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Question of the Week - Quantitative Methods
George purchases a share of stock for $35. At the beginning of the next year, he purchases another share of the same stock for $40. At the end of each of the two years, the stock pays a dividend of $1.5. At the end of the second year, George sells both the shares for $45 each. The time-weighted rate of return that George earns is
Question of the Week - Quantitative Methods 34 votes
18.5%
2 votes
0 ·
Comments
Anyone having the same problem?
Year 1: $40 + $1.5 / $35 = 18.57%
Year 2: $45 + $1.5 / $40 = 16.25%
Therefore total return = 1.1857 x 1.1625 = 1.3784
Annualised = 1.3784^0.5 = 17.4%
…of course the other way to roughly guesstimate it is to jump straight to the holding period return then annualising it…ie… [($45 + $3 dividends)/($35)]^0.5 = 17.11%… It's not very accurate but gives a fair idea of where the answer lays (i.e, the difference between this result and any of the 3 multiple-choice selections is: 0.91%, 0.29%, 1.39%)
Year 2: ($45 + $1.5) / $40 = 16.25%
Time-weighted return = (1.1857*1.1625)^.5 -1 = 17.4%