Rates Of Return
Contents
There are 3 Rate of Return (ROR) calculations available in Advisors Assistant. These calculations can produce different results depending on the cash flows that take place during the measuring period.
A cash flow is simply money flowing in or out of an investment or an account.
Advisors Assistant will calculate ROR using Time Weighted, Dollar Weighted, or the simple Return On Investment (ROI) or Percentage Gain method.
Links To Formulas And Explanations
Before reading further, please click on the links below to get an overview of the three methods.
Return On Investment Explained
Real World Example Of Differences Among Methods
Here is an actual example of an actual asset. This entire section is based on the fact that it's only by looking at an example that these calculation differences can be understood. Performance Report 40010 shows all 3 returns on one report.
•Asset ABC Corp. has a price per share of $12,96 on December 31, 2007,
•At the end of 2007, the asset had a value of $300,631.
•There was a withdrawal on Sep 3, 2008 of 73,358 at 11.40 per share.
•At the end of 2008, ABC was $8.23 per share. (After the big market crash.)
•There were no other cash flows from dividends, etc.
Time Weighted Return
The time weighted rate of return is -36.5%. This is because time weighted ROR does not take into account the fact that the investor sold off some of the investment during the period and took some money off the table.
Time weighted just measures that ONE share of ABC went from $12.96 to $8.23 and that no dividends were paid. If there had been any dividend or interest distributions, they would increase the return.
Dollar Weighted Return
Dollar ROR takes into account that $73,358 was taken out when the share price was $11.40, so that amount of money did not lose as much. It was out of the asset as the asset went from $11.40 to $8.23 per share.
Therefore, you'd expect this method to produce less of a loss. The Dollar ROR is -32.3%.
Return On Investment (ROI)
ROI also takes into account that money was withdrawn, but it does not take into account when it was withdrawn. It just figures that the withdrawn funds were out of the account the entire period. This is a major weakness of the ROI Calculation.
With this in mind, if taking money out of the investment after 8 months produced less of a loss (Dollar Weighted Calculation) then assuming that the money was taken out on Day 1 should produce even a higher return, (less of a loss.)
As expected, the ROI calculation produces a return of -29.7%.
Example Of A Gain With No Rate Of Return
Here is a hypothetical example that also shows the difference among the three methods and also shows how you can have a 0% time weighted return and have a 50% gain.
•On December 31, 2007 Mr. Smith invests $10,000 in the ABC Ultimate Security at $10.00 per share.
•On March 31, 2008, the price falls to $7.50 per share, but Mr. Smith stays put.
•On June 30, 2008, the price is $5.00 per share and Mr. Smith invests another $10,000. He now owns 3,000 shares.
•On December 31, 2008 the price is back to $10.00 per share and Mr. Smith now has an investment with a market value of $30,000 on an investment of $20,000 and an unrealized gain of $10,000.
•No dividends or other distributions took place.
Return On Investment - 50%
The ROI or Percentage Gain is 50%. Mr. Smith has a $10,000 gain on a total investment of $20,000.
Dollar Weighted Return - 66.5%
However, for the first half of the year, Mr. Smith only had $10,000 invested, so his average investment was less than $20,000. Because Dollar Weighted ROR reflects the cash flow timing, his Dollar Weighted Return is about 66.5%.
Time Weighted Return - 0%
Since Time Weighted ROR negates the cash flows so that it can calculate how good the underlying investment performed during the measuring period, it ignores the fact that Mr. Smith increased his risk and doubled downed on the investment in June. It calculated the performance of 1 share of the investment purchased on December 31, 2007 and theoretically sold on December 31, 2008. That share went from $10 to $10 and the return is 0%. The quality of the investment was not as good and Mr. Smith may think. However, Mr. Smith, as an investor, did very well.
Rate Of Return Question
In the above example what do you think would happen if Mr. Smith sold $5,000 worth of ABC on March 31, 2008 at $7.50 per share?
The Time Weighted ROR does not care about cash flows. The Time ROR is still 0%
Dollar Weighted ROR will increase to about 73.9% because, on the average, there is less money invested, and you still have the large gain from the June investment which is only partially offset by the smaller percentage loss from the sale in March.
The ROI will go down to about 41.7% because it records the gain and the loss, but it all takes place at the beginning of the year. Instead of a $10,000 gain there is only an $8,333 gain on $20,000 invested.
You can reproduce these results by setting up a dummy investment in Advisors Assistant. Enter the prices for December, March, June, and December (Security Icon on the Investment Sidebar Menu) and enter the transactions for Dec 2007, June 2008 and then March 2008. It will take about 10 minutes total.
What's Being Measured With ROR?
Time Weighted ROR is really the measurement of how good the INVESTMENT performed during the measuring period. It tells you the quality of the investment because it does not take into account any buys and sells during the measuring period. It does take into account dividends, interest, and capital gains distributions from mutual funds. Dollar Cost Averaging has no effect on this calculation.
Dollar Weighted ROR could be considered a measurement of how well the INVESTOR performed during the measuring period. It takes into account when, and for how much, buys and sells took place. It tracks the average amount invested and the gains from dividends, interest, and price gains. Dollar Weighted ROR is a good measurement of the investor's gains. Dollar Cost Averaging does affect this calculation and the method does a good job of calculating the effect.
Return On Investment (ROI) is a simplistic approach to the rate of return. It is a calculation that can easily be reproduced with a calculator. It does not take into account when the flows in and out of the investment took place, so it's not as good a representation of what really happened. You often see ROI shown on brokerage web sites because it can be calculated without lots of database access. Dollar Cost Averaging affects this calculation, but it doesn't matter how many buys or when they take place. It just looks at the total money in and out.
Financial Services Institute (Formerly AIMR)
Time weighted calculations use the Daily Valuation Method (http://en.wikipedia.org/wiki/True_Time-Weighted_Rate_of_Return) as outlined by the Financial Services Institute Handbook. The calculations and methodology have been checked by an FSA accredited by the Financial Services Institute.
This does not guarantee an accurate calculation because if the prices are wrong or the data put into the calculation is not accurate, such as a missing transaction, the calculation will not be accurate.
There are other methods, such as the Modified Dietz (http://en.wikipedia.org/wiki/Modified_Dietz_Method). If flows and rates of return are large enough, this method can become significantly inaccurate.
See Also
Calculation Methodologies & Assumptions