Return measures the percentage change in investment value over a period, including any income received. It’s the most fundamental measure of investment performance.
Beginner
What It Means
Return tells you how much you made (or lost) on an investment, expressed as a percentage of your starting value.
Basic Calculation
Return = (Ending Value - Beginning Value + Income) / Beginning Value
Example:
- Buy stock at $100
- Receive $3 dividend
- Sell at $110
- Return = ($110 - $100 + $3) / $100 = 13%
Types of Returns
| Type | What It Includes |
|---|
| Price Return | Price change only |
| Total Return | Price change + dividends/income |
| Annualized Return | Return expressed as yearly rate |
| Cumulative Return | Total return over entire period |
Why It Matters
Return is the bottom line - did your investment make money? Everything else (risk, volatility, Sharpe ratio) provides context, but return is what you actually earn.
Advanced
Return Calculation Methods
| Method | Formula | Use Case |
|---|
| Simple | (End - Start) / Start | Single period |
| Logarithmic | ln(End / Start) | Continuous compounding |
| Time-Weighted | Geometric link of sub-periods | Manager evaluation |
| Money-Weighted | IRR of cash flows | Investor experience |
Time-Weighted vs. Money-Weighted
| Type | Considers Cash Flows? | Best For |
|---|
| Time-Weighted (TWR) | No | Manager performance |
| Money-Weighted (MWR) | Yes | Investor experience |
Time-weighted return removes the effect of when money was added/withdrawn, isolating manager skill. Money-weighted return shows what the investor actually earned.
Annualization
Converting returns to annual rates:
Annualized Return = (1 + Total Return)^(1/Years) - 1
Example:
- 50% cumulative return over 3 years
- Annualized = (1.50)^(1/3) - 1 = 14.5% per year
Geometric vs. Arithmetic Mean
| Type | Formula | When to Use |
|---|
| Arithmetic | Sum / N | Expected single-period return |
| Geometric | (Product)^(1/N) - 1 | Actual compound growth |
Example: Years with +50% then -50%
- Arithmetic mean: (50 + -50) / 2 = 0%
- Geometric mean: √(1.5 × 0.5) - 1 = -13.4%
- Reality: $100 → $150 → $75 (you lost money!)
Arithmetic mean overstates compound returns. Always use geometric mean for multi-period performance.
Real vs. Nominal Returns
| Type | Definition |
|---|
| Nominal | Return before inflation adjustment |
| Real | Return after subtracting inflation |
Real Return ≈ Nominal Return - Inflation
Example:
- Nominal return: 8%
- Inflation: 3%
- Real return: ~5%
After-Tax Returns
Different return measures for tax impact:
| Measure | Description |
|---|
| Pre-Tax | Return before taxes |
| After-Tax (Pre-Liquidation) | After taxes paid during holding |
| After-Tax (Post-Liquidation) | After all taxes including sale |
Return Attribution
Breaking down where returns came from:
| Component | Description |
|---|
| Market Return | Broad market movement |
| Sector Allocation | Sector over/underweights |
| Stock Selection | Individual stock picks |
| Interaction | Combined effects |
Historical Context
Long-term annualized returns (US):
| Asset | Return | Period |
|---|
| Stocks | 10% | 1926-present |
| Bonds | 5% | 1926-present |
| T-Bills | 3% | 1926-present |
| Inflation | 3% | 1926-present |
Return Expectations
Historical returns don’t guarantee future returns. Current valuations, interest rates, and economic conditions affect forward expectations.
