Portfolio Optimization Tool
Sharpe Ratio & Portfolio Volatility Calculator
Risk-adjusted return and portfolio-level volatility, computed from your own numbers.
Two calculators in one tool: compute the Sharpe ratio from a series of periodic returns or directly from an annualized return and standard deviation, and separately compute a multi-asset portfolio's volatility from each asset's weight, individual volatility, and pairwise correlations using the weighted covariance formula.
Direct Answer
The Sharpe ratio measures risk-adjusted return: it equals (return minus the risk-free rate) divided by the standard deviation of returns, so a higher Sharpe ratio means more return earned per unit of volatility risk. Portfolio volatility for a multi-asset portfolio is not a simple weighted average of individual volatilities; it uses the weighted covariance formula sigma_p = sqrt(w' C w), where the covariance matrix incorporates every pairwise correlation, which is exactly why diversification can lower total risk even when no individual asset's own volatility changes.
What is the Sharpe Ratio?
The Sharpe ratio, developed by William F. Sharpe, is the most widely used risk-adjusted return metric: Sharpe ratio = (return − risk-free rate) / standard deviation. Enter either a series of periodic returns (the calculator computes the mean and standard deviation, then annualizes both) or an already-annualized return and standard deviation directly.
How Do You Calculate Portfolio Volatility?
Portfolio volatility (standard deviation) is computed with the weighted covariance formula sigma_p = sqrt(w' C w), where w is the vector of portfolio weights and C is the covariance matrix built from each asset's volatility and every pairwise correlation. Define 2-5 assets below with a weight and volatility, and set the correlation for each pair.
What Counts as a Good Sharpe Ratio?
As a rough guide, a Sharpe ratio below 1 is generally considered subpar, 1 to 2 is good, 2 to 3 is very good, and above 3 is excellent, though the right benchmark depends on the asset class, time period, and comparison strategy. Sharpe ratios should always be compared over the same time horizon: a short, unusually calm period can inflate the ratio, and a strategy's Sharpe ratio computed on monthly returns will not exactly match one computed on daily returns because the annualization (multiplying the mean, scaling the standard deviation by the square root of the number of periods) assumes returns are independent from period to period, an assumption real markets only approximate.
Why Does Diversification Lower Portfolio Volatility?
Because the weighted covariance formula includes a cross term for every pair of assets, weighted by their correlation. When two assets are perfectly correlated (correlation of 1), the portfolio's volatility is just the weighted average of their individual volatilities, no diversification benefit at all. As correlation falls below 1, some of each asset's price swings offset rather than compound, so the combined portfolio's standard deviation comes out lower than that weighted average, and the effect grows stronger the more negative the correlation gets. This is why holding assets that do not move in lockstep, not just holding more assets, is what reduces portfolio risk.
Frequently Asked Questions
What is the formula for the Sharpe ratio?
The Sharpe ratio equals (portfolio return minus the risk-free rate) divided by the portfolio's standard deviation of returns: Sharpe ratio = (R_p - R_f) / sigma_p. A higher Sharpe ratio means more return earned per unit of volatility risk taken.
How do you calculate portfolio volatility with more than one asset?
Portfolio volatility uses the weighted covariance formula: sigma_p = sqrt(w' C w), where w is the vector of asset weights and C is the covariance matrix built from each asset's volatility and every pairwise correlation. Unlike a simple weighted average, this formula accounts for diversification, so portfolio volatility is typically lower than the weighted average of the individual asset volatilities whenever correlations are below 1.
What counts as a good Sharpe ratio?
As a rough guide, a Sharpe ratio below 1 is generally considered subpar, 1 to 2 is good, 2 to 3 is very good, and above 3 is excellent, though the right benchmark depends on the asset class, time period, and comparison strategy. Sharpe ratios should always be compared over the same time horizon, since a short, unusually calm period can inflate the ratio.
Why does diversification lower portfolio volatility even without changing individual asset risk?
Because the weighted covariance formula includes cross terms for every asset pair, weighted by their correlation. When correlations are below 1, some of each asset's price swings offset rather than compound, so the combined portfolio's standard deviation comes out lower than a simple weighted average of the individual volatilities would suggest.
References
- Sharpe, W. F. (1966). "Mutual Fund Performance." The Journal of Business, 39(1), 119-138, the original reward-to-variability ratio this calculator implements.
- Sharpe, W. F. (1994). "The Sharpe Ratio." The Journal of Portfolio Management, 21(1), 49-58, the paper that formalized the modern ex-ante/ex-post Sharpe ratio and its annualization convention.
- Markowitz, H. (1952). "Portfolio Selection." The Journal of Finance, 7(1), 77-91, the mean-variance framework whose weighted covariance formula this calculator's portfolio volatility tool implements.
Educational Disclaimer
This tool is for educational purposes only. Results depend entirely on the inputs supplied and represent hypothetical calculations, not a specific investment strategy, forecast, or recommendation. Sharpe ratio annualization assumes independent, identically distributed period returns, an assumption real markets only approximate. This tool does not constitute investment advice.