What is average return on an investment?

Average return is the mean of a series of returns over a time period. It can be calculated as the arithmetic mean (simple average of periodic returns) or the geometric mean (compound annual growth rate). The geometric mean is almost always the correct measure for investment performance, as it accounts for compounding and is not distorted by volatile return sequences.

What is CAGR and how is it calculated?

CAGR (Compound Annual Growth Rate) is the rate at which an investment grows from its starting value to its ending value over a specific period, assuming profits are reinvested. Formula: CAGR = (Ending Value / Beginning Value)^(1/Years) - 1. Example: $10,000 grows to $18,000 over 7 years → CAGR = (18000/10000)^(1/7) - 1 = 8.76% per year.

What is the difference between time-weighted return and money-weighted return?

Time-weighted return (TWR) eliminates the effect of external cash flows (deposits/withdrawals), measuring the fund manager's actual performance. Money-weighted return (MWR/IRR) reflects the actual investor return, accounting for the timing and size of all cash flows. TWR is used to evaluate managers; MWR reflects personal investment outcomes.

What is a good annual return on investment?

The S&P 500 has returned approximately 10% annually (nominal) or 7% (inflation-adjusted) over the past century. A broadly diversified stock/bond portfolio typically returns 6-8% annually. A 'good' return depends on your risk tolerance, asset class, and time horizon. Beating inflation (3%) consistently in a risk-appropriate portfolio is a reasonable baseline goal.

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Average Return Calculator

Two modes: (1) IRR from starting/ending balance with deposits & withdrawals · (2) Average & cumulative return across multiple holding periods

Mode 1 - Average Return Based on Cash Flows

Enter starting balance, ending balance, and any deposits or withdrawals with dates. The calculator solves for the IRR (money-weighted return) that reconciles all cash flows.

#	Activity	Amount ($)	Date
-	Starting Balance	$
-	Ending Balance	$

📈 Cash Flow Results

Mode 1 - Money-Weighted Return

Annual IRR

9.24%

Total Gain/Loss

+$12,000

Holding Period

5.0 years

Total Return %

24.0%

Activity	Date	Amount	Days Elapsed	Weight

📊 Account Value Timeline

Mode 2 - Average & Cumulative Return (Multiple Periods)

Enter the return percentage and holding length for each investment period. The calculator computes the overall cumulative return, geometric mean (CAGR), and arithmetic mean.

#	Period Return (%)	Years	Months

📈 Multi-Period Return Results

Mode 2 - Time-Weighted

Geometric Mean (CAGR)

8.64%

Arithmetic Mean

10.2%

Cumulative Return

+132.4%

Total Period

10.5 yrs

#	Period Return	Years	Ann. Return	Growth Factor	Cumulative

📊 Cumulative Growth Visualization

Mode 1: How IRR from Cash Flows Works

The Internal Rate of Return (IRR) is the annualized return rate that makes the net present value (NPV) of all cash flows equal to zero. For an investment account with deposits and withdrawals, it's the most accurate measure of your actual personal return.

0 = -Starting Balance + Σ [CF_t / (1+IRR)^(t/365)] + Ending Balance / (1+IRR)^(T/365) CF_t = each deposit (+) or withdrawal (-) · t = days from start · T = total holding days Solved by binary search (500 iterations). Also called Modified Dietz or Money-Weighted Return (MWR).

Sign Convention

Starting balance: Treated as an outflow (money you put in)
Deposits: Additional outflows (money you add)
Withdrawals: Inflows (money you take out)
Ending balance: Final inflow (what you get back)

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IRR is called money-weighted return (MWR) in portfolio measurement context. It reflects your actual return because it's sensitive to the timing of your deposits and withdrawals. If you deposited a large amount just before a market crash, your MWR will be lower than the fund's reported time-weighted return.

Mode 2: Cumulative & Average Return Across Periods

When you have a sequence of returns across different time periods (e.g., year 1 returned +12%, year 2 returned -5%, year 3 returned +20%), this calculator computes the full picture:

Geometric Mean (CAGR)

The geometric mean is the single constant return rate that would produce the same cumulative result as the actual sequence of returns. It's the correct measure for multi-period investment performance.

