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Expected Return Calculator

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The total probability for all scenarios must equal 100%. 

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Whether you’re putting together your first portfolio or professionally reviewing investment strategies, Omni’s expected return calculator helps you estimate the potential return and risk of an investment. It simplifies the process of comparing options, assessing scenarios, and making financial decisions with a bit more confidence. Understanding the expected return concept is essential when you’re trying to weigh risk against potential reward.

Keep scrolling to learn:

  • How to calculate expected return;
  • How to apply the expected rate of return formula;
  • What the relationship is between risk and return; and
  • How to evaluate investment risk before making strategic decisions.

What is expected return? — Expected rate of return formula explained

Expected return is the average rate of return an investor expects to see from an investment based on a range of possible outcomes and their probabilities, usually relying on historical rates of return. Instead of guessing a single exact future outcome, it gives a sense of what the typical result might look like, balancing both potential gains and losses. For realized investments, an ROI calculator is a better choice.

Statistically, expected return is the expected value of an investment’s returns. It sums up all the possible outcomes weighted by how likely each one is, giving you a sense of the “middle ground” in the range of returns you might see. In finance, you’ll often find it used to compare different investments, identify opportunities, and help decide how to put together a portfolio.

The expected return formula, also known as the expected rate of return formula, is:

E(r)=∑i=1npi×riE(r)=\sum_{i=1}^n p_i \times r_i

where:

  • E(r)E(r) — Expected return;
  • pip_i — Probability of outcome in scenario ii; and
  • rir_i — Return expected in a given scenario ii.

How to calculate expected return with examples

To compute expected return:

  1. Take each possible return.
  2. Multiply it by the chance of that outcome happening.
  3. Then add everything up.

The probabilities must sum to 100% because they cover all the possible outcomes.

Suppose you’re building a portfolio of FAANG stocks. You’re looking at Stock A, which is Apple (AAPL), and Stock B, Amazon (AMZN). They have these possible outcomes:

Probability

Stock A return

Stock B return

30%

-5%

-12%

50%

10%

14%

20%

25%

35%

We’ll use the expected return formula to calculate the expected value of the return distribution.

For Stock A:

E(rA)= 0.30×(−5%)+0.50×10%+0.20×25%= 8.5%\begin{aligned} E(r_A) =&\ 0.30 \times (-5\%) \\ &+ 0.50 \times 10\% \\ &+ 0.20 \times 25\% \\ =&\ 8.5\% \end{aligned}

For Stock B:

E(rB)= 0.30×(−12%)+0.50×14%+0.20×35%= 10.4%\begin{aligned} E(r_B) =&\ 0.30 \times (-12\%) \\ &+ 0.50 \times 14\% \\ &+ 0.20 \times 35\% \\ =&\ 10.4\% \end{aligned}

In this case, Stock B shows a higher expected return of 10.4%. However, that doesn’t guarantee it will actually make 10.4% in the next period! If you want to analyze the profit and ROI of a completed stock investment, try our stock calculator.

Expected return represents the average return you’d expect based on the probabilities and return entered. So, think of it as more of a “best guess” driven by the numbers rather than a precise prediction.

💡 Learn how to find the expected value beyond investment returns.

What is the relationship between risk and return? — Comparing the investment risk

When it comes to investing, one of the key ideas is balancing risk and return. Usually, if an investment promises higher returns, it also entails greater uncertainty. So, investors don’t just look at the potential gains but also at investment risk before making a decision.

This investment risk is often measured by how far actual returns may deviate from the expected return. Two typical ways to measure this are variance and standard deviation. The larger these values are, the greater the level of return uncertainty.

The variance of returns is calculated as:

Var(r)=σ2=∑i=1npi(ri−rˉ)2{\rm Var}(r)=\sigma ^2=\sum_{i=1}^n p_i (r_i - \bar r)^2

Here, pip_i represents the probability of scenario ii occurring, rir_i is the return in that particular scenario, and rˉ\bar r stands for the expected return.

The standard deviation is just the square root of the variance:

SD(r)=σ=σ2​{\rm SD}(r)=\sigma=\sqrt{\sigma^2} ​

Let’s return to our FAANG example. Using a calculated expected return of 8.5% and 10.4%, we will compute the variance and standard deviation for both stocks:

Var(rA)= 0.30 (−5%−8.5%)2+0.50 (10%−8.5%)2+0.20 (25%−8.5%)2≈ 0.0140\begin{aligned} {\rm Var}(r_A) =&\ 0.30 \,(-5\% - 8.5\%)^2 \\ &+ 0.50 \,(10\% - 8.5\%)^2 \\ &+ 0.20 \,(25\% - 8.5\%)^2 \\ \approx&\ 0.0140 \end{aligned}
SD(rA)=0.0140≈0.118≈11.8%{\rm SD}(r_A)=\sqrt{0.0140} \approx 0.118 \approx 11.8\%

Let’s do the same for Stock B:

Var(rB)= 0.30 (−12%−10.4%)2+0.50 (14%−10.4%)2+0.20 (35%−10.4%)2≈ 0.0274\begin{aligned} {\rm Var}(r_B) =&\ 0.30 \,(-12\% - 10.4\%)^2 \\ &+ 0.50 \,(14\% - 10.4\%)^2 \\ &+ 0.20 \,(35\% - 10.4\%)^2 \\ \approx&\ 0.0274 \end{aligned}
SD(rB)=0.0274≈0.165≈16.5%{\rm SD}(r_B)=\sqrt{0.0274} \approx 0.165 \approx 16.5\%

In this scenario, Stock B has a higher expected return — about 10.4% compared to Stock A’s 8.5%. But it’s also riskier since its variance and standard deviation are both larger. This demonstrates the classic relationship between risk and return: if you’re aiming for bigger gains, you usually have to accept more uncertainty.

Our investment return calculator handles all the math, allowing you to compare investment opportunities in seconds.

How to use expected return calculator

Using our expected return calculator is straightforward:

  1. Input the probability for each market scenario. Make sure the probabilities add up to 100%.
  2. Enter the expected return for Stock A in each scenario. Use positive percentages for a gain or negative numbers for a loss.
  3. Repeat the same for Stock B.
  4. Add additional scenarios if needed. New rows will appear automatically as you enter data.
  5. Omni’s investment return calculator will compute the expected return, variance, and standard deviation for both stocks.
  6. Compare the investments to get a sense of how risky each stock is.

FAQs

What is the expected return?

Expected return is the probability-weighted average return you’d expect from an investment across all possible scenarios. While it is useful for comparing investment opportunities, it’s important to remember that this is just an estimate. It doesn’t promise future results because actual market conditions may differ from expectations.

How do I calculate expected return?

To compute expected return:

  1. Multiply each possible return by its probability.

  2. Add the results together using the expected return formula:

    E(r)=∑piri

  3. Ensure the probabilities of all outcomes add up to 100% to make calculations valid.

What is my expected return if I can lose 5% (40%) or gain 15% (60%)?

The expected return is 7%. Multiply each return by its probability and add the results:

E(r) = 0.40 × (-5%) + 0.60 × 15% = -2% + 9% = 7%

What is a good expected return for a portfolio?

A good expected return for a portfolio falls somewhere around 7% to 10% per year over the long term. Aggressive portfolios with 80%-100% stocks usually aim for returns north of 10%, while balanced portfolios with a mix of stocks and bonds often target 7%-9%. The exact expected return depends on your investment horizon, risk tolerance, and asset allocation.