Browse Investing

Expected Return: The Probability-Weighted Average Outcome Investors Anticipate

Investments

Learn expected return, how it is calculated, why it matters in portfolio theory, and why a high expected return does not automatically mean a better investment.

On this page

Expected return is the probability-weighted average return an investor anticipates from an asset or portfolio. It is a forward-looking estimate, not a guaranteed outcome.

Finance uses expected return because investors need a way to compare opportunities under uncertainty. It answers a simple question: if different outcomes are possible, what is the average result we should expect over many repetitions or under the assumed probability distribution?

Expected Return Formula

$$ E(R)=\sum_{i=1}^{n} p_i R_i $$

Where:

  • \(E(R)\) = expected return
  • \(p_i\) = probability of outcome \(i\)
  • \(R_i\) = return in outcome \(i\)

The probabilities should add up to 1.

Worked Example

Suppose an investment has three possible one-year outcomes:

  • 20% chance of a 12% gain
  • 50% chance of a 6% gain
  • 30% chance of a 4% loss

Then:

$$ E(R)=(0.20\times0.12)+(0.50\times0.06)+(0.30\times-0.04)=0.042 $$

So the expected return is 4.2%.

That does not mean the investment will earn exactly 4.2% next year. It means 4.2% is the average implied by the model’s probabilities.

Why Expected Return Matters

Expected return is foundational in:

In portfolio theory, expected return is the “reward” side of the risk-reward tradeoff.

Expected Return for a Portfolio

For a portfolio, expected return is the weighted average of the expected returns of the holdings:

$$ E(R_p)=\sum_{i=1}^{n} w_i E(R_i) $$

Where \(w_i\) is the weight of asset \(i\) in the portfolio.

This is why changing portfolio weights changes the portfolio’s expected return even before considering changes in risk.

Expected Return vs. Risk

A higher expected return is not automatically better.

Investors care about how much uncertainty, downside, or volatility must be accepted to pursue that return. That is why expected return is usually interpreted alongside:

Key Limitation

Expected return depends heavily on assumptions.

If the probabilities are unrealistic or if the future distribution of outcomes differs from the past, the estimate may be wrong. That is why expected return should be treated as a model input, not as a promise.

Confusing expected return with realized return

Expected return is an estimate. Actual return is what eventually happens.

Ignoring the distribution of outcomes

Two investments can have the same expected return but very different downside risk.

Treating historical averages as destiny

Past data can inform expectations, but it does not guarantee future returns.

  • Variance: Measures how dispersed outcomes are around the expected return.
  • Standard Deviation: The most common volatility measure used alongside expected return.
  • Sharpe Ratio: Measures excess return earned per unit of total risk.
  • Beta: Measures market-related sensitivity rather than total dispersion.
  • Capital Asset Pricing Model (CAPM): Connects expected return to systematic risk.

FAQs

Can expected return be negative?

Yes. If the probability-weighted average of the possible outcomes is below zero, the expected return is negative.

Why do investors still use expected return if it is uncertain?

Because investors still need a structured way to compare opportunities under uncertainty. Expected return is imperfect, but it is essential.

Is expected return the same as average historical return?

Not necessarily. Historical averages may be one input, but expected return is ultimately an estimate about the future.
Revised on Monday, May 18, 2026
Annualized Return
Mean Return