Expected Return Calculator
Calculate expected return, variance, and standard deviation for two stocks. Compare risk versus return with interactive charts and detailed breakdown tables.
About This Calculator
The Expected Return Calculator helps investors estimate the potential return and risk of two stocks or assets across multiple probability-weighted scenarios. By entering different market outcomes with their likelihoods and corresponding returns, you can compute the expected (average) return, variance, and standard deviation for each asset. This enables you to compare investment opportunities on both return potential and risk level.
The expected return is calculated using the formula E(R) = Σ(pᵢ × rᵢ), where pᵢ is the probability of each scenario and rᵢ is the return in that scenario. Variance measures the dispersion of possible returns around the expected return: Var(R) = Σ(pᵢ × (rᵢ − E(R))²), while standard deviation (the square root of variance) provides a more intuitive risk measure in the same units as returns. A higher standard deviation indicates greater uncertainty and risk.
How to use this calculator
Start with the default scenarios or enter your own. Each row represents a market scenario with its probability, expected Stock A return, and expected Stock B return. The probabilities across all scenarios must sum to 100%. Click 'Add Scenario' to include more outcomes. The calculator automatically computes the expected return, variance, and standard deviation for both stocks, and highlights which stock offers higher return and lower risk.
Regional Notes
India: Indian investors can use this calculator to compare equity mutual funds, stocks, or sector allocations. Standard deviation is commonly reported in mutual fund fact sheets as a measure of risk. The Securities and Exchange Board of India (SEBI) mandates risk-o-meter classifications based on standard deviation and other metrics.
United States: US investors frequently use expected return and standard deviation for portfolio optimization under Modern Portfolio Theory (MPT). The S&P 500 has historically delivered an average annual return of around 10% with a standard deviation of approximately 15-18%. The Sharpe ratio, which uses standard deviation, is widely used to evaluate risk-adjusted returns.
United Kingdom: UK investors can apply this tool to compare FTSE 100 stocks, investment trusts, or multi-asset funds. The Bank of England base rate serves as a common risk-free rate benchmark. Standard deviation and variance are key inputs for the Capital Asset Pricing Model (CAPM) used by UK financial advisors.
Frequently Asked Questions
What is expected return?
Expected return is the probability-weighted average return you would expect from an investment across all possible scenarios. It is calculated using the formula E(R) = Σ(pᵢ × rᵢ), where pᵢ is the probability of each scenario and rᵢ is the return in that scenario.
How do I calculate expected return of a portfolio?
To calculate expected return, multiply each possible return by its probability, then sum the results. The probabilities of all outcomes must sum to 100%. For a portfolio with multiple assets, calculate the weighted average of each asset's expected return based on its allocation percentage.
What is variance and standard deviation in investing?
Variance measures how far actual returns may deviate from the expected return by calculating the probability-weighted average of squared deviations. Standard deviation is the square root of variance and is expressed in the same units as returns (percentage), making it a more intuitive measure of investment risk.
What is a good expected return for a portfolio?
A good long-term expected return for a balanced portfolio is typically 7-10% per year. Aggressive portfolios with 80-100% stocks may target returns above 10%, while conservative portfolios with more bonds may aim for 5-7%. Expected returns vary by asset allocation, market conditions, and investment horizon.
What is the relationship between risk and return?
Higher expected returns generally come with higher risk and uncertainty. This trade-off is measured by variance and standard deviation. An investment with a higher expected return typically has a wider range of possible outcomes, meaning greater potential for both gains and losses.
What is the expected return formula?
The expected return formula is E(R) = Σ(pᵢ × rᵢ), where pᵢ is the probability of outcome i and rᵢ is the return in that scenario. For example, if there is a 30% chance of a 5% loss and a 70% chance of a 15% gain, the expected return is 0.30 × (-5%) + 0.70 × 15% = 9%.
Can expected return be negative?
Yes, expected return can be negative if the probability-weighted average of all possible outcomes results in a net loss. This typically happens when high-probability scenarios have negative returns or when the investment has significant downside risk with limited upside potential.
How many scenarios should I use for expected return calculation?
Using at least 3-4 scenarios covering optimistic, base case, and pessimistic outcomes provides a meaningful expected return estimate. More scenarios can improve accuracy, but the key is that they collectively cover the full range of possibilities and their probabilities sum to 100%.