Money Weighted Returns vs. Time Weighted Returns
What is the proper way to calculate investment returns? Unfortunately, the answer is somewhat complicated. The two most frequently used methodologies are the “money-weighted” and “time-weighted” methods. In addition, an approximation of the money-weighted method, known as the “Modified-Dietz” method, is also commonly used. These three methods can sometimes give very different results. The “correct” calculation method to use will depend on how you plan to use the results.
My objective in this post is to compare the three common return measures: the money-weighted return, the time-weighted return, and the Modified-Dietz return. I will provide examples of how these measures can differ and explain when each should be used.
Consider three investors, Larry, Moe, and Curly, who each contributed $1,000 at the end of each month in 2010 to an S&P500 index fund. Larry’s starting account value at the beginning of 2010 was $1,000, Moe’s was $10,000, and Curly’s was $100,000. The 2010 return of each investor, as calculated by each of the three methods, is shown here:
|2010 Returns||Starting Balance||Monthly Contribution||Ending Balance||Money Weighted Return||Time Weighted Return||Modified Dietz Return|
The first thing to notice is that the time-weighted return is the same for all three investors. This is because the time-weighted method weights each sub-period (in this case each month) equally, regardless of any cash flows in and out of the portfolio throughout the year. The time-weighted returns also match the total return (including dividends) reported for the S&P500 in 2010 (I haven’t assumed any fees or costs in this example). So, the time-weighted returns are a precise measure of how the underlying investments performed over the measurement period. The time-weighted measure is therefore the best method to use if the goal is measuring the performance of the underlying investments without regard to the timing and amount of any cash flows during the investment period.
Another observation we can get from the table is that the three methods give very similar results for Curly, but the answers vary more widely for Larry. This is because the money-weighted and Modified-Dietz methods weight the sub-periods based on the amount of cash invested. Since Curly’s contributions were relatively small when compared with his starting balance, his contributions throughout the year had less influence on the relative weightings of the sub-periods. However, Larry’s contributions throughout the year were large relative to his starting balance, so later months of the year were much more heavily weighted than the early months in the money-weighted and Modified-Dietz calculations. If there were no contributions or withdrawals throughout the year, then the three methods would give identical results.
The variation between the methods will also depend upon how uniform the monthly returns are throughout the year. For example, in 2009, the year started with large losses and finished with large gains, so a pattern of investment like Larry’s, whose starting balance was small relative to his monthly contributions, would have benefited from this return pattern. This can be seen clearly if we apply the same investment scenario to 2009.
|2009 Returns||Starting Balance||Monthly Contribution||Ending Balance||Money-Weighted Return||Time-Weighted Return||Modified-Dietz Return|
In 2008, the effect is reversed. The large losses in 2008 came at the end of the year, and these months were weighted more heavily in the money-weighted and Modified-Dietz returns. Again, the effect shows up most strongly in Larry’s portfolio since contributions were large relative to the starting amount.
|2008 Returns||Starting Balance||Monthly Contributions||Ending Balance||Money Weighted Returns||Time Weighted Returns||Modified Dietz Returns|
Finally, to show a year where returns were more uniform throughout the year, I’ve run this analysis for 2006. Even for 2006 we can see some meaningful variation between the methods, but it is less extreme than in some of the later years. If returns were perfectly uniform then the methods would match closely.
|2007 Returns||Starting Balance||Monthly Contribution||Ending Balance||Money Weighted Returns||Time Weighted Returns||Modified Dietz Return|
The time-weighted return is the right method to use if you are comparing your underlying investments to a fund, index, or manager whose returns are reported on a time-weighted basis. The time weighted return considers only the performance of the underlying investments and is not influenced by the timing of cash flows in and out of the portfolio. However, one drawback of the time-weighted method is that it requires a valuation of the entire portfolio at the time of each cash flow, and not all investors keep these detailed records.
The money-weighted return is the right method to use if you do care about the measuring the effect of cash flows in and out of the portfolio during the investment period. Unlike the time-weighted return, the money-weighted return calculation does not require a portfolio valuation at the time of each cash flow, so the record keeping required to calculate this return is less than for the time-weighted return. If your contributions or withdrawals are relatively small during the period being measured, then the easier to calculate money-weighted measures may provide a reasonable approximation of the time-weighted return.
The Modified-Dietz method is good approximation of the money-weighted method. If you are calculating returns by hand, the Modified-Dietz return is much easier to calculate than the money-weighted return, but spreadsheets such as Excel and Google Docs Spreadsheet provide easy to use functions for calculating money-weighted returns. There are many websites which claim that the Modified-Dietz method provides a good approximation of the time-weighted return, but, as can be seen in the tables above, this is frequently not the case. If you use the Modified-Dietz method, the returns should be interpreted as money-weighted returns.
Additional details on calculating each of these returns, and a link to the spreadsheet used to generate the tables above can be found here.