. It is for information, not financial, tax or legal advice.
Frequently asked questions
What does risk aversion do?
Higher values make the same loss hurt more than an equal gain helps.
What rate of return should I assume?
There is no guaranteed rate. Test a range of conservative and optimistic rates, and remember that fees and inflation reduce your real return.
Are investment returns guaranteed?
No. Real returns vary. Use these tools to compare scenarios, not to predict results.
Are the results guaranteed?
No. Results depend entirely on the numbers you enter and the formulas shown on this page. Please do not make financial decisions based on them alone; confirm important figures with a licensed professional.
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