Rate of Return (RoR)

1. Definition

The Rate of Return (RoR) is the net gain or loss of an investment over a specified time period, expressed as a percentage of the investment's initial cost.

2. Key Metrics

2.1. Nominal vs. Real Rate

• Nominal: The percentage increase in money.
• Real: The percentage increase in purchasing power. (Nominal Rate - Inflation Rate). This is what actually matters for wealth building.

2.2. CAGR (Compound Annual Growth Rate)

• Since investments fluctuate (volatility), a simple average is misleading.
• CAGR smoothes out the returns to show what the investment would have yielded if it had grown at a steady rate. It is the geometric mean of annual returns.

3. The Mathematics of Loss

This concept explains why Warren Buffett's Rule No.1 is "Never lose money." * There is an asymmetry between loss and the gain required to recover. * Examples: * Loss 10% $\rightarrow$ Requires 11% gain to recover. * Loss 50% $\rightarrow$ Requires 100% gain to recover. * Loss 90% $\rightarrow$ Requires 900% gain to recover. * This implies that risk management (limiting downside) is mathematically more important than chasing upside.

4. Formula

$$RoR = \frac{(Current\ Value - Initial\ Value)}{Initial\ Value} \times 100$$