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What are Time-Weighted Returns and Money-Weighted Returns?Posted on November 23, 2018

Patti and I follow the CORE in Nest Egg Care (NEC). We Recalculate annually to see if our Safe Spending Amount (SSA) can increase by more than inflation. (I recommend you Recalculate at least every three years; see Part 3, NEC.) Patti and I use November 30 for your 12-month return rates for our calculation. As reference, here is our calculation sheet from last year; read more here.

Our Investment Portfolio is at Fidelity®. Fidelity posts return rates for each account a few days after the end of each month. The summary page shows two different definitions of return rates for an account: the 12-month rate for an account is a money-weighted return. The summary also shows the rate for the S&P 500® Index as a point of comparison, which they state is a time-weighted return. And Retirement Withdrawal Calculators use time-weighted market returns for their construction of sequences of future returns we may face.

Uh-oh. Now my brain is muddled. What’s the difference in the two? It’s much simpler for me to track changes in our portfolio by using published time-weighted returns for each of our holdings. If I do that will I be accurate in my calculations over time? The purpose of this post is to answer those questions.

My summary: Time-weighted and money-weighted returns are essentially identical for nest eggers who put their SSA into cash soon after their Recalculation date. It’s faster and easier to simply look up the returns for each of the four securities we own and multiply by our design percentages for each that we had at the start of the year. That means on December 1, I’ll look up the time-weighted 12-month returns for each holding in our portfolio as of November 30. Within two business days I’ll complete my transactions to get to our SSA into cash for the upcoming year and will also be in perfect balance for the next 12-month period.

What are Time-Weighted Returns? A time-weighted return is the rate an investment changes in a year assuming an amount was invested for the complete year. This calculation includes the effect of dividends reinvested but ignores the effect of investment inflows or outflows. You can think of it as the daily return rates compounded for the year.

When you look up the returns for mutual fund or ETF at Morningstar or other site, you are looking at time-weighted returns calculated in the same way (i.e., dividends reinvested). When you compare a fund’s returns to an index – the S&P 500® index is an example – you are getting an apples-to-apples comparison of performance.

What are Money-Weighted Returns? (These are sometimes called Dollar-Weighted Returns.) A money-weighted return includes the effect of the timing of investment inflows and outflows during a year. The calculated return rate for an account recognizes that the amount you invested changed during the year and that each new increment of investment changed at a different rate and different length of time than for the whole year. It’s your personal return rate – combining those changes – that you experienced. This return will generally will differ from the time-weighted return.

Here’s an example: in our example year, the time-weighted annual return is 0%. You start with \$1,000 and with no additions or withdrawals you wind up with \$1,000. Daily returns compounded to +10% return for the first six months; returns compounded to -11.1% for the last six months. The total of the compounded daily returns for the year was 0%: (1 + 10%) * (1 – 11.1%) -1.

Let’s assume you added \$200 at the six-month mark. For the first six months, your \$1,000 investment grew by 10% to \$1,100. You added \$200 for a total of \$1,300 for the start of the next six months, and then this total declined by -11.1% or by -\$144.30. You wound up the year with \$1,155.70. Relative to the \$1,200 total you invested throughout the year, you experienced a decline of \$144.30. Just dividing the two (\$144.30/\$1200) would tell us that we experienced about a -3.5% decline.

I won’t go into the math of how to calculate the annual money-weighted return rate for this example, but the detailed calculation of money-weighted return works out to a -4.0% decline. That’s your personal return rate for the year.

We nest eggers don’t have to be concerned about the difference in the two: use time-weighted returns; they’re quicker and easier to find. We don’t need to be concerned about differences in the two for three reasons. The first reason is that we are only a few days off in the timing of our withdrawal for our SSA for the upcoming year. Return rates aren’t going to depart by much. I will have the 12-month returns ending November 30 on the morning of December 1. Within the next two business days I’ve sold securities to get our SSA into cash for the upcoming year – Rebalancing as I sell. I’m in perfect balance for the start of the new 12-month year at the end of those two business days. (See spreadsheet under Resources above that helps with Rebalancing.)

The second reason is that we are withdrawing a small percentage of the total. The smaller the percentage we withdraw (or add) during the year, the smaller the difference between the two returns.

The third reason: over time tiny distortions in a year are going to average out to be almost no distortion over, say, five or ten years.

Conclusion: I saw that several returns displayed on my portfolio page at Fidelity used different kinds of returns: money-weighted returns and time-weighted returns. Those terms muddled my brain. It’s easier to me to look up published time-weighted returns for my holdings to find the total return for our portfolio. I conclude it’s just fine to use those return rates in my annual calculation of our upcoming Safe Spending Amount (SSA).

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