An investor purchased a stock at the beginning of January for $13.45. At the end of June (6 months after the purchase), the stock paid a dividend of $0.25. Right after the dividend was paid, the investor sold the stock for $11.82.

What is the annualized realized return?

Question

An investor purchased a stock at the beginning of January for $13.45. At the end of June (6 months after the purchase), the stock paid a dividend of $0.25. Right after the dividend was paid, the investor sold the stock for $11.82.

What is the annualized realized return?

BlackTom AI · Accepted Answer

To tackle this problem, I will first identify the cash flows involved and the holding period.
The investor buys at 13.45 at the start of January. Over six months, a dividend of 0.25 is received at the end of June, and the stock is sold for 11.82 right after the dividend.
The six-month realized return is computed as: (selling price + dividend - purchase price) / purchase price.
Specifically: (11.82 + 0.25 - 13.45) / 13.45 = (12.07 - 13.45) / 13.45 = -1.38 / 13.45 ≈ -0.1025, i.e., -10.25% over six months.
To annualize a six-month return, one common method is to assume compounding over two equal six-month periods: (1 + R6)^2 - 1, where R6 is the six-month return.
Plugging in R6 = -0.1025: (1 - 0.1025)^2 - 1 = (0.8975)^2 - 1 ≈ 0.8055 - 1 = -0.1945, or about -19.45% annualized.
Now let’s evaluate each option:
Option A: -19.5%. This matches the calculated annualized return of approximately -19.45%, which is consistent with the six-month loss of about 10.25% being annualized with compounding.
Option B: 10.3%. This would imply a gain overall, which contradicts the actual cash flows where the sale price plus dividend is less than the purchase price.
Option C: -10.3%. This resembles the six-month return but is not annualized; the problem asks for annualized return, so this value omits the compounding effect over a full year.
Option D: 14.0%. A positive return contradicts the realized cash flows; there was a loss on the investment, not gain.
Option E: 19.5%. This is the magnitude of the incorrect positive interpretation and also contradicts the actual loss observed over the holding period.
In summary, the only option that aligns with both the six-month cash flows and the annualized compounding calculation is the negative annualized return, which reflects the loss incurred and the effect of compounding when annualizing a six-month return.

An investor purchased a stock at the beginning of January for $13.45. At the end of June (6 months after the purchase), the stock paid a dividend of $0.25. Right after the dividend was paid, the investor sold the stock for $11.82. What is the annualized realized return?

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