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Thursday, January 27, 2011

How to Calculate Time Weighted Return

Bowser in the Snow
DIY investors need to know how their investments are performing. Many don't. I know because I ask. And when I do, many times, I get a non-comprehending look back. Some of you know that I get on the soap box from time-to-time and rant and rail about knowing investment performance. Too many times I've seen people say their advisor is doing great because he or she made him x number of dollars in the last 3 months. It seems to be news to some people that making 6% when the market or benchmark makes 8% is actually not a good thing. I know it's percentages, and I know percentages are about the point where a goodly percentage (see can't get away from it!) of the population started to hate math; but it is important to deal with them  to assess performance.

Over decades, a small under-performance can subtract a lot  from a portfolio.

Thankfully,  the portfolio calculation is getting easier by the minute. The technology that does all the work is spreading. In fact, a recent post on Schwab's Performance Calculator described how easy it is to get performance for both portfolios and benchmarks at their site.

Still, as a member in good standing of the "although I can multiple 2 numbers using a calculator it is still worth knowing how to do without a calculator" fraternity, I think those investors not totally allergic to math should know how to calculate performance. Again, with today's technology this is easy.

To begin, pick out the accounts you need to do the calculation for. This is easy on most discount brokerage sites. For example, if you have 5 accounts (2 brokerage accounts, a Roth IRA, and 2 traditional IRAs) and you just want to track performance for the IRAs, you can set up a grouping for these 3 accounts and call it "IRAs" or even "My IRAs"(pretty clever naming, huh?). If you want, of course, you can do the calculation for all accounts.

If there are no additions or withdrawals to the accounts, all  we need to do is divide the ending portfolio value by the beginning value. For example, if the accounts totaled $1,000 and now are at $1,200, we've made 20%--we're doing great!

Actually not so fast - hold the smiley face. If the benchmark (passive portfolio we are comparing ourselves against that is typically made up of market indices) is up 30%, we actually haven't done that great.

But what about cash in and cash out? Maybe we deposited $200 into one of the IRAs! This is where the concept of time-weighted return (TWR) comes into play. The trick is to calculate return to the point before the deposit and then calculate return starting from the point after the deposit and multiply them. This is called linking. This approach measures how the investment performed and is independent of the cash flows.


Some Math

Let's look at a simple example:

Start with $1000 and assume it grows to $1150, at which point you put in $300 and it grows to $1725. What is your TWR?  Easy:
1150/1000 = 1.15
1725/1450 (we've added the 300 deposit to the 1150) = 1.19.
Multiply and get 1.3685 and the TWR is 36.85%.

To go one step further, suppose this was over a 2-year period. Then you may want to convert to an average annualized return. This is easy:  just take the .5 root of 1.3685 and get 1.169. Thus, on  an average annualized basis, you made 16.9%.

A little bit of thought reveals that some care needs to be taken when looking at TWR. Suppose you start with $1,000 and it increases to $1,200, at which point a deposit of $10,000 is made and at the end of the period the portfolio is $11,200. You made a 20% return on the smaller amount and a 0% return once the $10,000 was in the account. 

For my clients, I handle all of this very simply. I get daily valuations of portfolios. This actually only takes a few minutes a day. Then at the end of the month, I look at the history of the accounts (again only a few minutes); and if there are withdrawals or additions, I make the adjustments. If the client is with Schwab, of course, I don't have to worry about any of this.

18 comments:

  1. Nice article. I think the problem many people run into with calculating TWR is that the portfolio value is needed at the time of each cash flow in or out of the portfolio. This isn't always easy to figure out after the fact (for example when you sit down with your brokerage statement to calculate returns at the end of the year), so it is important to keep good records. I posted a similar article comparing time-weighted returns with other return calculation methods on my blog recently.

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  2. @Chad Good point. That's why I log in every day and record the value of the account. Then I can always go back later and look at "history" to see I need separate calculations over different time periods.
    I was reminded in reading your comment that investors have accounts at different brokers so they typically will need a further weighting to get broader performance numbers.
    Thanks for stopping by. I'm going to check out your blog.

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  3. This wasn't bad to calculate, but my head still hurts! You have a good point about how small differences in percent is not great in the long run. I think we'll have to get better about following this as well. I feel like you just smacked our hands too :)

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  4. @Shawn I think most people today don't have to do the calculation but still its good to know how . It is sort of "yield-to-maturity" which is difficult to calculate. You never have to do it but it is good to know where it comes from because that helps us understand the influences on yield.
    Thanks for stopping by.

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  5. How does the time weighted return (net) for a quarter correlate the predicted return for the fiscal year? For example, if my portfolio had a time-weighted net return of 2.76 percent for the first quarter, is that the likely overall net for the year? Many thanks for your help!

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  6. re: Anonymous There is a slight correlation because of momentum but overall your return very well could be negative for the year if the last 9 months are down more than 2.75%. To get the actual expected return you would need yto go back and find the average 9 month return over many 9 month periods.

