Dollar-Weighted and Time-Weighted Returns for a Stock Portfolio
Summary
The example distinguishes dollar-weighted return from time-weighted return when an investor changes the number of shares held during a multi-year investment. For dollar-weighted return, it translates purchases and liquidation into dated cash flows and calculates their internal rate of return. The timing and size of each investment therefore affect the result.
For time-weighted return, the answer focuses on the stock’s per-share price performance, linking subperiod returns so that the investor’s additions and sale do not determine the measure. In the stated example, the answer assumes no dividends and uses the initial and final share prices to report an annualized result. That shortcut depends on the lack of distributions and other cash flows affecting share value; with dividends, returns would need to include them. The response also contains an apparent inconsistency in the share price used to value the sale, so its cash-flow arithmetic should be checked before reuse.
Key ideas
- Dollar-weighted return is the internal rate of return of dated portfolio cash flows.
- The size and timing of contributions and withdrawals affect dollar-weighted performance.
- Time-weighted return links subperiod investment returns to reduce the effect of external cash flows.
- Price-only time-weighted calculations assume there are no dividends or other distributions.
- Check transaction prices and cash-flow arithmetic before relying on the example’s reported result.
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Full text
# Dollar/time weighted rate of return of Stock Investment
# 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!
## Answer by Alex C (score 1)
https://quant.stackexchange.com/a/50119
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.