1. What is Expected Return?

The Expected Return (ER) is a statistical measure that calculates the average return of an investment based on the probabilities of different outcomes. It represents the mean value of the probability distribution of possible returns.

2. How Does the Calculator Work?

The calculator uses the expected return formula:

Where:

• \( P_1, P_2, \ldots, P_n \) — Probabilities of each outcome (must sum to 1)
• \( R_1, R_2, \ldots, R_n \) — Returns for each outcome (in percentage)
• \( ER \) — Expected Return (in percentage)

Explanation: The formula calculates the weighted average of all possible returns, where the weights are the probabilities of each outcome occurring.

3. Importance of Expected Return Calculation

Details: Expected return is crucial for investment decision-making, portfolio optimization, risk assessment, and comparing different investment opportunities. It helps investors understand the potential average return they can expect from an investment over time.

4. Using the Calculator

Tips: Enter probabilities as comma-separated values (e.g., 0.3,0.4,0.3) and returns as comma-separated percentages (e.g., 10,15,5). Ensure probabilities sum to exactly 1 for accurate results.

5. Frequently Asked Questions (FAQ)

Q1: Why must probabilities sum to 1?
A: Probabilities represent all possible outcomes, so they must collectively account for 100% of the possibilities. If they don't sum to 1, the calculation is mathematically invalid.

Q2: How is expected return different from actual return?
A: Expected return is a statistical prediction based on probabilities, while actual return is the realized return that actually occurs. They may differ due to unforeseen events.

Q3: Can expected return be negative?
A: Yes, if the potential losses outweigh the potential gains in the probability distribution, the expected return can be negative.

Q4: What are the limitations of expected return?
A: It assumes probabilities are accurate and doesn't account for the variability or risk of returns (variance or standard deviation should also be considered).

Q5: How is this used in portfolio management?
A: Expected return is a key component in modern portfolio theory, helping investors optimize their portfolio allocation to maximize returns for a given level of risk.