Which of the following is correct about the compound annual growth rate?

CAGR represents a "smoothed out" growth rate. If an investment grows from ₹100 to ₹200 over 3 years with uneven growth (50% one year, -10% the next, then up again), CAGR calculates the equivalent constant rate that would produce the same result.

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Statement 1: "It is an average annualized return of an investment."

This is true but incomplete. CAGR does give an average return, but this doesn't capture its key characteristic.

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Statement 2: "It is calculated by taking the arithmetic mean of series of returns."

This is incorrect. CAGR uses geometric mean, not arithmetic mean.

Consider an investment with +50% growth in Year 1 and -50% decline in Year 2:

Arithmetic mean: $(50\% + (-50\%))/2 = 0\%$

Actual result: ₹100 → ₹150 → ₹75

The arithmetic mean suggests no change, but the investment actually lost money. CAGR accounts for compounding effects, while arithmetic mean does not.

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Statement 3: "It is a linear measure that does not account for the effects of compounding."

This is incorrect. CAGR is exponential, not linear, and specifically accounts for compounding effects.

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Statement 4: "It smoothens out the volatile nature of year by year growth/decay rates and provides more accurate results."

This is correct. CAGR converts volatile, year-by-year growth rates into a single steady rate.

Example comparison:

Investment A: +20%, +10%, +15% each year

Investment B: +50%, -10%, +5% each year

CAGR provides one comparable number for each investment instead of requiring analysis of multiple yearly rates.

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Statement 4 captures the most important characteristic of CAGR—it smoothens volatile returns into a single, steady growth rate.

The answer is Option 4.