The information set forth below was written by Financial Computer Support, Inc., vendors for DbCAMS, the asset management software system used by Financial Planning Associates, Inc. It is reproduced here by permission.
Time Weighted Rate of Return Key Concepts and Calculations
A Time Weighted Rate of Return (TWR) is a very well defined tool used to measure an asset or money manager’s performance. It is strictly time weighted whereas the IRR is both time and dollar weighted. Normally, the TWR is compared to the performance of a "benchmark" such as the S&P 500 Stock Index. This way a person can tell whether the manager is out-performing or under-performing the benchmark. The benchmark to which the manager’s performance is being compared should be a "fair representation" of the manager’s investment strategy.
When to Use the TWR
The TWR report is a tool that can be used to measure an advisor's performance. It considers the time value of money and the amount of time the investor's money has been under management (thus the term "Time Weighted"). This report should be compared against TWR rates for other advisors or to an industry index. When you want to show the client the performance of their own individual assets or groups of assets, use the Internal Rate of Return. The IRR is the best rate of return to use if a client wants to find out how his historical return compares to his desired or target rate of return.
What is the difference between the IRR and the TWR numbers?
The TWR is time weighted only, whereas the IRR is both dollar and time weighted. As an example of the difference, consider the following example. A client gives an investment manager $100,000 to invest for him for one year. At the end of the year the client’s account is worth $105,000. Assuming the manager invested the money at the beginning of the year and just let it ride for the entire year, both the IRR and the TWR for the year would be 5.00%.
Now, assume the client gives the manager an additional $95,000 dollars at the very end of year one. This gives the investment manager $200,00 to invest for year two. Again the manager allocates and invests the full $200,000 at the beginning of the year and lets it ride for the second year. At the end of the second year, the account is worth $220,000. Both the IRR and TWR for year two would be 10.00%.
What is the annualized TWR and IRR for the two year period? The TWR is (1.05 x 1.10) ^ (1/2)=(1.1550) ^ (1/2) =1.0747 or (1.0747-1)100=7.47%. The IRR is approximately {[(220,000-195,000)/147,500]+1} ^ (1/2)=[(25,000/147,500)+1] ^ (1/2)=1.1695 ^ (1/2) = 1.0814 or (1.0814 -1)100=8.14%. This is a first order approximation of the IRR and is used for illustrative purposes only. The actual calculated IRR is 8.24%.
The annualized IRR for the two year period is higher then the TWR because the investment manager had twice as much money to invest in year two when he made 10%, therefore the year two return is weighted twice as heavily. Remember, the IRR is time and dollar weighted, whereas the TWR is time weighted only.
How dbCAMS+ Calculates the TWR
dbCAMS+ uses the daily valuation method of calculating the TWR. This is one of the calculation methods suggested by the AIMR. This method requires that the date range for the TWR be broken into sub-periods. There can be no cash flow transactions within a sub-period and no sub-period can exceed a month in length. Cash flow points help define the number of sub-periods into which the TWR date range must be divided. A growth rate is calculated for each sub-period and then multiplied together to obtain a cumulative growth rate for the entire period. This is then converted to a percentage rate of return.
The first sub-period runs from the begin date to the first cash flow point, the end of the month, or the end of the date range whichever comes first. The second sub-period runs from this date to the next cash flow point, the end of the month, or the end of the date range whichever comes first. This process continues until the last sub-period is determined. The last sub-period must have the end of the day on the last date in the date range as its end point.
The beginning value of the first sub-period is calculated as the units at the end of the previous day times the close of business prices on the previous day. (Note: This value should be equal to the bottom line value of a Current Position Report. Assuming the CPR is run for the day before the begin date of the TWR date range and for the same set of assets.)
The end value for the first sub-period is calculated as the units at the beginning of the sub-period times the prices at the close of business on the sub-period’s end date. (Note: Both the beginning values and ending values should include any accrued income. Also, notice that by using this methodology only prices and accrued income can change during the sub-period. A growth rate for the sub-period is easily calculated as the sub-period ending value divided by the sub-period beginning value.
To calculate the beginning value for the next sub-period, the transaction amounts of any transactions occurring on that day are added to (subtracted from) the ending value of the first sub-period. The end value is again calculated using the units at the close of business on sub-period begin date times closing prices on the sub-period end date. Again, a growth rate is calculated for this sub-period. This process is repeated for each sub-period in the TWR date range.
Once the TWR growth rates have been calculated, the next step in calculating the TWR is to multiply each of these sub-period growth rates together. That is, the first sub-period’s growth rate is multiplied times the second sub-period’s growth rate. The result is multiplied times the third sub-period’s growth rate. This result is multiplied times the fourth and so on until all the sub-period’s growth rates have been multiplied (compounded) together. This is called geometric linking.
The final cumulative growth rate is converted to a percentage by subtracting one (this represents the original beginning value). The result is then multiplied by one hundred (this changes the number from a decimal to a percentage). The result is the TWR for the time period.
The most important thing to remember about this methodology is that no cash flow transactions take place between the beginning and end of each sub-period. This is accomplished by valuing the group of assets twice on the date of each cash flow. They’re valued once using that date’s prices but the beginning of the sub-period’s units and then again by adjusting this for the transactions that took place on that date. The last value is used as the beginning value for the next sub-period. By this "slight of hand," moneys can be moved from one asset to another or added or withdrawn by the clients without directly affecting (dollar weighting) the returns calculated. The only impact is through a change in the asset allocation and, therefore, the weighting of the individual asset’s returns from one sub-period to another. It's as if the total amount of money during the date range only changes from the generation of asset income and price changes. Using the TWR as a measure of the manager’s performance presumes that the addition or withdrawal of moneys under his control does not change the manager's stock selection, timing, and asset allocation strategy. This is what is meant when it is said that the TWR measures the manager’s performance not the performance of the group of assets.
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