Portfolio Metrics Formulas Explained

Portfolio Value and Portfolio Weight Formulas

Your portfolio's total value is the sum of the current market value of every position you hold, cash included. Add up shares times price for each stock, bond, or fund position, then add any cash balance sitting in the account. That single sum is your portfolio value. A holding's portfolio weight is that position's value divided by the portfolio's total value, expressed as a percentage.

Take a $50,000 account split across three positions: $30,000 in a stock index fund, $15,000 in a bond fund, and $5,000 in cash. Portfolio value is $50,000. The stock fund's weight is $30,000 divided by $50,000, or 60%. The bond fund's weight is 30%, and cash is 10%. Every other formula on this page, weighted return, portfolio beta, variance, and the blended expense ratio, starts by finding these same weights first, which is why getting this step right matters more than it looks.

Weighted-Average Portfolio Return Formula

Your portfolio's return over one period equals the weighted average of each holding's return, using the same portfolio weights from above. The formula is: portfolio return = (weight of holding 1 × its return) + (weight of holding 2 × its return), and so on for every position in the account.

Using the $50,000 account above, say the stock fund returned 12% for the year, the bond fund returned 3%, and cash earned 4%. The weighted return is (0.60 × 12%) + (0.30 × 3%) + (0.10 × 4%), which comes out to 8.5%. That is your true portfolio return. It is not the simple average of 12%, 3%, and 4%, which would incorrectly show 6.33%, and it is not the return of any single holding.

This formula only works cleanly when you added and withdrew no cash during the period. The moment you deposit or withdraw money mid-year, a simple weighted average overstates or understates your real return, because it treats every dollar as if it had been invested for the full period. That situation calls for a money-weighted return, an internal rate of return (IRR) on your actual cash flows, instead of the formula above. A fund manager is usually judged on the weighted-average, or time-weighted, version above, since that isolates investment skill from the timing of investor deposits. You, deciding when to add or withdraw your own money, usually care more about the money-weighted version, since it reflects what actually happened to your own dollars.

Portfolio Variance from a Covariance Matrix

Portfolio variance measures how much your total portfolio's return swings, and the formula weights not just each holding's own variance but how every pair of holdings moves together. For two assets, the formula is: portfolio variance = (weight of holding 1² × its variance) + (weight of holding 2² × its variance) + (2 × weight of holding 1 × weight of holding 2 × the covariance between them). With three or more holdings, the same idea expands into a full covariance matrix covering every pair of positions, formally written as w-transpose Σ w in matrix notation, but the two-holding version above shows exactly what that matrix multiplication is doing underneath.

Run the two-asset version on a portfolio that is 60% stocks (16% volatility) and 40% bonds (5% volatility), with a covariance between them of -0.001, reflecting bonds that tend to hold up when stocks fall. Portfolio variance = (0.6² × 0.16²) + (0.4² × 0.05²) + (2 × 0.6 × 0.4 × -0.001) = 0.009216 + 0.0004 − 0.00048 = 0.009136. Taking the square root gives a portfolio volatility, or standard deviation, of about 9.56%, the Financial Industry Regulatory Authority's (FINRA) standard measure of how far returns swing from their average. That figure is lower than a simple weighted average of the two volatilities would suggest (0.6 × 16% + 0.4 × 5% = 11.6%). The negative covariance between stocks and bonds is what pulls it down, and that gap is the entire mathematical case for diversification.

Portfolio Beta Formula

Portfolio beta measures how much your portfolio tends to move relative to a market benchmark, and you can calculate it two different ways that should land close to the same number. The simpler version is a weighted average of each holding's own beta: portfolio beta = (weight of holding 1 × its beta) + (weight of holding 2 × its beta), the same weighting approach as the return formula above, applied to beta instead of return. The second version calculates beta directly from your portfolio's own return history against the benchmark's: portfolio beta = covariance between the portfolio's returns and the market's returns, divided by the variance of the market's returns, per the U.S. Securities and Exchange Commission's (SEC) Investor.gov definition of the term.

Say your $50,000 account holds a stock fund with a beta of 1.1 and a bond fund with a beta of 0.2, at the same 60/30 stock/bond weights from the first section (cash carries a beta of 0, so it drops out of the calculation). Weighted beta = (0.60 × 1.1) + (0.30 × 0.2) = 0.72, meaning your portfolio should move about 72% as much as a benchmark like the S&P 500 on a typical day, in either direction.

Our own portfolio risk calculator reports volatility and the Sharpe ratio rather than beta, on purpose. Those two figures describe how much your specific mix swings without requiring you to pick a market-index benchmark to compare it against, while beta only means something once you have chosen one. Use the weighted-average formula above when you already know each holding's published beta, usually listed on the fund's own fact sheet.

