Question

Arthur buys $2,000 worth of stock. Six months later, the value of the stock has risen to $2,200, and Arthur buys another $1,000 worth of stock. After another eight months, Arthur's holdings are worth $2,700, and he sells off $800 of them. Ten months later, Arthur finds that his stock has a value of $2,100. Compute the annual time-weighted yield rate of the stock over the two-year period.

Answer 1

To compute the annual time-weighted yield rate of the stock over the two-year period, we need to calculate the rate of return for each period and then combine them.

Step-by-step explanation:

To compute the annual time-weighted yield rate of the stock over the two-year period, we need to calculate the rate of return for each period and then combine them.

First, let's calculate the rate of return for the first period:
Rate of return = (Ending value - Beginning value) / Beginning value = (2200 - 2000) / 2000 = 0.1 or 10%

Next, let's calculate the rate of return for the second period:
Rate of return = (Ending value - Beginning value) / Beginning value = (2700 - (2200+1000)) / (2200+1000) = 0.227 or 22.7%

Finally, let's calculate the overall annual time-weighted yield rate:
Annual time-weighted yield rate = (1 + Rate of return 1) * (1 + Rate of return 2) - 1 = (1 + 0.1) * (1 + 0.227) - 1 = 0.343 or 34.3%