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  7. Hi there,
    Would it not be for the TWR example sake to advise taking average over the years, instead of multiplying them and taking 0.5 root? It will get more complicated, when you try to do it for a several years? ;-) While every body can add them up and divide by the number of years in question.
    Just a thought

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  8. re: Financial Independence The type of question you are trying to answer is as follows: I started with $1,000 5 years ago and today I have $1,750. What average annualized compound return did I earn?
    To answer you divide the numbers and take the 1/5, i.e. .20 root - easy to do on the calculator. The answer is 11.84% (have to subtract 1 of course). As it turns out the return was achieved by different annual returns. One year +18%, next year -3.68% etc. You'll find taking the simple, rather that the geometric result will get you a number different than 11.84%.

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  9. i don't understand at all

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  10. Great post. That's why every transaction made, every money that comes and goes must be listed so you will have a reference to know if your investment is doing good or should you just move on to another career. Of course, this will take time so be sure you have the resources and exit know-how in any case you fail. Thanks for sharing.

    How to Retire Plan

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  11. So, I am not sure that the 'easy' formula works since it's not really time weighted. You can't just multiply two returns together to get a time-weighted return. You have to actually consider the time. In the example above, where you: "Start with $1000 and assume it grows to $1150, at which point you put in $300 and it grows to $1725" What if this happened over a one year period and you didn't deposit the $300 dollars in until the last day of the year? Your return is really 42.5% ($1,000 start, growing to $1,425, which is $1,725 less the $300 you dropped in at the last minute). If you lessen the extremes, and drop the $300 in on Dec 1, that 42.5% return becomes something less, but not the 36.85% you calculated above. Am I missing something?

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  12. You highlight a problem with TWR that bedevils investment managers. When starting accounts the money typically trickles in so for first 3 months you have $15,000 and then 6 months a rolled over 401(k) comes in for $1 million. TWR treats these cash flows the same. This is good in assessing one manager versus another manager but a 10% return on $1.0 million is clearly preferred to a 15% return on $15,000 - but both are treated the same.
    Here's another example that may help:
    Assume we are calculating the 6 month (non-annualized) TWR ending on 12/31/2009. The date range for this yield term would be 7/1/2009 through 12/31/2009, inclusive of gains on both the starting and ending dates. The following hypothetical details are used in this example:

    Market value at beginning of 7/1/09: $1,000



    Purchased additional $1,200 on 8/13/09

    Market value at end of 8/13/09 was $1,200 before the new purchase, market value was $2,400 after purchase



    Received a cash dividend on 9/30/09 for $50

    Market value at end of 9/30/09 was $2,500 (not counting the dividend)



    Market value at end of 12/31/09: $2,600



    No accrued interest.

    BMV1 = 1000; EMV1 = 1200; R1 = 20%

    BMV2 = 2400; EMV2 = 2550; R2 = 6.25%

    BMV3 = 2500; EMV3 = 2600; R3 = 4%



    and we then combine the sub-period returns together, to get the total period return:



    RTR = (1.2 x 1.0625 x 1.04) - 1 = 32.6%

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  13. I just came across this entry and I am so fascinated by the style you organize your blog post! Which methods do you mostly turn to in order to tell your readers that you provided a brand new post to your website?

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    Replies
    1. I really don't have a method. My readers just check back from time to time.

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  14. I am having a problem in the calculation of returns. I am trying to calculate return over a 16 year time horizon. I have the future value and the rate at which my assets will grow in individual years over the 16 years. I want to know that single rate which is the time weighted rate of return. I have managed to find that also but if i calculate the SIP amount based on that rate than there is a big difference. Please suggest.

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  15. I understand why cash contributions and withdrawals matter, but I don't see why a dividend paid, for example, has to be treated differently from an increase in market value of an equity, say, when looking at the account value at the end of a period.

    And what about advisor fees? Same argument -- at the end of the period, what's the difference between a loss in market value of $1000 and a fee of $1000 paid during that period?

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    Replies
    1. There is no difference between a dividend and an increase in market value. Everything that hits the bottom line is treated the same. What is the value of your account today? What is it before your next cash contribution from the outside? Divide the 2 and that's your return for the period. The next period start with the value of the account including the outside contribution (or withdrawl) and repeat. Time weighted return is a way of linking the returns.
      Please note that it isn't perfect as any investment manager will tell you. For example, if I start managing your accounts and I start with $10,000 and it is $20,000 at the end of the month when another account of yours which you rolled over finally comes in for $510,000 and the %530,000 30 days later is down to $515,000 you'll have a good time weighted return but your account will be down.
      For this reason investment managers sometimes delay the return calculation until most of the assets under management has come in.
      I hope this helps.

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    2. In terms of investment fees - you are right they are like a loss. If your return is 6.5% and you are paying 1% your bottom line is a return of 5.5%. It is why we stress fees so much. They make a huge difference over longer time periods!
      Taking it a step further you may want to to consider after tax returns adjusted for inflation. So take off a bit more;)

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