Investment ROI / IRR / NPV Complete Guide
"7-day annualized 5.2%!" "Up 30% over the past year!" "A new fund earned 12% in 7 days!" — Open any wealth-management app and you are bombarded with eye-catching return-rate numbers. But how are these return rates actually calculated? Why would two products both labeled "5% annualized" deliver wildly different gains in hand? Why can a 20% gain from regular investing still lose to inflation? This article explains the four key return-rate metrics — ROI, annualized return rate, CAGR and IRR — in depth, exposes the promotional traps that are easiest to fall for, and helps you pick the right metric and understand your true returns.
1. Types of Return Rate: Total Return vs Annualized Return
Every return rate is essentially "money earned ÷ money invested," but because the time dimension differs, they fall into two main categories:
- Total return rate (holding-period return): (ending value − initial investment) ÷ initial investment. It ignores how long you held the investment and only looks at how much you earned from start to finish.
- Annualized return rate: converts return rates of different time spans into a standardized "annual compound growth rate," making it easy to compare products side by side. It is the core metric ordinary investors use to judge an investment.
2. The Simple ROI Formula
ROI (return on investment) = (ending value − initial investment) ÷ initial investment × 100%.
Example: you invest ¥100,000 in a fund, and one year later the account is worth ¥125,000. ROI = (12.5 − 10) ÷ 10 = 25%.
ROI is simple and intuitive, but it only looks at total gains and ignores time, so it cannot measure investment efficiency. Whether it takes 1 year or 5 years to turn ¥100,000 into ¥125,000, the ROI is 25% either way — yet the reality is worlds apart.
3. Annualized Return: The CAGR Formula and Examples
CAGR (compound annual growth rate) is the investment world's "golden metric," reflecting the true annual compound growth rate of your money.
CAGR = (ending value / initial investment)^(1/years) - 1
Classic example: ¥10,000 grew into ¥30,000 over 5 years. What is the annualized rate?
CAGR = (3 ÷ 1)^(1/5) - 1 = 3^0.2 - 1 ≈ 24.6%, meaning an annualized rate of about 24.6%.
If you look at ROI alone, 200% sounds like a lot; but 24.6% annualized is the true level — that return already matches the caliber of a top fund manager.
4. IRR (Internal Rate of Return): Why It's More Accurate Than CAGR for Regular Investing
CAGR assumes you invest a lump sum at the start and take everything out at the end, but in reality most investments see money flowing in and out in batches: monthly regular investments of 1,000, insurance premiums paid over 3 years, dividends reinvested every quarter. In these scenarios CAGR is inaccurate, and you must use IRR (internal rate of return).
IRR takes into account the timing of each cash flow and works backward from "net present value = 0" to derive the true annualized return rate. Think of it as the true annualized rate that incorporates the time value of money.
Example: you invest ¥1,000 every month, and after 12 months the account is worth ¥13,200. Total invested is ¥12,000, a gain of ¥1,200, so ROI = 10%; but because the money went in gradually (the first payment was invested for 12 months, the last for only 1 month), the true IRR is only about 1.5%/month ≈ 19.6% annualized — far lower than the naive "10% × 12."
5. Where Investors Get Picked Off: 7-Day Annualized / Income per 10,000 Shares / 1-Year Rise and Fall
| Metric | What It Really Means | Common Trap |
|---|---|---|
| 7-day annualized return | The average daily return over the last 7 days × 365, converted to an annualized figure | A 7-day surge doesn't mean it holds all year; money funds occasionally peak and then quickly fall back |
| Income per 10,000 shares | The gain you actually receive per 10,000 shares held on a given day | On volatile days 1 share can mean 2-3 yuan, but most days it's only 0.4-0.6 yuan |
| Past-year rise and fall | The fund's NAV growth rate over the last 12 months | Heavily affected by the starting point; if this time last year was a "historical low," the 1-year gain looks extreme but can't be extrapolated linearly |
| Return since inception | The fund's total return from launch to today | Time spans vary from 5 to 10 years; convert to CAGR before comparing with other products |
6. How to Calculate the True Return on Regular Investing
Invest ¥1,000 per month for a year; the market dips first, then rises, and the final account value is ¥13,200:
- Total invested: ¥1,000 × 12 = ¥12,000
- Book gain: ¥13,200 - ¥12,000 = ¥1,200
- Simple return rate: ¥1,200 / ¥12,000 = 10% (which is wrong!)
- Using the IRR formula (calculated on monthly cash flow): monthly IRR ≈ 1.5%, annualized IRR ≈ 19.6% (compounded annually)
Why is the simple 10% wrong? Because the ¥1,000 from month 1 was actually invested for 12 months, while the ¥1,000 from month 12 was invested for only 1 month, giving an average holding period of about 6 months. IRR automatically accounts for this time weighting, so the result is closer to reality.
7. Benchmarks: Long-Term Returns by Asset Class
| Asset Class | Long-Term Annualized Return (approx.) | Risk Level | Best For |
|---|---|---|---|
| Yu'ebao / money-market funds | ≈ 2% | Very low | Spare cash, emergency funds |
| Bank fixed deposits / large-denomination CDs | 2% - 3% | Very low | Conservative investors, money not needed short-term |
| Pure bond funds | 3% - 5% | Low | Steady investors, replacing deposits |
| CSI 300 index (long-term holding) | 8% - 10% | Medium-to-high | Investors who can accept a 30% drawdown and hold ≥ 5 years |
| Equity-heavy balanced funds (top managers) | ≈ 15% | High | Investors who can tolerate volatility and hold long-term |
| Individual stocks (the few who beat the market long-term) | 15% - 25% | Very high | Professional investors |
8. Inflation Erosion: How Much Purchasing Power Does ¥1 Million Keep After 10 Years at 3% Inflation?
Nominal gain ≠ actual purchasing power. Using a long-term inflation estimate of 3% (CPI averages about 2-3% a year), today's ¥1 million discounted at 3% inflation over 10 years:
Actual purchasing power = 1,000,000 ÷ (1+3%)^10 ≈ 744,000, meaning about 256,000 of purchasing power has been eroded over the decade.
So the first goal of investing is to outpace inflation (≥ 3%), and the second is to outpace GDP growth (≈ 5%); anything above these counts as real "wealth growth."
9. Real After-Tax Return vs Nominal Return
Bank deposit interest (currently exempt from interest tax) and treasury bond income are tax-free, but fund dividends, wealth-management products, stock dividends and bond interest may all involve personal income tax. An annualized 4% product may yield only 3.4%-3.8% after tax. After also deducting 2-3% inflation, the real return rate is down to only about 1%. So don't just look at the nominal annualized figure — re-examine your portfolio with the formula "after-tax annualized − inflation rate = real annualized."
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