SamCalculator

Average Return Calculator

Calculate average annual investment returns using cash flows, deposits, withdrawals, and multiple investment holding periods.

Average Return Based on Cash Flow

Money-weighted annualized return (XIRR) from real account cash flows on actual dates

$
$

Cash Flow Entries

3 active / 8 shown

$
$
$
$
$
$
$
$

What Is Average Return?

Average return is the typical annual rate of return earned by an investment over a defined holding period. It is the single number that answers the question "how well did this investment grow per year?" The tricky part is that there are several mathematically different ways to compute it — arithmetic, geometric, money-weighted, and time-weighted — and they produce different answers whenever returns vary or cash flows happen at irregular times.

This page combines the two methodologies professional investors actually use. The Cash Flow tab measures the money-weighted return (XIRR) of a real account from a starting balance, an ending balance, and every dated deposit and withdrawal in between. The Average and Cumulative Return tab chains multiple holding-period returns into a single geometric average annual return (CAGR), cumulative return, and growth multiplier. Both run instantly in your browser, with charts and a printable investor report.

How Average Return Works

Arithmetic average

The simple mean of each period's return. Easy to compute and useful for risk modeling, but overstates real growth whenever returns vary. Two years of +50% then −50% give a 0% arithmetic average even though the account ended down 25%.

Geometric average (CAGR)

The constant annual rate at which the starting balance compounds into the ending balance with full reinvestment. CAGR is the standard way professionals report multi-year performance — it is the right answer to 'what did I actually earn per year?'

Money-weighted return (XIRR)

The single annualized rate that equates the present value of every dated cash flow to zero. Weights returns by how much money was invested at each moment, so it reflects the investor's actual experience including the timing of contributions and withdrawals.

Time-weighted return

Chains the returns between cash flows geometrically, removing the distortion of contribution timing. Mutual funds, ETFs, and managed accounts must report TWR for performance comparison because it isolates the investment manager's skill from the investor's timing.

Six Ways to Use This Calculator

01

Measure your real account

Pull your starting balance, ending balance, and every dated deposit or withdrawal from your brokerage statement. The Cash Flow tab returns your money-weighted annualized return — the same calculation a CPA or financial planner would run on your statements.

02

Compute CAGR across periods

Enter each year's (or each cycle's) percentage return with its holding length. The Cumulative tab chains them into a single CAGR and cumulative return — perfect for comparing strategies side-by-side.

03

Stress-test investment timing

Re-run the Cash Flow tab with hypothetical contribution dates to see how a different lump-sum-vs-dollar-cost-averaging approach would have changed your money-weighted return.

04

Translate a return into dollars

The 'Ending value of $10,000 and $100,000' metric translates an annualized percentage into a concrete dollar outcome that you can use for retirement, college, or down-payment goals.

05

Compare against benchmarks

Built-in benchmarks (high-yield savings, CDs, bonds, S&P 500, NASDAQ) and a custom benchmark slot show whether your return justifies the risk you took to earn it.

06

Build investment reports

Export CSVs of your cash flows or period returns, and print a one-page investor report with inputs, results, insights, and disclaimer for personal record-keeping or financial-planner review.

Best Practices for Measuring Returns

  • •Use money-weighted return for personal accounts. XIRR reflects how YOUR specific contributions and timing performed — it tells you the truth about your investor experience.
  • •Use time-weighted (CAGR) for strategy comparison. When comparing two strategies or two fund managers, time-weighted return strips out cash-flow timing and measures the underlying investment.
  • •Always quote CAGR, never arithmetic, for multi-year results. Arithmetic averages are mathematically lossy for compounding series and routinely overstate real growth — using them is the single most common source of investor self-deception.
  • •Subtract inflation for real return. A 7% nominal return at 3% inflation is closer to a 3.9% real return. Real return is what buys you groceries, college tuition, or retirement income — not the nominal number on your statement.
  • •Compare returns risk-adjusted. A 12% return from a single-stock bet is not better than an 8% return from a diversified index — confirm the volatility, drawdown, and consistency before celebrating a high CAGR.

Why Average Return Matters

Every long-term financial decision — retirement target, college fund, house down payment, financial independence date — collapses to a single mathematical question: what annualized return can you actually achieve? Underestimating it leaves you over-saving and over-cautious; overestimating it leaves a hole in the plan that only shows up close to the goal date. CAGR is the right number to use because it's the rate that turns a starting balance into an ending balance, with no ambiguity about averaging methodology.

