Portfolio Risk Return Calculator
Modern Portfolio Theory (MPT), developed by Harry Markowitz in 1952, shows that the risk of a portfolio is not simply the weighted average of individual asset risks. By combining assets with low correlation, you can reduce total portfolio risk without sacrificing return. This calculator computes the expected return, standard deviation (risk), and Sharpe ratio for a two-asset portfolio based on your input weights, individual returns, volatilities, and the correlation between the two assets.
Portfolio risk and return formulas
Expected Return = w1 * r1 + w2 * r2
Portfolio Variance = w1^2 * s1^2 + w2^2 * s2^2 + 2 * w1 * w2 * s1 * s2 * rho
Portfolio Std Dev (sigma) = sqrt(Portfolio Variance)
Sharpe Ratio = (Expected Return - Risk-Free Rate) / Sigma
where w = weight, r = return, s = std dev, rho = correlation
Source: Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91.
Interpreting the results
- A portfolio standard deviation lower than the weighted average of individual standard deviations shows diversification is working.
- Sharpe ratio above 1.0 indicates good risk-adjusted performance; above 2.0 is excellent.
- Lower correlation between assets increases diversification benefit and reduces portfolio volatility.
- Assets with negative correlation (rho = -1) would theoretically eliminate all risk when combined in the right proportion.
- In practice, correlations between asset classes tend to rise during market crises, reducing diversification benefit exactly when it is most needed.
Portfolio risk and return: frequently asked questions
What is the Sharpe ratio?
The Sharpe ratio measures risk-adjusted return. It equals (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation. A higher Sharpe ratio means more return per unit of risk. Ratios above 1.0 are generally considered good; above 2.0 is very good.
What is portfolio standard deviation?
For a two-asset portfolio, standard deviation (sigma) = sqrt(w1^2 * s1^2 + w2^2 * s2^2 + 2 * w1 * w2 * s1 * s2 * correlation), where w = weights, s = individual standard deviations. This is the formula from Modern Portfolio Theory (Markowitz, 1952).
What does correlation mean in portfolio theory?
Correlation measures how two assets move relative to each other, ranging from -1 (perfectly opposite) to +1 (perfectly together). Assets with low or negative correlation provide diversification benefits: combining them reduces total portfolio risk without proportionally reducing return.
What is the risk-free rate?
The risk-free rate is the theoretical return on a riskless investment, typically approximated by the current yield on 3-month U.S. Treasury bills. It is used as the baseline in the Sharpe ratio calculation. The Federal Reserve publishes current Treasury yields.
What is the efficient frontier?
The efficient frontier is the set of portfolios that offer the highest expected return for a given level of risk (standard deviation). Portfolios on the efficient frontier are considered optimally diversified. The concept was introduced by Harry Markowitz in his 1952 paper in the Journal of Finance.
Official sources
- Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 7(1), 77-91. Published by the American Finance Association.
- Sharpe, W. F. (1966). Mutual Fund Performance. Journal of Business, 39(1), 119-138.
- Federal Reserve: Selected Interest Rates (H.15) for current risk-free rate.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.