CAGR = [(1+r₁)^t₁ × (1+r₂)^t₂ × … × (1+rₙ)^tₙ]^(1/T) - 1 r = period return (decimal) · t = holding years for that period · T = total years

Arithmetic Mean

The simple average of all annualized period returns. It's easier to calculate but overstates long-term compounding because it ignores the sequence-of-returns effect. Always compare arithmetic and geometric means together.

Arithmetic Mean = (r₁_ann + r₂_ann + … + rₙ_ann) / n Where each period return is annualized: r_ann = (1+r)^(1/t) - 1

Cumulative Return

The total percentage gain or loss over all periods combined, without annualizing:

Cumulative Return = [(1+r₁)^t₁ × (1+r₂)^t₂ × … × (1+rₙ)^tₙ] - 1

Return Metrics: A Complete Guide

There are multiple ways to measure investment returns, each appropriate for different purposes. Understanding which metric to use - and when each is misleading - is essential for evaluating your portfolio and comparing investments.

1. Holding Period Return (HPR)

The simplest return measure: total gain or loss over any holding period, without annualizing.

HPR = (Ending Value - Beginning Value + Income) / Beginning Value Example: Buy at $10,000, receive $500 dividends, sell at $12,000 → HPR = ($12,000 - $10,000 + $500) / $10,000 = 25%

2. Annualized Return (CAGR)

Converts any holding period return into an equivalent annual rate for fair comparison across different time periods.

CAGR = (1 + HPR)^(1/Years) - 1 Example: 25% HPR over 3 years → CAGR = (1.25)^(1/3) - 1 = 7.72% per year

3. Arithmetic Mean Return

The simple average of multiple periodic returns. Easy to calculate but consistently overstates long-term compounding. A classic example shows why:

Year 1: +50%, Year 2: -50% → Arithmetic Mean = 0% But: $1,000 × 1.50 = $1,500 → $1,500 × 0.50 = $750 → Actual loss = 25% Geometric Mean = √(1.50 × 0.50) - 1 = -13.4% → Correctly reflects real loss

4. Geometric Mean Return (CAGR)

Accounts for the compounding effect of returns. The only correct measure for comparing multi-period investment performance. Always lower than the arithmetic mean when returns vary.

Geometric Mean = [(1+r₁)(1+r₂)…(1+rₙ)]^(1/n) - 1

5. Time-Weighted Return (TWR)

Eliminates the effect of external cash flows by dividing the total period into sub-periods between each cash flow event, computing a return for each sub-period, then linking them geometrically. Used by fund managers to report performance because it removes the impact of investor timing.

TWR = [(1+HPR₁) × (1+HPR₂) × … × (1+HPRₙ)]^(1/years) - 1 Each HPR spans one sub-period (between cash flow events)

6. Money-Weighted Return (MWR / IRR)

The discount rate that makes NPV of all cash flows (including timing) equal to zero. Reflects the actual investor's experience - affected by when they deposit and withdraw money. If an investor put a large sum in at a market peak, their MWR will be worse than the fund's TWR.

Metric	Accounts for Timing?	Best Used For	Main Limitation
HPR	No	Simple period comparison	Can't compare different periods
Arithmetic Mean	No	Expected 1-period return	Overstates long-run compounding
CAGR / Geometric Mean	No (cash flows)	Multi-period annualized return	Ignores cash flow timing
TWR	Eliminates it	Evaluating fund managers	Doesn't reflect investor outcome
MWR / IRR	Yes, fully	Measuring personal return	Affected by cash flow timing

The Arithmetic-Geometric Gap: Why It Matters

The difference between arithmetic and geometric mean return is called the variance drag. It directly reduces your actual compounded wealth:

Geometric Mean ≈ Arithmetic Mean - (Variance / 2) Where Variance = standard deviation of annual returns, squared S&P 500: Arithmetic mean ~11.8%, Standard deviation ~20% → Geometric ≈ 11.8% - (0.04/2) = 9.8%

This formula, derived by Harry Markowitz, shows that higher volatility directly reduces your realized compounded return, even if the average return stays the same. It's one of the mathematical foundations of why diversification improves risk-adjusted returns - by reducing variance, you raise the geometric mean without changing the arithmetic mean.

