Portfolio Expected Return and Volatility Calculator

Purpose and model boundary

This calculator works out the expected return and the risk of a portfolio of up to 12 holdings. For each holding you enter a name, its weight (its share of the money), its expected yearly return and its volatility (how much its yearly return typically swings). You can also say how closely each pair of holdings moves together. The main result is the expected return of the portfolio (yearly). Beside it are the portfolio's volatility, its Sharpe ratio, and the largest holding and its weight. Two tables show each holding's share of the risk and what happens as money moves between your two largest holdings. Two charts draw the same results.

Every figure on this page is computed by the spreadsheet; the page adds nothing to it. To bring a portfolio back to target weights, use the Asset Allocation Rebalancing Calculator; to see what fees take from a return over time, use the Investment Fees Drag Calculator.

The model is educational. It is not a forecast of any market, it is not an optimiser that picks the best portfolio, and it is not financial, investment, tax or legal advice.

Inputs and units

• Your holdings, a table of up to 12 rows. A row counts when it has all four values; an empty row anywhere is skipped. At least 2 holdings are needed.
  • Holding: a name, used to label the tables and the charts.
  • Weight: the holding's share of the money, from 0% to 100%.
  • Expected return: the yearly return you expect from the holding, from -20% to 30%. Enter it after fees.
  • Volatility: the typical yearly swing of the holding's return (its standard deviation), from 0% to 100%, in steps of 1%.
• Correlations between your holdings (optional), a 12 × 12 table whose rows and columns are the holdings' numbers in the first table. Each entry is from -1 to 1: 1 means the two always move together, 0 that they move independently and -1 that one rises when the other falls. A pair can be entered in either half of the table; if both halves are filled they must agree.
• Correlation for pairs left blank, from 0 to 1. Every pair you leave blank uses this value; 0.5 is shipped.
• Risk-free rate (yearly), from 0% to 20%, the return you could get without risk. The Sharpe ratio measures the expected return above it.

Weights, returns, volatilities and rates are percentages; correlations are plain numbers.

Governing relationships

Write wᵢ for the weight of holding i divided by the total of the weights, μᵢ for its expected return, σᵢ for its volatility and ρᵢⱼ for the correlation of holdings i and j (ρᵢᵢ = 1). Then:

• the covariance of two holdings is Σᵢⱼ = ρᵢⱼ × σᵢ × σⱼ;
• the expected return of the portfolio is μ = Σ wᵢ μᵢ;
• its variance is V = Σᵢ Σⱼ wᵢ wⱼ Σᵢⱼ, and its volatility is σ = √V;
• the Sharpe ratio is (μ − risk-free rate) ÷ σ;
• holding i's share of the risk is wᵢ × (Σⱼ Σᵢⱼ wⱼ) ÷ V. The shares add up to 100%, and a holding that tends to move against the rest can have a negative share;
• holding i's contribution to volatility is wᵢ × (Σⱼ Σᵢⱼ wⱼ) ÷ σ. The contributions add up to σ;
• the weighted average of the volatilities is Σ wᵢ σᵢ. The portfolio's volatility is never above it, and is below it whenever some pair is less than perfectly correlated.

The correlations used must be able to hold at once: no set of returns can have, for example, A and B and A and C almost perfectly correlated while B and C move almost perfectly opposite. The workbook tests this by factorising the table as L × Lᵀ (a Cholesky factorisation that allows zero pivots, so correlations of exactly 1 or -1 are accepted) and refusing the table when the factor does not reproduce it to within 0.0000001.

The curve moves money between your two largest holdings. Every other holding keeps its weight; the two largest share their combined weight, from all of it in the second largest to all of it in the largest, in 29 equal steps (30 points). For each point the expected return and volatility follow from the same formulas. Your portfolio is one point on that curve.

Calculation sequence

The spreadsheet first checks every input and counts the listed holdings. It divides each weight by their total, builds the correlations used (each pair from either half of the table, or the value for blank pairs), factorises them and checks the factor. It then works out each holding's risk terms, the portfolio's expected return, variance, volatility and Sharpe ratio, each holding's share of the risk and contribution to volatility, the two largest holdings and the 30 points of the curve. A block of consistency checks confirms the arithmetic before the status is returned.

Outputs and interpretation

The headline is the expected return of the portfolio (yearly). Beside it are the volatility of the portfolio (yearly), the Sharpe ratio, the largest weight and the largest holding. The first table lists each holding with its weight used, expected return, volatility, share of the risk and contribution to volatility; the second lists the 30 points of the curve. The second largest holding, the weighted average of the volatilities, the weights as entered added up and the workbook's self-check are returned to the API and MCP.

