A financial analyst is evaluating two investment strategies, Strategy A and Strategy B, over a 3-year period. Strategy A yielded returns of 5% in year 1, 7% in year 2, and 6% in year 3. Strategy B yielded returns of 4% in year 1, 8% in year 2, and 7% in year 3. Assuming an initial investment of $10,000 for both, which strategy would result in a higher cumulative return at the end of 3 years?
- AStrategy B
- BStrategy A
- CCannot be determined without knowing the compounding frequency
- DBoth strategies would result in the same cumulative return
Show answer & explanationAnswer & explanation
Correct answer: A. Strategy B
Cumulative return is calculated by multiplying (1 + annual return) for each year. For Strategy A: (1+0.05) * (1+0.07) * (1+0.06) = 1.05 * 1.07 * 1.06 = 1.19091. This means a 19.091% cumulative return. For Strategy B: (1+0.04) * (1+0.08) * (1+0.07) = 1.04 * 1.08 * 1.07 = 1.199376. This means a 19.9376% cumulative return. Strategy B has a slightly higher cumulative return. My explanation and answer key are currently contradictory, let me re-calculate and fix. Recalculation: Strategy A: (1 + 0.05) * (1 + 0.07) * (1 + 0.06) = 1.05 * 1.07 * 1.06 = 1.19091. Cumulative return = 19.091% Strategy B: (1 + 0.04) * (1 + 0.08) * (1 + 0.07) = 1.04 * 1.08 * 1.07 = 1.199376. Cumulative return = 19.9376% Strategy B has a higher cumulative return. The correct answer should be B. I will correct the answer key and options accordingly. The original answer was A, which is incorrect. The prompt asks for a higher cumulative return. Corrected Explanation: Cumulative return is calculated by multiplying (1 + annual return) for each year. For Strategy A: (1+0.05) * (1+0.07) * (1+0.06) = 1.05 * 1.07 * 1.06 = 1.19091, representing a 19.091% cumulative return. For Strategy B: (1+0.04) * (1+0.08) * (1+0.07) = 1.04 * 1.08 * 1.07 = 1.199376, representing a 19.9376% cumulative return. Therefore, Strategy B results in a higher cumulative return.
Why the other options are wrong
- B. Incorrect. Strategy A's cumulative return is 19.091%, which is lower than Strategy B's.
- C. Incorrect. Cumulative return can be determined from annual returns, assuming annual compounding which is typical for such problems unless specified otherwise.
- D. Incorrect. The cumulative returns are different.
Cumulative Return
Cumulative return measures the total percentage change in an investment's value over a specified period, taking into account the effect of compounding.
- Calculated by multiplying (1 + rate of return) for each period.
- Reflects the total growth of an investment over multiple periods.
- Different from average annual return, as it accounts for compounding.
Memory trick: Grow it, grow it, year by year, the total gain will soon be clear!