NISM Certifications · NISM-Series-V-A: Mutual Fund Distributors · Mutual Fund Scheme Performance
A scheme's annual returns were +20% in year 1 and -20% in year 2. What is its compounded annual growth rate over the two years, approximately, and how does it compare with the arithmetic average return of 0%?
The CAGR is about -2.02 percent, lower than the arithmetic average of zero. Compounding 1.20 and 0.80 leaves 0.96 of the capital, and its square root is about 0.9798. Volatility drags compounded return below the simple average.
- A0%, equal to arithmetic average
- B-2.02%, lower than arithmetic averageCorrect
- C+2.02%, higher than arithmetic average
- D-4.00%, lower than arithmetic average
Explanation
Value grows 1.20 x 0.80 = 0.96 of the initial amount. CAGR = sqrt(0.96) - 1 = 0.9798 - 1 = -2.02%. The total loss is 4% over two years, which is the wrong figure if used as annual. Volatility makes CAGR lower than the arithmetic mean.
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