The money-weighted (XIRR) result on the Cash Flow tab is just as important for a different question: did MY timing of contributions and withdrawals beat or lag the underlying investment? If your XIRR is well below the asset class's CAGR, you have a behavioural issue (probably buying high and selling low). If it's above, you got lucky with timing — but don't bank on it repeating.

Tricky Cases You Should Know

Cumulative return below −100% is impossible

An investment cannot lose more than 100% of its value, so no period's return can be below −100%. If your data has it, check whether you've mixed up percentage return and dollar loss.

XIRR can have multiple solutions

When the cash flow series changes sign more than once, the IRR equation can have multiple roots. The calculator uses Newton-Raphson then a bisection fallback to find the economically meaningful one — but the result is most reliable when there is a clear net inflow at the start and outflow at the end.

Short periods inflate annualization

Annualizing a one-month return is mathematically valid but practically misleading: a 5% one-month return projects to 79% annualized, which is rarely sustainable. Use long holding periods (1+ years) for meaningful CAGR.

Arithmetic = Geometric only when constant

The two averages agree only when every period's return is identical. As soon as returns vary, the geometric is lower, and the gap grows with the variance. The calculator surfaces both so you can see the spread.

Negative average is a real result

If the cumulative product is below 1, both averages are negative. The calculator returns them honestly. A negative CAGR is the right number — don't truncate or take its absolute value.

Money in early dominates XIRR

A large deposit at the start of a long, strong-performing period dominates the XIRR. Conversely, a single large withdrawal during a drawdown can drag the XIRR sharply negative — that's the design, since money-weighted return reflects investor timing.

Core Formulas

Compound Annual Growth Rate (CAGR)

CAGR = (Ending ÷ Beginning)^(1 ÷ Years) − 1

The constant annual rate that turns a starting value into an ending value over a given number of years with full reinvestment. Identical to the geometric average of period returns.

Cumulative Return

Cumulative = ∏(1 + rᵢ) − 1

The total compounded growth from start to finish, computed by chaining individual period returns multiplicatively. Equivalently, (Ending ÷ Beginning) − 1.

Arithmetic Average Return

r̄ = (r₁ + r₂ + … + rₙ) ÷ n

Simple mean of period returns. Overstates real growth whenever returns vary, so it's used mainly for risk modeling (volatility, Sharpe ratio) rather than reporting actual performance.

Geometric Average Return

rg = [∏(1 + rᵢ)]^(1 ÷ n) − 1

Geometric mean of period returns; identical to CAGR when all periods are the same length. Always equal to or less than the arithmetic average. This is the correct multi-period average.

Money-Weighted Return (XIRR)

Solve r in Σ Cᵢ ÷ (1 + r)^(dᵢ ÷ 365) = 0

The annualized rate that equates the present value of every dated cash flow Cᵢ to zero. Found numerically with Newton-Raphson; equivalent to Excel's =XIRR().

Common Return Calculation Mistakes

  • •Reporting an arithmetic average as 'annual return' for a multi-year series, instead of the geometric (CAGR) figure.
  • •Treating a money-weighted return as if it measures the investment's performance — it measures the investor's experience, which is a different question.
  • •Comparing a nominal return to an inflation-adjusted target. Nominal and real returns must always be compared in the same units.
  • •Annualizing very short-period returns. A single quarter's return extrapolated to a year tells you almost nothing about long-term performance.
  • •Forgetting to net out account fees, expense ratios, sales loads, and taxes — the difference between gross and net return is often the difference between meeting a financial goal and missing it.
  • •Comparing two managers using different averaging methods (one arithmetic, one geometric) and concluding one outperformed when they actually didn't.

Important Disclaimers

  • •Investment returns are not guaranteed. Historical performance does not predict future results — past CAGR is descriptive, not prescriptive.
  • •Money-weighted and time-weighted returns answer different questions. Pick the methodology that fits the question before comparing across accounts.
  • •All projections assume the inputs you enter are accurate. Verify starting balance, ending balance, and every dated cash flow against your custodian statements before relying on the result.
  • •This tool is for educational use only and is not investment, tax, or financial advice. Consult a qualified financial professional before making investment decisions.

