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

Let's break down the problem step by step and keep track of the cash flows and time period.

First, determine the six‑month return. The investor buys at 13.45, receives a dividend of 0.25 after 6 months, and sells at 11.82 right after the dividend.

Six-month total proceeds = sale price + dividend = 11.82 + 0.25 = 12.07.

Six-month gain (or loss) = total proceeds − initial investment = 12.07 − 13.45 = −1.38.

Six-month return r6 = gain / initial investment = −1.38 / 13.45 ≈ −0.1025, i.e., −10.25% over 6 months.

Next, annualize this six‑month return. If we assume a compounding period of twice per year (semiannual compounding), the annualized return r annual satisfies (1 + r6)² = 1 + r annual.

Compute: (1 − 0.1025)² = (0.8975)² ≈ 0.8055.

Thus, 1 + r annual ≈ 0.8055, so r annual ≈ 0.8055 − 1 = −0.1945, i.e., −19.45%.

Rounding to one decimal place or to the nearest tenth of a percent, the annualized realized return is about −19.5%.

Regarding the answer provided: the computed value −19.5% aligns with the mathematical result of annualizing a −10.25% six‑month return using semiannual compounding. Since no alternative options are shown to compare, we focus on the calculation steps and the final figure being approximately −19.5%.

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? 单项选择题

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