What is Expected Return?
Expected return represents the profit or loss that an investor anticipates earning on an investment, calculated by multiplying potential outcomes by their respective probabilities and summing these results.
Key Takeaways
- The expected return predicts the probable profit or loss from an investment.
- It’s calculated by combining potential outcomes and their probabilities.
- Although expected returns offer insight, they cannot be guaranteed.
- The expected return for a diversified portfolio is the weighted average of the individual expected returns of its components.
Understanding Expected Return
Expected return calculations play a crucial part in financial decision-making and theories, such as the Modern Portfolio Theory and various options pricing models. For instance, an investment with a 50% chance of gaining 20% and a 50% chance of losing 10% has an expected return of 5% (50% x 20% + 50% x -10%).
Additionally, expected return helps in evaluating whether an investment is likely to result in overall gain or loss, particularly through its expected value (EV):
Expected Return = Σ (Returnᵢ x Probabilityᵢ)
where ᵢ represents each known return and its probability in the data series.
Usually, expected returns are based on historical data, making them useful estimates yet inherently uncertain due to both systematic and unsystematic risks that can affect future performance.
Calculating Expected Return
For individual investments or portfolios, the equation for expected return takes a broader context:
Expected return = risk-free rate + Beta (expected market return - risk-free rate).
Where:
- rₐ = expected return
- rₓ= risk-free rate
- β = beta (relative volatility)
- rm= market return
This informs us that excess returns above the risk-free rate depend on the investment’s beta, reflecting its market volatility.
Limitations of Expected Return
Relying solely on expected return calculations is risky because it doesn’t incorporate the potential variability or risk. Examining standard deviation alongside expected return can offer a broader understanding of investment risk.
For example, consider two hypothetical investments:
- Investment A: Annual returns of 12%, 2%, 25%, -9%, 10%.
- Investment B: Annual returns of 7%, 6%, 9%, 12%, 6%.
Both have an 8% expected return, but differ considerably in risk, as seen through their standard deviations: 11.26% for Investment A and only 2.28% for Investment B.
Expected Return Example
Expected return can be calculated for portfolios as a weighted average of individual expected returns. Imagine a tech-focused portfolio:
- Alphabet Inc.: $500,000 with 15% expected return
- Apple Inc.: $200,000 with 6% expected return
- Amazon.com Inc.: $300,000 with 9% expected return
Given a total portfolio value of $1 million, the expected return is:
(50% x 15%) + (20% x 6%) + (30% x 9%) = 11.4%
How Is Expected Return Used in Finance?
Expected return is essential for financial models and investment theory, helping determine whether investments have a positive or negative net outcome based on historical data and shaping future expectations.
What Are Historical Returns?
Historical returns reveal past performance of an asset, aiding in predicting future performance and assessing how a security might react under varied economic scenarios.
How Does Expected Return Differ From Standard Deviation?
Expected return provides a projected performance estimate, while standard deviation measures the historical volatility around this projection, highlighting risk.
The Bottom Line
Expected return gives a valuable performance estimate for an investment or portfolio, balancing potential gains against risks. It’s a crucial tool for comparing investment options and aligning them with your financial goals.
Related Terms: Modern Portfolio Theory, Standard Deviation, Risk-Free Rate, Beta, Capital Asset Pricing Model.
References
- Professor Eric Zivot, University of Washington. “Chapter 1, Introduction to Portfolio Theory”.
- Professor Bruce C. Dieffenbach, University at Albany. “Financial Economics: Black-Scholes Option Pricing”.
- Riaz Hussain, University of Scranton. “3. Basics of Portfolio Theory”.
