Nominal rate of return
The rate of return measures the gain or loss on an investment as a percentage of the amount invested. The simple (nominal) rate of return over a period is Rate of return = (final value − initial value + income received)/initial value × 100. Example: an investment of ₹50,000 grows to ₹60,000: return = 10,000/50,000 = 20%. If a share bought at ₹200 pays a dividend of ₹10 and is sold at ₹230, the return is (30 + 10)/200 = 20%.
The nominal rate does not adjust for inflation and, for periods longer than a year, does not tell you the yearly rate.
Compound annual growth rate (CAGR)
CAGR is the constant yearly rate at which an investment would have to grow, with compounding, to go from its beginning value to its ending value over n years: CAGR = (Ending value/Beginning value)^(1/n) − 1. Example: ₹10,000 grows to ₹14,641 in 4 years. (14641/10000)^(1/4) = 1.1, so CAGR = 10%.
CAGR is a smoothed rate: it ignores the ups and downs in between and assumes steady growth. It is useful for comparing investments over different periods.
CAGR versus average return
Suppose an investment rises 50% in year 1 and falls 50% in year 2. The simple average of the yearly returns is 0%, but the value has actually fallen to 1.5 × 0.5 = 0.75 of the original. CAGR = √0.75 − 1 ≈ −13.4%. The arithmetic average can therefore mislead; CAGR reflects the actual change in value.
Key points
- Nominal return = (gain + income)/initial investment.
- CAGR = (EV/BV)^(1/n) − 1.
- CAGR assumes a constant rate each year with compounding.
- The average of yearly returns is not the same as CAGR.
Common mistakes
- Dividing the total percentage gain by n to get a yearly rate; this ignores compounding.
- Leaving out dividends or interest received when computing return.