# Measuring Returns and CAGR

> Learn how to measure trading and investment returns correctly: simple and log returns, CAGR, arithmetic versus geometric averages, and money weighted returns.

Source: https://learn.tradelabsai.com/portfolio/measuring-returns-and-cagr/  
Track: Portfolio and Performance · Level: Intermediate · Updated: 2026-10-03  
Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice.  
Cite as: TradeLabs Learn, "Measuring Returns and CAGR", https://learn.tradelabsai.com/portfolio/measuring-returns-and-cagr/

Every performance figure starts with a return, yet returns are easy to measure wrongly. A strategy that gains 50% one year and loses 50% the next has an average return of zero but has lost a quarter of its money. Deposits and withdrawals distort account growth. Monthly returns cannot simply be added to get an annual figure. This lesson covers the core return measures and when to use each, starting with the compound annual growth rate (CAGR), the standard way to express growth over several years.

## Simple and log returns

| Measure | Formula | Notes |
|---|---|---|
| Simple return | (end value divided by start value) minus 1 | Intuitive; percentages compound by multiplying |
| Log return | natural log of (end divided by start) | Adds across periods; convenient in statistics |

For small moves the two are almost identical: a 1% simple return is a 0.995% log return. For large moves they differ: a 50% gain is a 40.5% log return. See [NumPy and Pandas for Traders](https://learn.tradelabsai.com/programming/numpy-and-pandas-for-traders/).

## Compound annual growth rate

CAGR is the constant yearly rate that would turn the starting value into the ending value over the period.

```
CAGR = (Ending value / Starting value) ^ (1 / Years) - 1
```

**Example: Calculating CAGR**
An account grows from $10,000 to $18,000 over 5 years. The ratio is 1.8. Raising 1.8 to the power of 1 divided by 5 gives about 1.1247, so the CAGR is about 12.5% a year. Simply dividing the total gain of 80% by 5 gives 16%, which overstates growth because it ignores compounding. Check: $10,000 growing at 12.47% for 5 years gives about $18,000. Try your own numbers with the [Compound Growth and CAGR Calculator](https://learn.tradelabsai.com/tools/cagr-calculator/).

## Arithmetic versus geometric average

| Year | Return | Account value from $100 |
|---|---|---|
| 1 | +50% | $150 |
| 2 | minus 50% | $75 |

The arithmetic average return is (50 plus minus 50) divided by 2, which is 0%. The geometric average, which is what CAGR measures, is the square root of (1.5 times 0.5) minus 1, about minus 13.4% a year. The account lost 25%. The gap between the two averages grows with volatility, which is why reducing volatility can raise long run compound growth even with the same average return. See [Volatility](https://learn.tradelabsai.com/markets/volatility/) and [Compounding and Geometric vs Arithmetic Returns](https://learn.tradelabsai.com/math/compounding/).

## Volatility drag

A useful approximation links the two averages:

```
Geometric mean ≈ Arithmetic mean - (Volatility ^ 2) / 2
```

With an arithmetic mean of 10% and volatility of 20%, the geometric mean is roughly 10% minus 2%, or 8%. With volatility of 40%, it falls to about 2%. Large swings erode compounding.

## Annualising returns

| Data | To annualise a mean return | To annualise volatility |
|---|---|---|
| Daily (stocks) | Multiply by about 252, or compound | Multiply by the square root of 252 |
| Weekly | Multiply by 52 | Multiply by the square root of 52 |
| Monthly | Multiply by 12 | Multiply by the square root of 12 |

Crypto trades every day, so analysts often use 365. Annualising short track records produces dramatic but unreliable figures: a 5% gain in one month does not mean an 80% year. See [Statistical Significance in Trading](https://learn.tradelabsai.com/math/statistical-significance/).

## Time weighted versus money weighted returns

| Measure | What it shows | Use |
|---|---|---|
| Time weighted return | Performance of the strategy, ignoring the timing of deposits and withdrawals | Comparing managers and strategies |
| Money weighted return (IRR) | Your actual experience, including when money was added or removed | Personal results |

If you add a large deposit just before a losing period, your money weighted return falls below the time weighted return. Fund managers report time weighted returns because clients control the timing of flows. See [Investor Reporting](https://learn.tradelabsai.com/industry/investor-reporting/).

## What to include

Honest returns include commissions, spreads, financing costs, fees and, for comparison with benchmarks, dividends. Pre cost returns from backtests should always be labelled as such. See [Transaction Costs](https://learn.tradelabsai.com/orders/transaction-costs/) and [Fake Performance and Track Record Verification](https://learn.tradelabsai.com/start-here/fake-trading-performance/).

## Frequently asked questions

### What is CAGR?

The compound annual growth rate: the constant yearly return that would grow a starting value into the ending value over a given number of years.

### Why is average return different from CAGR?

The arithmetic average ignores compounding; CAGR is a geometric average, which is lower when returns are volatile.

### Should I use time weighted or money weighted returns?

Use time weighted returns to judge a strategy and money weighted returns to understand your own results with deposits and withdrawals.

Next, learn the most famous risk adjusted measure in [Sharpe Ratio](https://learn.tradelabsai.com/portfolio/sharpe-ratio/).

## Continue learning

- Next lesson: [Sharpe Ratio](https://learn.tradelabsai.com/portfolio/sharpe-ratio/)
- Related: [Reinforcement Learning](https://learn.tradelabsai.com/machine-learning/reinforcement-learning/): Reinforcement learning trains agents to act by rewarding good outcomes. Learn how it applies to trading and execution, how rewards are designed and why it is hard.
- Related: [Compounding and Geometric vs Arithmetic Returns](https://learn.tradelabsai.com/math/compounding/): Compounding means returns earn returns over time. Learn the formulas, why losses hurt more than gains help, volatility drag and how it shapes position sizing.
- Related: [Compound Growth and CAGR Calculator](https://learn.tradelabsai.com/tools/cagr-calculator/): Free CAGR calculator. Enter a starting value, ending value and number of years to see the compound annual growth rate, total return and doubling time.
- Related: [Sharpe Ratio](https://learn.tradelabsai.com/portfolio/sharpe-ratio/): The Sharpe ratio measures return per unit of risk. Learn the formula, how to annualise it, what counts as a good Sharpe ratio, its limitations and common mistakes.
- Related: [Maximum Drawdown](https://learn.tradelabsai.com/portfolio/maximum-drawdown/): Maximum drawdown measures the largest fall from a peak to a trough in an account or strategy. Learn how to calculate it, recovery maths, duration and how to use it.
- Related: [Time Value of Money](https://learn.tradelabsai.com/math/time-value-of-money/): A dollar today is worth more than a dollar tomorrow. Learn present and future value, discounting, annuities and NPV, the maths behind bonds, valuations and options.