Estimate arithmetic average return, geometric average return, and ending investment value.
This tool provides estimates for informational purposes only and is not a substitute for professional financial, tax, academic, medical, fitness, or legal advice. Results vary based on your assumptions, rates, region, and provider rules. Always confirm key figures before making decisions.
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Understanding investment returns β and the difference between the types of return calculations β is essential for evaluating how your portfolio is performing, comparing investment options, and making informed financial planning decisions. This comprehensive guide explains the mathematics of average investment returns, how CAGR (Compound Annual Growth Rate) differs from simple averages, the historical performance of major indices in the UK and US, how to account for inflation, and how tax treatment differs between ISAs and Roth IRAs.
There are two fundamentally different ways to calculate average investment returns, and confusing them leads to serious errors in financial planning:
Arithmetic mean return (simple average): Sum all the annual returns and divide by the number of years. If a portfolio returned +20%, β10%, and +15% over three years, the arithmetic mean is (20 β 10 + 15) Γ· 3 = 8.33% per year.
Geometric mean return (CAGR): The compound annual growth rate that, if applied consistently, would produce the same ending balance from the same starting balance. Using the same example: Β£100 β Β£120 (after +20%) β Β£108 (after β10%) β Β£124.20 (after +15%). CAGR = (Β£124.20 Γ· Β£100)^(1/3) β 1 = 7.49% per year.
The arithmetic mean always overstates actual compound growth. Only the CAGR (geometric mean) accurately represents the true annualised growth rate of an investment over multiple periods. For evaluating real portfolio performance, always use CAGR.
The Compound Annual Growth Rate formula is:
CAGR = (Ending Value Γ· Beginning Value)^(1 Γ· Number of Years) β 1
Examples:
CAGR is the most commonly cited metric for investment performance comparisons because it provides a single comparable number regardless of the starting value. However, it smooths over the actual volatility experienced β a high CAGR investment may have had severe drawdowns along the way.
The gap between arithmetic and geometric mean return is larger when returns are more volatile. This has important practical implications:
The formula connecting them: Geometric mean β Arithmetic mean β (Variance / 2). Where variance is the standard deviation squared. For a portfolio with 8% arithmetic mean return and 15% standard deviation: geometric mean β 8% β (0.15Β² / 2) = 8% β 1.125% = 6.875%.
Nominal return is the raw investment return before adjusting for inflation. Real return adjusts for inflation to show purchasing power gains.
Real Return = [(1 + Nominal Return) Γ· (1 + Inflation Rate)] β 1
Or approximately: Real Return β Nominal Return β Inflation Rate (for small values).
Why this matters: If your portfolio returns 8% per year but inflation is 3% per year, your real (purchasing power) gain is approximately 5% per year β not 8%. Over 20 years, the difference between nominal and real wealth accumulation is dramatic.
Historical UK inflation (CPI) has averaged approximately 2.5β3% per year over the long run. In the US, CPI has averaged approximately 2.5β3% per year. However, both the UK and US experienced significantly higher inflation in 2021β2024 (UK CPI peaking at 11.1% in October 2022; US CPI peaking at 9.1% in June 2022), which temporarily compressed real returns on all asset classes.
The S&P 500 is the most widely cited US stock market benchmark, tracking the 500 largest publicly traded US companies. Long-run historical performance:
| Period | S&P 500 CAGR (Nominal) | S&P 500 CAGR (Real) |
|---|---|---|
| Since 1926 (long-run) | ~10% per year | ~7% per year |
| Last 30 years (1994β2024) | ~10.5β11% per year | ~8β9% per year |
| Last 10 years (2014β2024) | ~12β13% per year | ~9β10% per year |
These figures include dividend reinvestment. The S&P 500 has also experienced significant bear markets β drawdowns of 30%+ in 2001β2002, 2008β2009, and 2020, and 20%+ in 2022. Long-run averages do not guarantee future returns or protection from near-term volatility.
The FTSE 100 is the primary UK equity benchmark, representing the 100 largest UK-listed companies by market capitalisation. Performance has been somewhat lower than the S&P 500 over the past decade, partly due to sector composition (more value stocks, banks, and resource companies; fewer technology companies):
| Period | FTSE 100 CAGR (Nominal) | Notes |
|---|---|---|
| Since inception (1984) | ~7β8% per year (total return) | Including dividends reinvested |
| Price return only (no dividends) | ~3β4% per year | FTSE 100 level was ~1,000 in 1984, ~7,500 in 2024 |
| Last 10 years (2014β2024) | ~5β7% per year (total return) | Underperformed S&P 500 in this period |
Many UK investors who want broader exposure use the FTSE All-World or FTSE Developed World index instead of the FTSE 100 alone. The FTSE All-World tracks ~3,800 stocks globally and has historically delivered returns closer to the S&P 500 (approximately 8β10% nominal annual return over long periods) due to its heavy US weighting.
Bonds (fixed income) have historically delivered lower long-run returns than equities but with lower volatility and shorter maximum drawdown periods. UK and US government bond (gilts / Treasuries) long-run returns:
A mixed portfolio (e.g., 60% equities / 40% bonds) has historically delivered a CAGR of approximately 7β9% nominal, with meaningfully lower volatility than a 100% equity portfolio.
