## Calculating Investment Returns

Jan 012011

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 ReturnsStarting BalanceMonthly ContributionEnding BalanceMoney Weighted ReturnTime Weighted ReturnModified Dietz Return
Larry\$1,000\$1,000\$14,668.0426.51%15.05%25.56%
Moe\$10,000\$1,000\$25,022.6819.69%15.05%19.47%
Curly\$100,000\$1,000\$128,569.0215.72%15.05%15.70%