Measuring Returns: ROI and CAGR

A price chart that goes up feels like a win. But “it went up” is the least interesting thing you can say about an investment. The very first question a careful investor asks is the simplest one: how much did it actually grow? And “how much” splits neatly into two numbers — the total gain you pocketed (ROI) and the steady per-year rate that gain works out to once compounding is in the picture (CAGR). Get these two straight and you can already cut through most of the noise.

ROI: The Honest but Forgetful Number

Before you read — take a guess

Guess before reading: when you compute ROI, what should the gain be measured against?

The highest price the asset ever touchedThe raw dollar gain, with no comparison at allThe price you finally sold atWhat you originally put in (your cost)

Return on Investment (ROI) is the most basic measure: how much you made relative to what you put in.

$\text{ROI} = \frac{\text{final value} - \text{initial value}}{\text{initial value}}$

Worked example

You invest $80, sell for $100, and collected $4 in dividends along the way. Total proceeds are $104.

$\text{ROI} = \frac{104 - 80}{80} = \frac{24}{80} = 0.30 = 30\%$

Always include cash flows

ROI should count everything you received — dividends, interest, coupons — not just the price change. Leaving out the $4 dividend understates the return at 25% instead of 30%.

The catch: ROI has no clock

ROI tells you the size of the gain but nothing about how long it took. A 30% return is spectacular in one year and forgettable over ten. Watch how the same ROI means completely different things depending on the holding period:

Investment	ROI	Years held	Roughly per year
Fund A	30%	1	~30%
Fund B	30%	5	~5.4%
Fund C	30%	10	~2.7%

Same headline number, three very different investments. To compare them fairly, we need to put everything on a per-year footing — which is exactly what CAGR does.

Why is ROI alone a poor way to compare two investments?

It double-counts the initial investmentIt can never be negativeIt ignores how long the money was investedIt always overstates dividends

CAGR: Growth on a Per-Year Footing

Before you read — take a guess

Guess: an investment doubles over several years. Its compound annual growth rate is…

Smaller than you'd get by just splitting the total gain evenly across the yearsLarger than the total gainThe same as the total gain itselfExactly the total gain divided evenly across the years

The Compound Annual Growth Rate (CAGR) is the single steady yearly rate that would take you from your starting value to your ending value, as if it grew the same amount every year.

$\text{CAGR} = \left(\frac{\text{End}}{\text{Start}}\right)^{1/\text{years}} - 1$

The real path zig-zags; CAGR is the one smooth curve that connects the first dot to the last. Drag the rate and the horizon below and watch compounding bend the line away from naive straight-line growth:

Compounding pulls awayStart: $1,000

Compound growthSimple growth

Annual rate8%

Years20

Final value: $4,661
CAGR: 8%

Simple growth adds the same amount each year. Compound growth earns interest on past interest — so it curves upward and leaves the straight line behind.

Worked example

$1,000 grows to $2,000 over 10 years:

$\text{CAGR} = \left(\frac{2000}{1000}\right)^{1/10} - 1 = 2^{0.1} - 1 \approx 1.0718 - 1 = 7.18\%$

Not 100%, not 10% — about 7.2% per year. Compounding does the heavy lifting: at 7.18%, each year’s gain is computed on a bigger and bigger base.

CAGR ≠ average return

Here’s a subtlety that trips people up. Suppose a fund returns +50% one year then −50% the next. The average return looks like 0%. The actual result?

$1.50 \times 0.50 = 0.75 \quad\Rightarrow\quad \text{you lost } 25\%$

The CAGR over those two years is (0.75)^(1/2) − 1 ≈ −13.4% per year. Volatility drags compound growth below the simple average — which is why CAGR (a geometric mean) is the honest growth number, not the arithmetic average.

The volatility drag

The arithmetic average return always overstates what you actually earned when returns bounce around. A +50% / −50% pair averages 0% but leaves you down 25%. The bigger the swings, the bigger the gap.

Pick the right word for each blank.

Pick the right option for each blank, then check.

ROI ignores , while CAGR expresses growth as a single rate. Because returns compound, CAGR is a mean and sits below the simple average when returns are volatile.

A stock triples in value over a few years. How do its ROI and CAGR relate?

CAGR is larger than ROICAGR equals the total gain split evenly across the yearsROI is large; CAGR is a much smaller per-year rateROI and CAGR come out the same

Putting It Together

Two numbers, two jobs: ROI tells you how big the gain was, CAGR tells you how fast it grew once compounding is accounted for. Chunk them into one picture:

Big picture

How much did it grow?

Measuring returns
- ROI — total gain
  - (final − initial) ÷ initial
  - Counts all cash flows (dividends, coupons)
  - Time-blind — has no clock
- CAGR — per-year rate
  - (End / Start)^(1/years) − 1
  - Geometric mean — bakes in compounding
  - Sits below the arithmetic average when returns swing

The two return numbers: total gain (ROI) and the steady, compounding-aware yearly rate (CAGR).

A mixed recap — it pulls from everything above:

Question 1 of 40 correct

Which metric expresses growth as a single annual rate that accounts for compounding?

Total proceedsCAGRThe arithmetic averageROI

Check your answer to continue.

Key Takeaways

What to remember

ROI is the total gain relative to what you put in: (final − initial) / initial. Always count dividends, interest, and coupons — not just the price change.
ROI has no clock. The same 30% means ~30%/year over one year but only ~2.7%/year over ten — so ROI alone can’t fairly compare investments.
CAGR fixes that by putting growth on a per-year footing: (End / Start)^(1/years) − 1. Doubling your money in 10 years is ~7.2%/year, not 10%.
CAGR ≠ the average return. It’s a geometric mean, so it sits below the simple average whenever returns swing — that gap is the volatility drag.