Frequently Asked Questions

Average return is the typical annual rate of return earned by an investment over a defined holding period. It can be expressed two different ways: arithmetic average return (simple mean of each period's return) and geometric average return, also called the Compound Annual Growth Rate (CAGR), which is the constant annual rate that grows your starting balance into your ending balance. Geometric return is the right answer when comparing investments because it accounts for compounding; arithmetic return overstates real growth whenever returns vary year to year.

CAGR (Compound Annual Growth Rate) is the smoothed annual growth rate that turns a beginning value into an ending value over a given number of years, assuming the gains are reinvested. The formula is CAGR = (End ÷ Begin)^(1 ÷ Years) − 1. CAGR is mathematically identical to the geometric average return and is the standard way professionals report long-term performance. The Average and Cumulative Return tab on this page calculates CAGR directly from your list of period returns and holding lengths.

Arithmetic return is the simple average of each period's return: (r₁ + r₂ + … + rₙ) ÷ n. Geometric return compounds them: [(1 + r₁) × (1 + r₂) × … × (1 + rₙ)]^(1 ÷ n) − 1. They agree only when every period's return is identical. Whenever returns vary, geometric is lower — and only the geometric (CAGR) figure correctly answers 'what was my actual annualized return?' Two years of +50% then −50% gives a 0% arithmetic average but a −13.4% geometric return, because $100 → $150 → $75.

Mid-period deposits and withdrawals make a simple end-vs-begin calculation meaningless — your account grew partly because of investing performance and partly because you added money. The money-weighted (XIRR / IRR) method on the Cash Flow tab solves this by finding the single annualized rate at which the present value of every cash flow (starting balance, every deposit, every withdrawal, ending balance) sums to zero on the actual dates. The result reflects how YOUR specific contributions and timing performed — but it lets a single well-timed deposit dominate the answer.

XIRR is the irregular-interval extension of the Internal Rate of Return. It computes the annualized rate of return for cash flows that happen on any calendar dates, not just at regular monthly or annual intervals. This is how a brokerage account, a 401(k), or a real-estate investment is properly measured. XIRR finds the rate r where Σ Cᵢ ÷ (1 + r)^(dᵢ ÷ 365) = 0, using Newton-Raphson iteration. The Cash Flow tab on this page implements XIRR — give it your real dates and it returns the same answer Excel's =XIRR() function would.

Benchmarks for long-term annualized returns (nominal, pre-tax): savings accounts and CDs run 0.5–5% depending on the rate environment; investment-grade bonds 3–5%; the S&P 500 has averaged about 10% over the last 80 years; NASDAQ growth indexes have averaged 11–13% over recent decades. Subtract 2–3% for inflation to convert nominal to real return, and a few more percentage points for taxes outside of a tax-advantaged account. Any single year can deviate dramatically — judge a return by the asset class, the holding period, and the risk taken to achieve it.

Cumulative return is the total growth from start to finish, expressed as a percentage of the original investment. The formula is Cumulative Return = (Ending Value ÷ Beginning Value) − 1, equivalent to chaining individual returns as ∏(1 + rᵢ) − 1. The Average and Cumulative Return tab does this for you automatically: enter each period's return and holding length, and it reports both the cumulative percentage and the growth multiplier (e.g. 'your $10,000 grew to $13,800, a 38% cumulative return').

Money-weighted return is the IRR (or XIRR for irregular dates) calculated on all the actual cash flows in and out of an account. It answers: 'what was my annualized return given the actual timing of every dollar I deposited or withdrew?' Heavy contributions just before a strong market lift the money-weighted return above the underlying investment's performance; heavy contributions just before a drawdown depress it. The Cash Flow tab uses money-weighted return; use it when you want to measure investor experience, not fund performance.

Time-weighted return measures the performance of the investment itself, independent of when you contributed or withdrew. It does so by isolating the return between each cash flow, then chaining those sub-period returns geometrically. Mutual funds, ETFs, and managed accounts are required to report TWR for performance comparison because it removes the distortion of investor contribution timing. The Average and Cumulative Return tab supports a time-weighted mode for that purpose — use it when comparing strategies or fund managers, not your personal account.

Yes. If the cumulative return is negative, both the arithmetic and geometric averages are negative. A −20% year followed by a +10% year produces an arithmetic average of −5% per year and a geometric average of −5.7% per year — both meaningful, both negative. Money-weighted returns can also turn negative if withdrawals and end balances together fall below contributions and starting balance over the period. Negative numbers are valid output, not an error — they tell you the realised return was a loss after compounding.

Related Calculators