Money Weighted Returns vs. Time Weighted Returns<\/em><\/p>\n

What is the proper way to calculate investment returns?\u00a0 Unfortunately, the answer is somewhat complicated.\u00a0 The two most frequently used\u00a0\u00a0methodologies\u00a0are the \u201cmoney-weighted\u201d and \u201ctime-weighted\u201d methods.\u00a0 In addition, an approximation of the money-weighted method, known as the \u201cModified-Dietz\u201d method, is also commonly used.\u00a0 These three methods can sometimes give very different results.\u00a0 The \u201ccorrect\u201d calculation method to use will depend on how you plan to use the results.\u00a0<\/p>\n

My objective in this post is to\u00a0compare the three common return measures: the money-weighted return, the time-weighted return, and the Modified-Dietz return.\u00a0 I will provide examples of how these measures can differ and explain when each should be used.<\/p>\n

Consider three investors, Larry, Moe, and Curly, who each contributed $1,000\u00a0at the end of each\u00a0month in 2010 to an S&P500 index fund.\u00a0 Larry\u2019s starting account value at the beginning of 2010 was $1,000, Moe\u2019s was $10,000, and Curly\u2019s was $100,000.\u00a0 The 2010 return of each investor, as calculated by each of the three methods, is shown here:<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t

2010 Returns<\/th>	Starting Balance<\/th>	Monthly Contribution<\/th>	Ending Balance<\/th>	Money Weighted Return<\/th>	Time Weighted Return<\/th>	Modified Dietz Return<\/th>\n\t<\/tr>\n<\/thead>\n
Larry<\/td>	$1,000<\/td>	$1,000<\/td>	$14,668.04<\/td>	26.51%<\/td>	15.05%<\/td>	25.56%<\/td>\n\t<\/tr>\n\t
Moe<\/td>	$10,000<\/td>	$1,000<\/td>	$25,022.68<\/td>	19.69%<\/td>	15.05%<\/td>	19.47%<\/td>\n\t<\/tr>\n\t
Curly<\/td>	$100,000<\/td>	$1,000<\/td>	$128,569.02<\/td>	15.72%<\/td>	15.05%<\/td>	15.70%<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n The first thing to notice is\u00a0that the time-weighted return is the same for all three investors.\u00a0 This is because the time-weighted\u00a0method weights each sub-period (in this case each month)\u00a0equally, regardless of any cash flows in and out of the portfolio throughout the year.\u00a0 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).\u00a0 So, the time-weighted returns are a\u00a0precise\u00a0measure of how the underlying investments performed over the measurement period.\u00a0 The time-weighted measure is therefore\u00a0the 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\u00a0during the investment period.\u00a0<\/p>\n Another observation we can get from the table\u00a0is\u00a0that the three methods give very similar results for Curly, but the answers vary more widely for Larry.\u00a0 This is because the money-weighted and Modified-Dietz methods weight the sub-periods based on the amount of cash invested.\u00a0 Since Curly\u2019s contributions were relatively small when compared with his starting balance,\u00a0his contributions throughout the year had less influence on the relative weightings of the sub-periods.\u00a0 However, Larry\u2019s 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.\u00a0 If there were no contributions or withdrawals throughout the year, then the three methods would give identical results.<\/p>\n The variation between the methods will\u00a0also depend upon how uniform the monthly returns\u00a0are throughout the year.\u00a0 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.\u00a0 This can be seen clearly if we apply the\u00a0same\u00a0investment\u00a0scenario\u00a0to 2009.