# Dollar/time weighted rate of return of Stock Investment

Question: Stock initially trades for \$120 per share. An investor decides to purchase 1300 shares. After 5 years, the portfolio is worth \$245,570.00. At that time, the investor decides to purchase an additional 120 shares. At the end of year 10, the portfolio is now worth \$286,130.00. The investor then decides to sell 140 shares. At the end of year 15, the portfolio is now worth \$415,372.80. a) Find the dollar weighted rate of return b) Find the time weighted rate of return

Okay I have tried using Excel to solve this but each time my results have been wrong, how do I set this up? Any help is greatly appreciated!

To find the Dollar Weighted Return, also known as the IRR (Internal Rate of Return) we need to know the cash inflows and outflows for the portfolio. Let's see:

At time 0 there is an inflow of 156,000 (purchased 1300 shares at 120)

At time 5 the stock price is 188.90 (=245,570/1300) and there is an inflow of 22,668 (=120*188.90)

At time 10 we own 1420 shs, stock price is 201.50 (=286,130/1420), outflow is -28,210 (=-140*210.5)

At time 15 we own 1280 shs, price is 324.51, liquidating outflow is -415,372.80

Now we need to find the internal rate of return for the following cash flows

{156000,0,0,0,0,22668,0,0,0,0,-28210,0,0,0,0,-415372.80}

Using the Excel function =IRR() applied to this array of cash flows we find a DWR or IRR of 6.67% per year.

For the Time Weighted Return we do not take into account the amounts invested but only the return per share in each of the subperiods (we link them together). Assuming there are no dividends (none were mentioned in the question) we can just compute the price return on a single share. The price went from 120 to 324.51 in 15 years, so that is an annual TWR of -1+(324.51/120)^(1/15) = 6.857% per year.