Expected return is a crucial concept in the field of finance and investing, representing the profit or loss that an investor anticipates on an investment based on historical rates of return (RoR). While the expected return provides a reasonable framework for investment decisions, it is important for investors to remember that these returns are not guaranteed.
Key Takeaways
- The expected return is the anticipated profit or loss on an investment.
- Expected returns are inherently uncertain and cannot be guaranteed.
- For a diversified portfolio, the expected return is calculated as a weighted average of the expected returns of each individual investment.
Expected Return Theory
Expected return is fundamental in finance, underpinning various theories and models, including the Modern Portfolio Theory (MPT) and the Black-Scholes options pricing model. These theories utilize expected return to ascertain the likelihood of achieving positive or negative net outcomes from investments.
Calculating Expected Return
The calculation for expected return helps various stakeholders evaluate investment opportunities based on potential performance across different scenarios. The expected return (ER) can be mathematically expressed as:
[ \text{Expected Return} = \Sigma (\text{Return}_i \times \text{Probability}_i) ]
Where "i" represents each possible return and its associated probability.
For example, consider an investment that has a 50% chance of realizing a gain of 20% and a 50% chance of suffering a loss of 10%. The expected return calculation yields:
[ \text{Expected Return} = (0.50 \times 20\%) + (0.50 \times (-10\%)) = 5\% ]
This means, statistically, the investor can expect a 5% return, though actual results may vary due to inherent risks.
Risk Considerations
Investors must also factor in risks when evaluating expected returns. Two primary types of risk influence the returns on investments:
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Systematic Risk: This impacts the entire market or a specific market sector. For instance, an economic downturn can negatively affect all sectors.
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Unsystematic Risk: This pertains to individual firms or industries and is often related to company-specific events such as management changes, product recalls, or competitive disruptions.
Formal Expected Return Formula
For individual financial investments or portfolios, a more sophisticated formula helps assess expected return:
[ \text{Expected return} = \text{Risk-free rate} + \beta \times (\text{Expected market return} - \text{Risk-free rate}) ]
Where: - ( r_a ) = expected return - ( r_f ) = risk-free rate of return - β (Beta) = measure of volatility relative to the market - ( r_m ) = expected market return
The expected return thus reflects not only the anticipated growth of an investment but also the risk premium required for the inherent uncertainty.
Limitations of Expected Return
While expected return serves as a guideline, it is not without limitations. Investors need to consider the historical performance data and the statistical risk metrics, including standard deviation, to fully understand potential volatility and risk.
Example of Investment Evaluation
Suppose an investor analyzes two hypothetical investments with the following historical annual returns:
- Investment A: 12%, 2%, 25%, -9%, 10%
- Investment B: 7%, 6%, 9%, 12%, 6%
Both investments have an average expected return of 8%. However, a deeper dive into the risk reveals that Investment A carries a standard deviation of 11.26%, making it significantly more volatile than Investment B, which boasts a standard deviation of 2.28%.
Application in Portfolio Management
Expected return can be applied to individual securities or an entire investment portfolio. In practice, investors utilize the expected returns of their various holdings to form an overall portfolio return estimate. Here’s an illustration using multiple securities:
Assume a portfolio with: - Alphabet Inc. (GOOG): $500,000 invested, expected return 15% - Apple Inc. (AAPL): $200,000 invested, expected return 6% - Amazon.com Inc. (AMZN): $300,000 invested, expected return 9%
Calculating the total portfolio's expected return:
[ \text{Total Expected Return} = (0.50 \times 15\%) + (0.20 \times 6\%) + (0.30 \times 9\%) = 11.4\% ]
Conclusion
The expected return provides investors with an anticipated average return on investments over time. However, it is vital to incorporate risk assessments, including the volatility of returns, into the decision-making process. Although riskier assets typically demand a higher expected return to compensate for uncertainties, investors should remember that expected return is fundamentally a statistical estimate based on historical data and market dynamics. Understanding the interplay between expected return, risk, and historical performance is essential for effective portfolio management and investment strategy formulation.
Additional Terms Related to Expected Return
- Historical Returns: Refers to past performance of an asset, crucial for predicting future returns.
- Standard Deviation: A key statistical measure that gives insights into the volatility or risk of an investment or portfolio.
- Beta: A measure of the sensitivity of an asset's returns to market returns, reflecting systematic risk.
Investors who grasp these concepts will be better equipped to navigate the complexities of the financial markets and make informed investment decisions.