Calculate The Expected Return

Expected Return Formula:

\[ E(r) = \sum (p_i \times r_i) \]

Expected Return (E(r)):

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1. What is Expected Return?

The expected return is a statistical measure that calculates the average of a probability distribution of possible returns. It represents the mean value of the probability distribution of investment returns and is a key concept in portfolio theory and risk management.

2. How Does the Calculator Work?

The calculator uses the expected return formula:

\[ E(r) = \sum (p_i \times r_i) \]

Where:

\( E(r) \) — Expected return (%)
\( p_i \) — Probability of scenario i (unitless)
\( r_i \) — Return in scenario i (%)

Explanation: The formula multiplies each possible return by its probability and sums all these products to get the overall expected return.

3. Importance of Expected Return Calculation

Details: Expected return is fundamental in investment analysis, portfolio optimization, and risk assessment. It helps investors make informed decisions by quantifying the average return they can expect from an investment considering different possible outcomes.

4. Using the Calculator

Tips: Enter probabilities as decimal values (must sum to 1) and returns as percentages. Separate values with commas. For example: probabilities "0.3, 0.4, 0.3" and returns "5, 10, -2".

5. Frequently Asked Questions (FAQ)

Q1: What if my probabilities don't sum to exactly 1?
A: The calculator requires probabilities to sum to 1 (within a small tolerance). This ensures a valid probability distribution.

Q2: Can I use percentages for probabilities?
A: No, probabilities should be entered as decimal values between 0 and 1. For example, use 0.25 instead of 25%.

Q3: How many scenarios can I calculate?
A: You can calculate as many scenarios as needed, but the number of probabilities must match the number of returns.

Q4: What does a negative expected return mean?
A: A negative expected return indicates that, on average, you would expect to lose money from the investment based on the given scenarios.

Q5: Is expected return the same as guaranteed return?
A: No, expected return is an average of possible outcomes. The actual return may be higher or lower than the expected value.