# Understanding Expected Return: A Guide to Investment Profitability

> **Definition**
>
> Expected return is the profit or loss an investor expects based on historical rates of return and calculated as a weighted average of potential outcomes.

## What Is Expected Return?

The expected return is the profit or loss an investor expects from an investment based on past returns. Thus, the expected return is like a long-term average of past [returns](https://www.investopedia.com/terms/h/historical-returns.asp).

### Key Takeaways

*   The expected return is an estimation based on historical rates of return, representing the anticipated average outcome of an investment's performance over time, but it is not guaranteed.  
    
*   Investors can use the expected return to analyze whether an investment, or an entire portfolio, has a potential positive or negative average net outcome.  
    
*   Expected return calculations are fundamental to financial theories such as modern portfolio theory (MPT) and options pricing models like Black-Scholes, which assess the potential profitability and risk of investments.  
    
*   Understanding the distinction between systematic and unsystematic risk is crucial, as these risks impact the likelihood of achieving the expected return.  
    
*   While the expected return helps gauge investment potential, it should be considered alongside other risk measures, like standard deviation, to understand an investment's risk profile more fully.

![Expected Return](https://www.investopedia.com/thmb/Lkz_S7M0A2oo54Dzt3Cvd2cAZOw=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/ExpectedReturn-4196761-Final-25b2aa6c16ce4a89a778a1e55302136b.jpg)

*— Investopedia / Paige McLaughlin*

## Understanding the Theory Behind Expected Return

Expected return calculations are crucial in business and financial theory, as seen in [modern portfolio theory (MPT)](https://www.investopedia.com/terms/m/modernportfoliotheory.asp) and the [Black-Scholes](https://www.investopedia.com/terms/b/blackscholes.asp) model.

The expected return helps determine whether an investment has a positive or negative average net outcome.

The expected return is calculated as the [expected value (EV)](https://www.investopedia.com/terms/e/expected-value.asp) of an investment's potential returns, shown by this formula:

> Expected Return = Σ (Returni x Probabilityi)

Where "i" indicates each known return and its respective probability in the series

For example, if an investment has a 50% chance of gaining 20% and a 50% chance of losing 10%, the expected return would be 5% = (50% x 20% + 50% x -10% = 5%). The 5% expected return may never be realized, as the investment is inherently subject to [systematic](https://www.investopedia.com/terms/s/systematicrisk.asp) and [unsystematic](https://www.investopedia.com/terms/u/unsystematicrisk.asp) risks.

> **Important**
>
> Systematic risk affects a market sector or the entire market, whereas unsystematic risk applies to a specific company or industry.

## Calculating Expected Return: The Formula Explained

For individual investments or portfolios, a formal equation for expected return is:

![Expected return](https://www.investopedia.com/thmb/bBnADCPGc3wIc6-AmEZg2nTkx6U=/1280x0/filters:no_upscale():max_bytes(150000):strip_icc()/expectedreturncorrected-e0e026cf96334027b60d468d7fc59866.jpg)

*Expected return = risk free premium + Beta (expected market return - risk free premium).*

Where:

*   ra = expected return;
*   rf \= the [risk-free rate of return](https://www.investopedia.com/terms/r/risk-freerate.asp);
*   β = the investment's [beta](https://www.investopedia.com/terms/b/beta.asp); and
*   rm =the expected market return

The expected return above the risk-free [rate of return (RoR)](https://www.investopedia.com/terms/r/rateofreturn.asp) depends on the investment's beta, or relative volatility compared to the broader market. The expected return and [standard deviation](https://www.investopedia.com/terms/s/standarddeviation.asp) are two statistical measures that can be used to analyze a portfolio.

The portfolio's expected return is the average of its possible returns. The standard deviation of a portfolio measures the amount that the returns deviate from its mean, making it a proxy for the portfolio's risk.

## Limitations of Expected Return

Before making any investment decisions, investors [review the risk characteristics](https://www.investopedia.com/terms/r/riskreturntradeoff.asp) of opportunities to determine if the investments align with their portfolio goals. Assume two hypothetical investments exist. Their annual performance results for the last five years are:

*   _Investment A:_ 12%, 2%, 25%, -9%, and 10%
*   _Investment B_: 7%, 6%, 9%, 12%, and 6%

Both of these investments have expected returns of 8%. However, when analyzing the risk of each, as defined by the standard deviation, investment A is approximately five times riskier than investment B.

Investment A has a standard deviation of 11.26% and investment B has a standard deviation of 2.28%. Standard deviation is a common statistical metric to measure an investment's historical volatility or risk.

![Standard Deviation = Square Root((Sum(Each data point - Mean)^2)/(Number of data points - 1))](https://www.investopedia.com/thmb/xXHM42dRuVzZY_PkkJqhHEfTekI=/1280x0/filters:no_upscale():max_bytes(150000):strip_icc()/latex_c5e1bbb85d06910d235265c0e25fad31-5c78596246e0fb0001a5eff0.jpg)

*Standard Deviation Formula. — Investopedia *

**Where:**

_xi_ \=Value of the _ith_ point in the data set

_x_ \=The mean value of the data set

_n_ \=The number of data points in the data set  

## Practical Examples of Expected Return Calculations

The expected return can apply to a single [security](https://www.investopedia.com/terms/s/security.asp) or asset or be expanded to analyze a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.

For example, assume an investor has the following portfolio:

*   Alphabet Inc., ([GOOG)](https://www.investopedia.com/markets/quote?tvwidgetsymbol=goog): $500,000 invested and an expected return of 15%
*   Apple Inc. ([AAPL](https://www.investopedia.com/markets/quote?tvwidgetsymbol=aapl)): $200,000 invested and an expected return of 6%
*   Amazon.com Inc. ([AMZN](https://www.investopedia.com/markets/quote?tvwidgetsymbol=amzn)): $300,000 invested and an expected return of 9%

With a total portfolio value of $1 million, the weights of Alphabet, Apple, and Amazon in the portfolio are 50%, 20%, and 30%, respectively. The expected return of the total portfolio is:

(50% x 15%) + (20% x 6%) + (30% x 9%) = 11.4%

## How Is Expected Return Used in Finance?

Expected return calculations determine whether an investment has a positive or negative average net outcome. The equation is usually based on historical data and therefore cannot be guaranteed for future results, however, it can set reasonable expectations.

## What Are Historical Returns?

Historical returns are the past performance of a security or index, such as the [S&P 500](https://www.investopedia.com/terms/s/sp500.asp). Analysts review historical return data to predict future returns or to estimate how a security might react to a particular economic situation, such as a drop in consumer spending.

## How Does Expected Return Differ From Standard Deviation?

Expected return and standard deviation are two statistical measures used to analyze a portfolio. The expected return of a portfolio is the anticipated returns a portfolio may generate, making it the average distribution. The standard deviation of a portfolio measures the amount that the returns deviate from its mean, making it a proxy for the portfolio's risk.

## The Bottom Line

The expected return is the average return that an investment or portfolio should generate over a certain period. Riskier assets require a higher expected return to offset the added risk. Expected return is not a guarantee, but a prediction based on historical data and other relevant factors.

> **Article Sources**
>
> 1.  University of Washington. "[Chapter 1, Introduction to Portfolio Theory](https://faculty.washington.edu/ezivot/econ424/introductionPortfolioTheory.pdf)."
>     
> 2.  University at Albany, SUNY. "[Financial Economics: Black-Scholes Option Pricing](https://www.albany.edu/~bd445/Economics_802_Financial_Economics_Slides_Fall_2013/Black-Scholes_Option_Pricing.pdf)."