The expected return of a portfolio is the weighted average of the expected returns of its components: E(Rp) = Ξ£ [wi Γ E(Ri)], where wi is the weight of asset i and E(Ri) is its expected return.
Risk-adjusted return accounts for the volatility (risk) taken to achieve a given return. The Sharpe Ratio is the most common measure: Sharpe Ratio = (Portfolio Return β Risk-Free Rate) Γ· Standard Deviation of Portfolio Returns. A Sharpe Ratio above 1.0 is considered good; above 2.0 is excellent. The risk-free rate is typically the 3-month Treasury bill rate (US) or Bank of England base rate (UK).
How investment returns are taxed has a major impact on long-term wealth accumulation:
| Account Type | Country | Tax Treatment |
|---|---|---|
| Stocks and Shares ISA | UK | All growth and dividends completely tax-free forever; Β£20,000/year contribution limit |
| SIPP (pension) | UK | Contributions tax-deductible; growth tax-free; 25% tax-free lump sum at retirement; remainder taxed as income |
| Roth IRA | US | Contributions after-tax; growth and qualified withdrawals tax-free; no RMDs; $7,000/year limit |
| Traditional IRA / 401(k) | US | Contributions may be tax-deductible; growth tax-deferred; withdrawals taxed as ordinary income; RMDs from 73 |
| General investment account | UK / US | UK: CGT on gains above Β£3,000/year (2024/25); US: capital gains tax (0%, 15%, or 20% depending on income/holding period) |
The UK Stocks and Shares ISA is arguably the most tax-efficient retail investment wrapper in the world for long-term investors β unlimited tax-free growth once invested, with no tax on withdrawal. For US investors, the Roth IRA provides comparable tax-free growth, though with lower contribution limits ($7,000 vs Β£20,000). Maximising both before investing in taxable accounts is the cornerstone of tax-efficient investing in each country.
CAGR (Compound Annual Growth Rate) is the annualised rate of return that produces the same result as the actual investment performance. Formula: CAGR = (Ending Value Γ· Beginning Value)^(1 Γ· Years) β 1. For example, a portfolio growing from Β£10,000 to Β£17,000 in 6 years has a CAGR of (1.7)^(1/6) β 1 = 9.26% per year. CAGR is the correct measure for comparing investment performance over time.
The arithmetic mean adds all annual returns and divides by years. The CAGR is the true compound annual growth that accounts for the compounding effect β it is always equal to or lower than the arithmetic mean for volatile investments. For financial planning (calculating future portfolio value), always use CAGR. The gap between arithmetic mean and CAGR is larger for higher-volatility investments.
The S&P 500 has delivered an approximate nominal CAGR of 10% per year since 1926 and approximately 7% in real (inflation-adjusted) terms. Over the past 30 years (1994β2024), nominal returns have been approximately 10.5β11% per year. Past performance does not guarantee future results, and the index has experienced multiple significant drawdowns of 30%+ along the way.
The FTSE 100 has delivered approximately 7β8% per year nominal total return (including dividends reinvested) since its inception in 1984. Price-only return (without dividends) has been approximately 3β4% per year, as the FTSE 100 price level has risen more slowly than the S&P 500. For broader UK/global equity exposure, many investors use the FTSE All-World or FTSE Developed World index instead.
Real return is the investment return adjusted for inflation. If your portfolio returns 8% but inflation is 3%, your real return (purchasing power gain) is approximately 5%. Only real returns represent actual increases in what your money can buy. Long-term financial planning should use real return assumptions β the historical real return of global equities is approximately 5β7% per year before taxes.
The Sharpe ratio measures return per unit of risk: (Portfolio Return β Risk-Free Rate) Γ· Standard Deviation. It allows comparison of investments with different risk levels on a like-for-like basis. A Sharpe Ratio of 1.0+ is good; 2.0+ is excellent. An investment returning 12% with high volatility may have a lower Sharpe ratio than one returning 8% with low volatility, making the 8% option superior on a risk-adjusted basis.
Within a Stocks and Shares ISA, all investment growth and income is completely free from UK Capital Gains Tax and income tax, with no limit on the total amount held. Outside an ISA, capital gains above Β£3,000 (2024/25 allowance) are subject to CGT at 10% (basic rate) or 20% (higher/additional rate) for investments β or 18%/24% for property. Dividends above Β£500 (2024/25 allowance) are taxed at 8.75%, 33.75%, or 39.35% depending on tax band.
The choice depends primarily on whether you expect to be in a higher or lower tax bracket in retirement than now. If higher (younger, lower current income): Roth IRA is generally better β pay tax now at a lower rate, enjoy tax-free withdrawals in retirement. If lower (already in peak earnings): traditional IRA or 401(k) deductions reduce your current high-rate tax bill, with the expectation of lower-rate withdrawals in retirement. Both offer tax-deferred/free compounding, making either significantly better than a taxable account for long-term investing.