What Is Expected Return (E(R))?

Expected Return, represented as E(R), is the anticipated return from an investment or portfolio calculated using a probability-weighted average of possible outcomes.

Expected Return (E(R)) is the anticipated return from an investment or a portfolio based on the probability-weighted average of all possible outcomes. It is a fundamental concept in finance and investment that helps in assessing the potential profitability of an investment. Mathematically, it is expressed as follows:

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

where \( P_i \) represents the probability of outcome \( i \) occurring, and \( R_i \) is the corresponding return for outcome \( i \).

Importance of Expected Return

Expected return is vital for investors because it:

• Helps in Decision Making: Influences investment choices by estimating potential future gains.
• Risk Assessment: Facilitates evaluation of investment risks by comparing expected returns with actual returns.
• Portfolio Management: Aids in constructing and managing diversified portfolios to achieve desired financial goals.

Types of Expected Return

1. Arithmetic Mean Expected Return

The arithmetic mean expected return is a simple average of all possible returns weighted by their probabilities.

2. Geometric Mean Expected Return

The geometric mean expected return considers the compounding effect of returns over multiple periods, giving a more accurate long-term perspective.

Calculating Expected Return

Example Calculation

Suppose you have an investment with three possible scenarios:

1. Economic Boom: 30% probability, 20% return
2. Steady Growth: 50% probability, 10% return
3. Economic Downturn: 20% probability, -5% return

The expected return (E(R)) is calculated as:

$$ E(R) = (0.3 \times 20\%) + (0.5 \times 10\%) + (0.2 \times (-5\%)) = 6\% + 5\% - 1\% = 10\% $$

Historical Context

The concept of expected return has its roots in the early 20th century with the development of modern portfolio theory (MPT) by Harry Markowitz in the 1950s. This theory emphasizes the importance of balancing risk and return, and the expected return is a cornerstone of this model.

Applicability in Modern Finance

Portfolio Diversification

Expected return is crucial in modern portfolio theory, helping investors to create portfolios that maximize returns for a given level of risk.

Capital Asset Pricing Model (CAPM)

In the CAPM, the expected return is part of the formula used to determine the required return on an asset, considering its systematic risk (beta).

$$ E(R_i) = R_f + \beta_i (E(R_m) - R_f) $$

where \( E(R_i) \) is the expected return on the investment, \( R_f \) is the risk-free rate, \( \beta_i \) is the beta of the investment, and \( E(R_m) \) is the expected return of the market.

Comparisons and Related Terms

Standard Deviation

While the expected return focuses on the average outcome, standard deviation measures the dispersion of possible returns, providing insight into investment risk.

Variance

Variance quantifies the degree of variation from the expected return, indicating the consistency of returns.

Frequently Asked Questions (FAQs)

What factors influence the expected return?

Various factors, including market conditions, economic indicators, past performance, and investor sentiment, can influence the expected return.

How reliable is the expected return?

While it provides a useful estimate, expected return is not a guarantee of future performance. It is based on probabilities and assumptions, which may change.

Can the expected return be negative?

Yes, if the probability-weighted average of outcomes results in a negative value, the expected return can be negative, indicating a potential loss.

References

1. Markowitz, Harry. “Portfolio Selection.” The Journal of Finance, vol. 7, no. 1, 1952, pp. 77-91.
2. Sharpe, William F., et al. Investments. Prentice Hall, 2009.
3. Fama, Eugene F., and Kenneth R. French. “The Capital Asset Pricing Model: Theory and Evidence.” Journal of Economic Perspectives, vol. 18, no. 3, 2004, pp. 25-46.

Summary

Expected return (E(R)) is a crucial financial concept used to anticipate the profitability of an investment or portfolio by computing the probability-weighted average of all possible outcomes. It plays a significant role in decision-making, risk assessment, and portfolio management, making it an indispensable tool for modern finance and investment strategies.