\u00a0<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t 2009 Returns<\/th> Starting Balance<\/th> Monthly Contribution<\/th> Ending Balance<\/th> Money-Weighted Return<\/th> Time-Weighted Return<\/th> Modified-Dietz Return<\/th>\n\t<\/tr>\n<\/thead>\n Larry<\/td> $1,000<\/td> $1,000<\/td> $15,762.37<\/td> 44.85%<\/td> 26.45%<\/td> 42.33%<\/td>\n\t<\/tr>\n\t Moe<\/td> $10,000<\/td> $1,000<\/td> $27,142.63<\/td> 33.75%<\/td> 26.45%<\/td> 33.12%<\/td>\n\t<\/tr>\n\t Curly<\/td> $100,000<\/td> $1,000<\/td> $140,945.30<\/td> 27.49%<\/td> 26.45%<\/td> 27.43%<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n In 2008, the effect is reversed.\u00a0 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.\u00a0 Again, the effect shows up most strongly in Larry’s portfolio since contributions were large relative to the starting amount.<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t 2008 Returns<\/th> Starting Balance<\/th> Monthly Contributions<\/th> Ending Balance<\/th> Money Weighted Returns<\/th> Time Weighted Returns<\/th> Modified Dietz Returns<\/th>\n\t<\/tr>\n<\/thead>\n Larry<\/td> $1000<\/td> $1,000<\/td> $9,884.03<\/td> -43.91%<\/td> -36.99%<\/td> -47.75%<\/td>\n\t<\/tr>\n\t Moe<\/td> $10,000<\/td> $1,000<\/td> $15,554.50<\/td> -40.20%<\/td> -36.99%<\/td> -41.51%<\/td>\n\t<\/tr>\n\t Curly<\/td> $100,000<\/td> $1,000<\/td> $72,259.25<\/td> -37.49%<\/td> -36.99%<\/td> -37.66%<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n Finally, to show a year where returns were more uniform throughout the year, I’ve run this analysis for 2006.\u00a0 Even for 2006 we can see some meaningful variation between the methods, but it is less extreme than in some of the later years.\u00a0 If returns were perfectly uniform then the methods would match closely.<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t 2007 Returns<\/th> Starting Balance<\/th> Monthly Contribution<\/th> Ending Balance<\/th> Money Weighted Returns<\/th> Time Weighted Returns<\/th> Modified Dietz Return<\/th>\n\t<\/tr>\n<\/thead>\n Larry<\/td> $1,000<\/td> $1,000<\/td> $13,094.99<\/td> 1.46%<\/td> 5.50%<\/td> 1.46%<\/td>\n\t<\/tr>\n\t Moe<\/td> $10,000<\/td> $1,000<\/td> $22,589.70<\/td> 3.81%<\/td> 5.50%<\/td> 3.80%<\/td>\n\t<\/tr>\n\t Curly<\/td> $100,000<\/td> $1,000<\/td> $117,536.81<\/td> 5.25%<\/td> 5.50%<\/td> 5.25%<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n Conclusions<\/strong><\/p>\n 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.\u00a0 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.\u00a0 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.\u00a0<\/p>\n 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.\u00a0\u00a0 Unlike the time-weighted return, the money-weighted return calculation\u00a0does 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.\u00a0 If\u00a0your contributions or withdrawals\u00a0are 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.<\/p>\n The Modified-Dietz method is\u00a0good approximation of\u00a0 the money-weighted method.\u00a0 If you are calculating returns by hand, the Modified-Dietz\u00a0return 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.\u00a0\u00a0 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,\u00a0this is frequently not the case.\u00a0 If you use the Modified-Dietz method, the returns should be interpreted as money-weighted <\/em>returns.<\/p>\n Calculation Details<\/strong><\/p>\n Additional details on calculating each of these returns, and a link to the spreadsheet used to generate the tables above can be found here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":" Money Weighted Returns vs. Time Weighted Returns What is the proper way to calculate investment returns?\u00a0 Unfortunately, the answer is somewhat complicated.\u00a0 The two most frequently used\u00a0\u00a0methodologies\u00a0are the \u201cmoney-weighted\u201d and \u201ctime-weighted\u201d methods.\u00a0 In addition, an approximation of the money-weighted method, known as the \u201cModified-Dietz\u201d method, is also commonly used.\u00a0 These three methods can sometimes give 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