Question

Arthur buys $2,200.00 worth of stock. Six months later, the value of the stock has risen to $2,500.00 and Arthur buys another $1,000.00 worth of stock. After another eight months, Arthur’s holdings are worth $3,100.00 and he sells off $800.00 of them. Ten months later, Arthur finds that his stock has a value of $2,300.00.

Compute the annual dollar-weighted yield for Arthur over the two-year period.

Write your answer as a percentage, rounded to three decimal places.

Answer 1

In this question purchase of stock or investments are cash outflows and represented by using negative cash flows, On the other hand sale or value at end of year 2 are cash inflows and are represented by positive cash flows

For sake for finding the the Annual dollar weighted yield over two years, we will divide the period of two years into 12 sub periods, with each sub period equal to 2 months

We will following cash flows

Month	Cash flows
0	-2200
2	0
4	0
6	-1000
8	0
10	0
12	0
14	800
16	0
18	0
20	0
22	0
24	2300

Now we will find the two monthly return(dollar weighted return) or Two monthly IRR of above cash flow using IRR function in excel

Formula to be used in excel: =IRR(values)

where values are cash flows

Using IRR function in excel, we get Two monthly return or Two monthly IRR = Two monthly dollar weighted return = -0.324208%

Annual Dollar weighted yield = (1+ Two monthly dollar weighted return)⁶ - 1 = (1-0.324208%)⁶ - 1 = (0.9967579)⁶ - 1 = 0.980704 - 1 = -0.019296 = -1.9296%= -1.930% (rounded to three decimal places)

Hence Annual Dollar weighted yield for Arthur over two years = -1.930%