Sequence of Returns Risk

The arithmetic mean doesn't capture the sequence in which returns occur, but the sequence matters enormously - especially near retirement. Two investors can have identical arithmetic mean returns but vastly different outcomes if the poor returns come at different times relative to their withdrawal schedule.

Accumulation phase: Sequence matters less - dollar-cost averaging actually benefits from early losses
Distribution phase: Early losses (selling assets at low prices to fund withdrawals) permanently reduce capital, a risk not captured by average return statistics

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Never evaluate a retirement income plan using only average or CAGR return assumptions. Monte Carlo simulation or historical sequence analysis is necessary to capture sequence-of-returns risk properly.

Historical Market Returns Reference

Asset Class	Period	Arithmetic Mean	Geometric Mean
US Large Cap (S&P 500)	1928-2024	~11.8%	~10.0%
US Small Cap	1928-2024	~14.2%	~11.7%
International Developed	1970-2024	~10.5%	~8.5%
Emerging Markets	1990-2024	~11.2%	~7.8%
US 10-yr Treasury	1928-2024	~5.0%	~4.6%
US 3-mo T-Bill (cash)	1928-2024	~3.3%	~3.3%
US Real Estate (REITs)	1972-2024	~11.0%	~9.5%
Gold	1971-2024	~8.2%	~5.9%

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Note the systematic gap between arithmetic and geometric means. The gap is largest for volatile assets (small cap, emerging markets, gold) and smallest for stable ones (T-bills). This is the variance drag in action - high volatility impairs compounding.

Frequently Asked Questions

Should I use arithmetic or geometric mean to measure returns?

Use the geometric mean (CAGR) for measuring actual multi-period investment performance - it correctly reflects compounding and is not distorted by volatility. The arithmetic mean is useful for estimating the expected return in a single upcoming period, but it overstates what you'll actually earn over multiple compounding periods. The difference can be significant: a 20% standard deviation creates ~2% variance drag (11% arithmetic → ~9% geometric).

What is the difference between IRR and CAGR?

CAGR assumes a single lump-sum investment and measures the growth from beginning to ending value. IRR handles multiple cash flows (deposits and withdrawals) at different times, making it more accurate for portfolios with ongoing contributions or distributions. If there are no intermediate cash flows, IRR and CAGR are equivalent. IRR is the correct metric for evaluating personal portfolio performance including all contributions and withdrawals.

Why is my personal IRR different from what the fund reported?

Funds report Time-Weighted Return (TWR) to eliminate the effect of investor cash flow timing. Your personal IRR is the Money-Weighted Return (MWR), which reflects when you actually invested. If you added money before a market crash, your MWR will be worse than the fund's TWR. If you happened to add money before a strong rally, your MWR will be better. Neither is wrong - they measure different things: TWR measures the fund's performance; MWR measures your personal outcome.

What is a good average annual return?

Context matters. For a 100% equity portfolio: 7-10% nominal (4-7% real) is consistent with long-run historical returns. For a balanced 60/40 portfolio: 5-7% nominal. For bonds: 3-5%. For cash: 2-5% (depending on rates). Beating your benchmark on a risk-adjusted basis is a better goal than hitting a specific number - if you're taking less risk than the market, you should expect lower returns, and vice versa.

How does annualizing returns work for periods shorter or longer than one year?

Annualizing converts any holding period return to an equivalent annual rate: Annualized Return = (1 + Holding Period Return)^(1/Years) - 1. A 6-month return of 5% annualizes to (1.05)^(1/0.5) - 1 = 10.25%. A 3-year return of 30% annualizes to (1.30)^(1/3) - 1 = 9.14%. Annualizing short periods (< 1 year) to make comparisons can be misleading - a lucky 3-month result annualizes to an unrealistically high rate.