NISM Certifications · NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investments
A portfolio has returns of +20% in year 1 and -20% in year 2. What is the approximate compound annual growth rate (CAGR) over the two years?
The CAGR is about minus 2.02 percent. A 20 percent gain followed by a 20 percent fall leaves 96 percent of the capital, and the square root of 0.96 minus one gives the annual compounded rate. The arithmetic average of zero ignores compounding.
- A0%
- B-2.02%Correct
- C-4%
- D+2.02%
Explanation
Growth factor = 1.20 x 0.80 = 0.96, so the total return is -4%. CAGR = sqrt(0.96) - 1 = 0.9798 - 1 = -2.02%. The 0% option is the arithmetic mean, which ignores compounding. The -4% option is the total two-year change and not the annual rate.
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