Understanding TWR on Investment Assets
I will start in the same place I did with Internal Rate of
Return; the dictionary definition. I will then dive into what that means for
the rest of us.
“Time Weighted Return - Portfolio accounting method that measures investment performance (income and price changes) as a percentage of capital “at work,” effectively eliminating the effects of additions and withdrawals of capital and their timing that distort Dollar-Weighted return accounting.”
Barrons Dictionary of Finance and Ivestment Terms
The capital at work is your investment, including any reinvesting dividends, capital gains or interest. The latter are all considered investments because you have the option of taking them out of the fund but sometimes choose to have them reinvest. Reinvesting is just a convenient way of putting money in the fund; rather than having a check sent to you that you cash and then sending your check back into the fund it’s all taken care of for you.
The next term we see is “effectively eliminating”. A true TWR is does not effectively eliminate the effect of cash flows, it completely eliminates them. I will give a little more detail later on the use of the term effective.
What we are trying to accomplish with TWR is removing the biggest negative of the IRR; cash flow sensitivity. When you send money into your fund or take it out of your fund that’s not a decision under the control of the manager. It’s not fair to reward or punish a manager for cash flows that the manager has no control over.
In order to compare the performance of two or more manager’s we need to remove the effects of everything that is not under the manger’s control. Any cash flows to or from the investor, any fees that may have been charged by a third party to select and monitor the manager, or any fees the custodian may charge to house the account. None of these are the responsibility of the manager. However, some of these fees should be taken into account when measuring the performance of a third party firm or financial advisor.
Now to the meat of this, how do we calculate a time weighted return? From a formula perspective, the TWR is much easier than the IRR to calculate.
R = EMV / BMV
R = Return
EMV = Ending Market Value
BMV = Beginning Market Value
The astute among you will immediately note that this does not take into account cash flows. You would be correct; you are missing one big piece of information here. You have to do this daily or on the days when cash flows occur. I will walk through the simple example I did in the IRR walkthrough.
| 01/01/06 | Deposit | $12,000 |
| 06/30/06 | Withdraw | 4,000 |
| 06/30/06 | Ending Value | 9,000 |
To complete this, we have to add another piece of information. That is the Value on 6/29/06. Since this is all made up, let’s just say it’s worth $12,997.
| 01/01/06 | Deposit | $12,000 |
| 06/30/06 | Current Value | 12,997 |
| 06/30/06 | Withdraw | 4,000 |
| 06/30/06 | Ending Value | 9,000 |
First we do the first sub-period:
R = 12,997 / 12,000 = 1.083083
Then we do the second sub-period:
R = 9000 / (12,997 - 4000) = 9000 / 8,997 = 1.000333
Now that we have the two sub-period returns, we need to geometrically link them. This is done very simply by multiplying them.
1.083083 * 1.000333 = 1.083443
To get the return as a percentage you simply subtract 1. Your return for the six month period is 8.3%. You can convert this to annual return by either converting it first to a daily return then converting to an annual return using 360 or actual days. The other option of course is to simply assume that six months is half the year and use only two periods.
Using the daily method:
1.083443 ^ (1/360) = 1.000445 – Convert the six month return to a daily return
1.000445 ^ 360 = 1.173849 – Convert the daily return to an annual return
Subtract 1 to get the percentage and your annualized return is 17.4%
Using the two period return:
1.083443 ^ 2 = 1.173849 - There are two periods so we raise it to the second power
Converting it to a percentage is the same as the previous example above.
How did this remove the effect of the cash flow? Well, we did one return before the cash flow and one return after the cash flow. We completely ignored the cash flow; actually we did not ignore it, we removed it from the equation, its not sticking in the middle of it like it was for the IRR.
You may have noticed that I snuck a couple of new terms in on you. One was sub-period and the other was geometric linking. A sub-period is the time between cash flows or valuations. AIMR recommends that you revalue at least monthly. So if nothing happens (no cash flows etc…) you end up linking a bunch of monthly returns. Geometric linking is just a technical way of saying multiply the results.
This whole thing begs the question, if the TWR is superior to the IRR then why don’t we only use the TWR. As you might imagine, this is a complex question to answer.
Sometimes the financial advisor does not know the difference between TWR and IRR; in my experience this is very rare. An advisor may not know all the subtleties of the TWR but they understand the difference between Time Weighted and Dollar Weighted returns.
More often, it’s a much more practical limitation. It is difficult in terms of computing power to continually revalue a portfolio or its individual positions. It requires very clean data which is difficult to come by.
This means that the advisor or more likely the assistant must go through and mark or ensure that every cash flow was marked correctly as impacting the return. If the advisor has to have an assistant go through all the data then that’s a business expense, these expenses are covered by fees from clients – that’s you. So in order to cover expenses advisors would have to raise fees.
There are some ways to help mitigate this, using approximation methods such as Modified Dietz or the Modified BAI approximation methods (more on approximation methods another time). But they just help mitigate the problem, they do not solve it. Remember the term “effectively eliminating”? This is where that term comes from. These alternate methods are ways to sort of skip some of the data so the smaller cash flows may not be taken into account.
Also, there are times when financial advisors do control cash flow’s and you may want to know the impact of that decision on your performance. There are several strategies like Dollar Cost Averaging that have this impact on your portfolio and its performance.
Now, bear with me while I step up on my investment management software political soapbox for a minute. I think that the IRR for use as a means of measuring investment performance for individual investors should stop. I personally feel that the need to directly compare two or more managers or financial planners is much more critical. AIMR by the way agrees (okay, I guess I agree with AIMR)
Strategies like Dollar Cost Averaging (DCA) are risk mitigation strategies so the return is not the main goal, its risk mitigation. If you want to assess the risk of a portfolio you don’t look at the return directly, you look at the return as it relates to risk.
Call your attention to who’s performance is being measured, by using an IRR on a position that you are using a DCA strategy on, you are rewarding or penalizing the fund manager. This manager does not have control of the money, its your financial advisor that has control. Using an IRR pushes the impact to the wrong return number.
You want to push that impact up to the return number that aggregates all fund selection and strategies to your financial planner. The impact these decisions have on the performance within a portfolio will show
because money is sitting in cash earning a different (it
could be lower or higher) return than the money invested in an
individual funds.
You have to use the right measure to determine if your planner is earning their fee, it could be performance, relative performance (compared to an index or goal) or risk. It is your responsibility to use the right measures and the planners responsibility to provide the right data.
Lastly, I kind of glossed over data quality and its impact on selection of a performance measurement method. I think it is the responsibility of the data providing institution (the custodian) to provide clean usable consistent data and the responsibility of software vendors to create methods to calculate performance in an accurate and timely manner.
The biggest mess in this industry is the data; the custodians all provide different data in different proprietary formats and that makes it nearly impossible for the software vendors to accomplish their job. Most custodians do not provide sufficent data to advisors to calculate performance accuately. They provide sufficient data to do the accounting most of the time, but the data for performance and tax calculations is woefully inadequate.
Okay, I’ll step of my soap box and stop ranting. This ended up being much longer than I anticipated. I do hope this was helpful and that you understand TWR more than you did when you arrived here.
My next article in this area will be on risk measurement and understanding how that should impact your investment decisions.