An investor bought a stock for $100 at Month 0.

Six months after the purchase (Month 6), the stock paid a dividend of $10 and the stock price at that time (just after dividend was paid) was $120.

By the end of the year (Month 12), the investor received a second dividend of $10 and decided to sell the stock for $98.

What is the investor's realized return for the year? Hint: as a first step, calculate the realized return for each 6-month subperiod.

Round your answer to a percentage with two decimal places and do not use the “%” sign, i.e. if the answer is 1.23% then write 1.23

Include a negative sign if your answer is negative.

Question

An investor bought a stock for $100 at Month 0.

Six months after the purchase (Month 6), the stock paid a dividend of $10 and the stock price at that time (just after dividend was paid) was $120.

By the end of the year (Month 12), the investor received a second dividend of $10 and decided to sell the stock for $98.

What is the investor's realized return for the year?  Hint:  as a first step, calculate the realized return for each 6-month subperiod.

Round your answer to a percentage with two decimal places and do not use the “%” sign, i.e. if the answer is 1.23% then write 1.23

Include a negative sign if your answer is negative.

BlackTom AI · Accepted Answer

The scenario describes an investor who buys a stock and receives two cash dividends during the year, with price changes between periods. We will break the problem into two 6-month subperiods and compute the holding period return (HPR) for each, then combine them to obtain the annual realized return.

First subperiod (Month 0 to Month 6): start with an investment of 100. At Month 6, the investor receives a dividend of 10 and the stock price is 120 (just after the dividend). The total value at the end of the subperiod, including the dividend received, is 120 + 10 = 130. Therefore the holding period return for this 6-month interval is (end value + dividends - initial investment) / initial investment = (130 - 100) / 100 = 30 / 100 = 0.30, i.e., 30%.

Second subperiod (Month 6 to Month 12): the starting value for this period is the 120 price from Month 6. At Month 12, the investor again receives a dividend of 10 and sells the stock for 98. The end value plus dividend is 98 + 10 = 108. The HPR for this subperiod is (end value plus dividend - starting value) / starting value = (108 - 120) / 120 = -12 / 120 = -0.10, i.e., -10%.

To aggregate the two subperiod returns into the annual realized return, use the compounding formula: (1 + HPR1) × (1 + HPR2) − 1. Substituting HPR1 = 0.30 and HPR2 = -0.10 gives: (1 + 0.30) × (1 - 0.10) − 1 = 1.30 × 0.90 − 1 = 1.17 − 1 = 0.17, which equals 17% when expressed as a percentage.

Note on rounding: the final result should be expressed as a percentage with two decimal places and without the percent sign, so 17% becomes 17.00. The steps above show how the two six-month periods contribute to the total annual return, accounting for both price changes and the two cash dividends received during the year.

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