Tuesday, November 30, 2010 7 comments ++[ CLICK TO COMMENT ]++

Measuring returns: Time-weighted vs Dollar-weighted

Writing for The Globe & Mail, Preet Banerjee has a good column pointing out how different ways of measuring returns produces different results:

Time-weighted returns v dollar-weighted returns

Let's assume that a portfolio has three years of 20-per-cent annual returns, followed by three years of 0-per-cent annual returns. The time-weighted return is 10 per cent on average for those six years. But this is not accurate if you only invested $1 at the beginning, and then added $100,000 at the start of year four.

The end value of this portfolio after six years would be less than $100,002, because while the $1 grew at 20 per cent per year for three years, the $100,000 didn't grow at all.

The dollar-weighted return in this case would be virtually nothing. That's in stark contrast to the time-weighted average return of 10 per cent a year.

Time-weighted returns can help you figure out whether the investment was a good one in hindsight, but dollar-weighted returns will help you figure out how well you are actually deploying your money in those investments.
Although a subtle point, I think it is worth tracking both, the time-weighted return and the dollar-weighted return. Most amateur investors, at least based on my observation on the Internet, only track the dollar-weighted return. Typically, many do this using a spreadsheet and computing the IRR (internal rate of return), or by using some online tool.

I personally think it may be helpful to track both, especially if you are a concentrated investor since a few large positions can dictate your true return but doesn't indicate how good you are—your strikeout ratio. For example, my time-weighted return over the last 5 years or so, is around 3.95% per year, while the dollar-weighted return is around 0.8%. Neither of these returns are going to impress anyone but the dollar-weighted return may imply a far worse skill level than it seems. The gap between the two is very large because I saved a lot of money in the last few years and I have mostly been in cash (spectacular concentrated bet disasters, such as Ambac, also matter but less so than it seems). However, the success ratio, although not that impressive, isn't too bad. Of 27 investments I have made since I started investing, around 70% generated a positive return, with around 40% generating above a 10% cumulative return (not sure about annual return).

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7 Response to Measuring returns: Time-weighted vs Dollar-weighted

Jae Jun
December 3, 2010 at 9:37 AM

How do you calculate time weighted returns? The only way I know how is to use an online site but would prefer to do this via a spreadsheet.

Parker Bohn
December 3, 2010 at 12:27 PM

Just pretend like you are a hedge fund and I've invested a dollar with you.  The time-weighted return is what you would owe me on that dollar (ie adjusted for all other inflows and outflows).

The way I do it is by having a line for each month on a spreadsheet.  Since I make any contributions at the start of a month, it is very easy for me to calculate the percent change attributable to investment returns each month.

Also, when annualizing, be sure to calculate the geometric mean (ie CAGR), not the arithmetic mean.  An arithmetic mean would tell you that a 50% gain is equal to a 50% loss, which is obviously garbage.

Parker Bohn
December 3, 2010 at 12:47 PM

Ha!  I didn't even notice at first, but the article Sivaram quotes actually gets it wrong by using the arithmetic mean to annualize.  The actual annualized return on 3 years of 20% returns followed by 3 years of 0% returns is not 10% (as the article states), but rather 9.5%.

I assume the quoted writer was just trying to keep it simple, but sometimes I've noticed people stating the "average" return for their fund or the market in a technically truthful but purposefully misleading way.

Parker Bohn
December 3, 2010 at 12:56 PM

BTW, Sivaram, I tend to think time-weighted returns are a much better indication of skill than dollar-weighted returns.

In your case, you said "the gap between the two is very large because I saved a lot of money in the last few years", but I hardly think saving money should be counted as evidence of a lack of skill.

Sivaram Velauthapillai
December 4, 2010 at 3:23 PM

I don't know what's the cleanest way of doing it but, as Parker Bohn alludes to, one needs to track the periodic returns--monthly returns or yearly returns, or even the weekly if one wanted to--in some manner and then compound the returns. I use some software package, MS Money (discontinued), so I can't say how it would be done in spreadsheets exactly but what I would do is:

* Track the portfolio returns monthly (preferably) or annually at worst. The computation would be a simple dollar-weighted return for that period e.g. if your portfolio size was $100 and you made $10 that month, it would be 10% return for that month (the ideal time-weighted return will involve tracking returns on a daily basis but that's not worth it for amateur investors)

* Then you just compound the returns over the period you are looking at. For example, if you earned 10% in first month, 15% in next, -10% in 3rd, the time-weighted cumulative return would be 1.1*1.15*0.9, and you should take the 3rd root (since 3 periods here) to get at the per-month return. In this case, the time-weighted (3 period) cumulative return is 1.139 or 13.9% and the monthly return is 4.4% (3rd root of 13.9%). (If you are using a spreadsheet, I tend to use the count() function to figure out what the root should be.)

In the example above, the time weighted return (I was using 3 months but it could be whatever) is 4.4% per month. The actual dollar-weighted return can be something totally different since the dollar-weighted return depends on the amount of dollars (or the weight of dollars). If a lot of capital was invested in the 3rd month, the return would be very different.

Sivaram Velauthapillai
December 4, 2010 at 3:26 PM

Yep... should be 9.5%. Author mistakenly used simple compounding or he is rounding the numbers. The article is very casual--intended for general public, not hardcore amateur investors--and it's not clear if he is simplifying things or not. Whatever it is, the real number, as you point out, should be 9.5%, not 10%.

Sivaram Velauthapillai
December 4, 2010 at 3:28 PM

Agreed... time-weighted returns is more indicative of your decisions. Ultimately, the dollar-weighted returns are what matter, but as a newbie investor whose goal is to continuously improve, time-weighted says a lot more about your skill.

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