Expected Return Calculator

Expected return is the probability-weighted average of all possible returns from an investment. It represents the mean of the probability distribution of future returns, giving you an estimate of what you might earn across different market conditions. It's a foundational concept in portfolio theory and risk assessment.

Expected return is calculated by multiplying each possible return by its probability of occurring, then summing all those products. For example, if a stock has a 15% chance of returning −5%, a 50% chance of returning 10%, and a 35% chance of returning 20%, the expected return is (0.15 × −5) + (0.50 × 10) + (0.35 × 20) = 11.25%.

Variance measures how spread out the possible returns are around the expected return. A higher variance means more uncertainty (higher risk), while a lower variance indicates more predictable returns. It's calculated as the probability-weighted sum of squared deviations from the expected return.

Standard deviation is the square root of variance and expresses risk in the same units as the return (percentage). A stock with a standard deviation of 10% has returns that typically fluctuate about 10 percentage points around the expected return. Lower standard deviation generally means less risk.

Yes — for the expected return calculation to be mathematically valid, all state probabilities must sum to exactly 100%. The calculator shows you your total probability so you can verify this. If they don't sum to 100%, the results will be inaccurate.

Expected return is a forward-looking estimate based on probable outcomes — it's the average you'd expect over many trials. Actual return is what your investment truly earns over a specific period. In any given period, actual returns can differ significantly from the expected return due to market uncertainty.

The calculator computes expected return, variance, and standard deviation independently for Stock A and Stock B using the same set of market states and probabilities. This lets you compare the risk-reward trade-off between the two: a stock with a higher expected return but also higher standard deviation carries more risk than one with a lower but more stable return.

This calculator focuses on individual stock statistics (expected return, variance, standard deviation) across multiple states. For full portfolio analysis — including covariance and correlation between stocks — you would need to extend the model. However, the outputs here are the essential building blocks for any mean-variance portfolio optimization.