ROI Mastery & Annualized Performance Theory

Investment Metrology: The Physics of ROI & Wealth Velocity

Return on Investment (ROI) is a performance measure used to evaluate the efficiency or profitability of an investment. In quantitative finance, ROI is the ratio between net profit and cost of investment. However, for longitudinal analysis, Investment Velocity—measured via CAGR—provides a more accurate representation of capital growth relative to time exposure.

1. Simple ROI vs. Annualized Returns

A common fallacy in retail investing is comparing absolute ROI without a temporal denominator. A 100% ROI achieved over 10 years is vastly different from a 100% ROI achieved over 2 years. The latter represents a periodic growth rate that is significantly higher, allowing for more rapid capital redeployment.

2. The Rule of 72: Geometric Doubling

The Rule of 72 is an actuarial heuristic used to estimate the time required for an investment to double in value at a fixed annual rate of return. It is derived from the natural logarithm of 2 ($ln(2) \approx 0.693$). For most common interest rates, 72 provides a more divisible numerator that accounts for the effects of compounding slightly better than 69.3.

3. Risk-Adjusted Returns & Volatility

Modern Portfolio Theory (MPT) suggests that ROI should never be viewed in isolation. The Sharpe Ratio measures the excess return per unit of deviation (volatility). An investment with a 12% ROI and low volatility is mathematically superior to one with a 15% ROI but extreme drawdown potential, as the risk of total capital impairment is significantly higher in the latter.