Question

Suppose you purchase 100 shares of coca cola stock at the beginning of year 1 and purchase another 100 shares at the end of year 1. you sell all 200 shares at the end of year 2. assume that the price of coca cola stock is $50 at the beginning of year 1, $55 at the end of year 1, and $65 at the end of year 2. assume no dividends were paid on coca cola stock. your dollar-weighted return on the stock will be ____ your time-weighted return on the stock.

Multiple Choice
a. higher than the same as
b. less than
c. exactly proportional to
d. More Information is necessary answer this question.

Answer 1

To calculate the dollar-weighted return and the time-weighted return of the investment, we consider the initial and final values, as well as the holding period. The dollar-weighted return in this case is higher than the time-weighted return.

Step-by-step explanation:

To calculate the dollar-weighted return and the time-weighted return, we need to find the investment's initial value, final value, and the holding period. Let's calculate them step by step:

1. Initial Investment: The initial value of the investment is 100 shares purchased at $50 per share, which equals $5,000.
2. Final Investment: The final value is 200 shares sold at $65 per share, which equals $13,000.
3. Holding Period: The holding period is 2 years.

To calculate the dollar-weighted return, we need to consider the timing and size of the cash flows. In this case, you made two investments, one at the beginning and one at the end of year 1. We can calculate the return using the formula:

Dollar-weighted return = (Final Value - Initial Value) / Initial Value

Substituting the values, the dollar-weighted return is (13000 - 5000) / 5000 = 1.6, or 160%.

Now, let's find the time-weighted return, which eliminates the impact of the timing and size of the investment. We can calculate the return for each period and then multiply them:

Return for Year 1: (55 - 50) / 50 = 0.1, or 10%

Return for Year 2: (65 - 55) / 55 = 0.1818, or 18.18%

Time-weighted return = (1 + 0.10) * (1 + 0.1818) - 1 = 0.2978, or 29.78%

Therefore, the dollar-weighted return of 160% is higher than the time-weighted return of 29.78%.