With the shipped example, Stocks at 60% expecting 7% with a volatility of 16%, Bonds at 40% expecting 4% with 6%, the correlation table blank so the pair takes 0.5, and a risk-free rate of 4%, the portfolio expects 5.80% a year with a volatility of 11.00% and a Sharpe ratio of 0.16. The weighted average of the volatilities is 12%, so holding the two together lowers the risk. Stocks are 60% of the money but carry 85.7% of the risk; Bonds carry 14.3%. Moving money between them runs from 4.00% expected at 6.00% volatility, all in Bonds, to 7.00% at 16.00%, all in Stocks.

With three funds, US stocks 50% (7%, 16%), international stocks 30% (7.5%, 18%) and bonds 20% (4%, 6%), US and international stocks correlated 0.85 and each with bonds 0.2, the portfolio expects 6.55% with a volatility of 13.21% and a Sharpe ratio of 0.19. The shares of risk are 58.8%, 38.5% and 2.7%: the bonds hold a fifth of the money but almost none of the risk.

The first chart sets each holding's share of the money (grey) against its share of the risk (blue). The second chart places each holding and the portfolio by volatility and expected return, with the curve dashed; the portfolio usually sits to the left of its holdings because they do not all move together.

Validation and status logic

The workbook evaluates the conditions below from top to bottom and returns the first matching status.

NOT VALID is a refusal, not a numeric answer: every number reads zero, every name is blank and the tables are empty. CHECK accompanies a computed result but calls for the stated review. The self-check is reported separately as arithmetic-integrity evidence; it does not replace this ordered status chain.

Assumptions and limitations

Each holding's expected return, volatility and correlations are assumptions you supply, held fixed for one year; the model does not estimate them from prices. Returns are treated through their means, volatilities and correlations only, so the model says nothing about how heavy the tails of the returns are. Weights must be from 0% to 100%: there is no borrowing, leverage or short selling. Fees, taxes and currency risk are not modelled, so enter returns after fees. The curve moves money only between the two largest holdings; it is not the efficient frontier of all your holdings and it does not search for the best portfolio. Amounts are nominal, with no allowance for inflation.

Restrictions and non-computing states

This calculator enforces its numeric limits, the 2 to 12 listed holdings and the agreement of the two halves of the correlation table before it accepts a result. A table of correlations that no set of returns could have is refused rather than adjusted.

Errors and warnings

A request rejected by the page's input limits is not a computed result. A transport or service failure cannot establish a fresh workbook answer. Review the workbook's References and Disclaimer, and check any plan with a qualified professional before using a result for a real decision.

Sources and further reading

Every weight, expected return, volatility, correlation and rate comes from the inputs, not market data. The workbook's References sheet lists the same five sources. They describe the methods the model follows; they do not endorse this calculator.

• H. Markowitz, "Portfolio Selection", The Journal of Finance 7(1), 1952: the mean and variance of a portfolio from its weights, expected returns and covariances, the basis of the portfolio's expected return and volatility here (retrieved 2026-10-18).
• W. F. Sharpe, "The Sharpe Ratio", The Journal of Portfolio Management 21(1), 1994: the expected return above a risk-free rate divided by the volatility (retrieved 2026-10-18).
• S. Maillard, T. Roncalli and J. Teïletche, "The Properties of Equally Weighted Risk Contribution Portfolios", The Journal of Portfolio Management 36(4), 2010: each holding's contribution to the portfolio's volatility, which together add up to that volatility (retrieved 2026-10-18).
• NIST/SEMATECH e-Handbook of Statistical Methods, section 6.5.4.1, "Mean Vector and Covariance Matrix": the covariance matrix of several variables, each entry a correlation times two standard deviations (retrieved 2026-10-18).
• G. H. Golub and C. F. Van Loan, Matrix Computations, 4th edition, Johns Hopkins University Press, 2013, section 4.2: the Cholesky factorisation of a symmetric positive semidefinite matrix, which the workbook uses to test whether the correlations can all hold at once (retrieved 2026-10-18).

The NIST section was read in full for this page. For the other four, the citation details (authors, title, journal or publisher, volume, year and identifier) were confirmed from their bibliographic records; their full texts were not read for this page, and each entry above describes only the method the calculator takes from it.

This is an educational estimate, not financial, investment, tax or legal advice. Expected returns, volatilities and correlations are assumptions about the future, not measurements of it; check any plan with a qualified professional.