Suppose you bought a stock for $45 on January 1. Thirty days later, you received a dividend of $2.20, and you sold the stock for $44.30. Given this information and assuming 360 days in a year, the annualized return is ________.

Question

BlackTom AI · Accepted Answer

To evaluate the annualized return, first compute the holding period return (HPR) over the 30-day period. The HPR is (dividend + ending price - initial price) / initial price. Here, (2.20 + 44.30 - 45) / 45 = 1.50 / 45 = 0.03333, i.e., 3.333% over 30 days.

Option by option analysis:

59%: This would imply a much smaller holding period or a much larger gain. If you annualize 3.333% over 30 days by a factor of 12 (since 360 days/year ÷ 30 days), you get 3.333% × 12 ≈ 40%. A value as high as 59% would require a higher 30-day return or a shorter holding period, which is not the case here.

25%: If someone mistakenly used a simpler shortcut or misapplied the annualization factor, they might arrive at 25%. However, 3.333% over 30 days annualized over 360 days indeed yields 40%, not 25%, so this option miscalculates the scaling.

40%: This is the correctly computed annualized return. The 3.333% 30-day return scales by 360/30 = 12 periods per year, giving 0.03333 × 12 = 0.40, i.e., 40%.

12%: This would correspond to treating the 30-day period as exactly one month with a 12-month year but forgetting the compounding effect or miscounting the days. The calculation should multiply by 12, not by 1, so 3.333% × 12 = 40% rather than 12%.

9%: This option is too low and would result from underestimating or misapplying the annualization factor (for example, using a 9% result from a much smaller multiplier than 12). Properly scaling 3.333% over 30 days to a 360-day year cannot yield as low as 9%.

In summary, after computing the 30-day holding period return and correctly annualizing by multiplying by 12, the correct annualized return is 40%.

MSB-250-300-002 Topic 8 Quiz

Suppose you bought a stock for $45 on January 1. Thirty days later, you received a dividend of $2.20, and you sold the stock for $44.30. Given this information and assuming 360 days in a year, the annualized return is ________.

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