NISM Certifications · NISM-Series-XV: Research Analyst · Fundamentals of Risk and Return
A stock gave returns of +20% in year 1 and -20% in year 2. What is its two-year holding period return and the approximate arithmetic mean return?
The two-year holding period return is -4%, because 1.20 multiplied by 0.80 gives 0.96. The arithmetic mean is 0%, since +20 and -20 average to zero. The gap shows that arithmetic means overstate compounded performance in volatile series.
- A0% holding period return; 0% arithmetic mean
- B-4% holding period return; 0% arithmetic meanCorrect
- C+4% holding period return; 0% arithmetic mean
- D-4% holding period return; -2% arithmetic mean
Explanation
Holding period return = 1.20 x 0.80 - 1 = 0.96 - 1 = -4%. Arithmetic mean = (20 - 20)/2 = 0%. Option 0% for HPR ignores compounding; +4% has the wrong sign; -2% for the mean divides the HPR by 2 wrongly.
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