Portfolio Turnover Ratio Formula

Portfolio turnover ratio measures how much of a fund's holdings got replaced yearly. The SEC requires every mutual fund to disclose it, using one specific formula in Form N-1A: turnover rate = the lesser of total purchases or total sales of securities, divided by the average monthly net asset value, for the fiscal year, excluding securities with a maturity of one year or less at the time they were bought.

Take a fund with $200 million in average monthly net assets that bought $150 million of new securities and sold $180 million over the year. Because the rule uses the lesser of the two figures, turnover uses the $150 million purchase figure: $150,000,000 divided by $200,000,000 equals 75% portfolio turnover for the year. A fund with 75% turnover is replacing three-quarters of its holdings annually, which tends to raise both transaction costs and the taxable capital gains a fund distributes to shareholders holding it in a taxable account.

If you are trying to gauge your own personal account's turnover rather than a fund's, the same core idea applies at a smaller scale. Divide the smaller of your total dollar purchases or total dollar sales over the year by your average account value. There is no regulatory filing requirement at the personal-account level, only the same logic funds use to disclose theirs.

Blended Portfolio Expense Ratio Formula

Your portfolio's blended expense ratio is the weighted average of every fund's own expense ratio, using each fund's dollar weight in your total account. An expense ratio, per SEC Investor.gov, is the percentage of a fund's assets used each year to cover its operating costs, and it comes out of the fund's return before you ever see it.

Using the same $50,000 account, say the stock fund charges a 0.05% expense ratio, the bond fund charges 0.15%, and cash carries no expense ratio at all. Blended expense ratio = (0.60 × 0.05%) + (0.30 × 0.15%) + (0.10 × 0%) = 0.03% + 0.045% + 0% = 0.075%. On $50,000, that is $37.50 a year, pulled automatically from fund returns rather than billed separately. Swap the bond fund for one charging 0.65% instead of 0.15%, holding everything else equal, and the blended ratio jumps to 0.225%, or $112.50 a year. One expensive fund can move your whole portfolio's cost more than its dollar weight alone suggests, because cost differences compound the same way returns do.

Portfolio NAV Formula

Net asset value (NAV) is what a mutual fund or exchange-traded fund (ETF) share is worth, and the formula is simple: NAV per share = (total fund assets minus total fund liabilities), divided by total shares outstanding. SEC Investor.gov defines a fund's total NAV as its assets minus its liabilities, then divides that figure by shares outstanding to get the per-share price you actually see quoted.

A fund holding $500 million in securities and cash, with $10 million in liabilities like accrued management fees, has a total NAV of $490 million. Divide that by 20 million shares outstanding and each share is worth $24.50. Mutual funds calculate this figure once per business day, after the major U.S. exchanges close, which is why a mutual fund purchase always executes at that day's closing NAV rather than a live, intraday price the way a stock or ETF trade does. Plug in a fund's own published numbers with our NAV calculator to check the math yourself.

Portfolio Gamma Calculation

Portfolio gamma has nothing to do with your stock-and-bond mix. It measures how fast an options portfolio's delta changes as the underlying price moves, and it only applies if you hold options contracts. According to the Options Industry Council, gamma is the rate of change in an option's delta for every $1 move in the underlying security's price, and it runs highest for options trading close to their strike price.

To find your whole portfolio's gamma, sum the gamma of every options position you hold, each multiplied by the number of contracts and the contract multiplier, 100 shares for a standard equity contract: portfolio gamma = the sum, across every position, of (contracts × that position's gamma × 100). A trader holding 10 call contracts with a gamma of 0.05 each, and 5 put contracts with a gamma of -0.03 each, has a portfolio gamma of (10 × 0.05 × 100) + (5 × -0.03 × 100) = 50 minus 15, or 35. That means the portfolio's overall delta, its directional exposure, would shift by about 35 for every $1 move in the underlying stock. A rising portfolio gamma means directional risk can change quickly as the market moves, which is why options traders track it separately from every other formula on this page.

Where to Run These Numbers Instead of Calculating by Hand

Every formula above works on paper, but you do not have to run any of them by hand once you know how they work. Our portfolio calculator already computes weighted expected return, volatility, and the Sharpe ratio from your actual stock, bond, real estate, and cash amounts, using the same weighted-average and variance math shown above, and our portfolio risk calculator breaks the risk side out further. Neither tool replaces knowing the formula behind it. They exist so you can check your own hand calculation, or skip it once you trust the mechanics. Start with your own account values in the portfolio calculator to see these formulas applied to your actual numbers.

Frequently asked questions