Personal Rates of Return: Money Weighted vs. Time Weighted

There was a good question in my last retirement portfolio update about how my personal rate of return was 41% YTD, which was actually higher than any individual mutual fund in my portfolio*. The reason for this is mainly due to terminology, which can be especially confusing since the definitions seem to have shifted with time.

The two primary types are money-weighted and time-weighted returns, listed below with commonly associated names. Both have been called “personal rates of return” in the past.

Time-Weighted Returns Money-Weighted Returns
Reported returns
Portfolio returns
Investment returns
Geometric mean return
Dollar-weighted returns
Internal Rate of Return (IRR)

Time-Weighted Return Details
This methodology does not account for any cash inflows or outflows. In a way, finding your return using this method assumes that you don’t make any transactions at all. For a year-to-date calculation, it’s the same as asking how $100 invested on January 1st would end up today.

My favorite term for this method is Investment Return, because it essentially tracks the performance of your investments, and nothing else. If you have 30% US Stocks, 30% International Stocks, 30% Bonds, and 10% Orange Juice Futures, such a set of investments will have a unique performance from January 1st until today. Along the same lines, this time-weighted performance is what you get when looking up the total returns of a specific mutual fund (example). This also makes it easy to compare to a benchmark, such as the S&P 500 Index.

Money-Weighted Return Details
This methodology does account the size and timing of any cash inflows or outflows into your portfolio. Here’s an example of the difference. In your brokerage statements, look for any reference to accounting for “deposits and withdrawals”. Below is a chart of the S&P 500 index for all of 2009. Let’s say you started with $10,000 invested in the S&P 500 on January 1st. Then in early April before the tax deadline, you hurry and purchase $5,000 more worth.

As you might imagine, your $5,000 inflow was some good timing, and the performance of that money is a lot better (+25%) than the performance of your $10,000 from January 1st (+17%). If you managed to get your money in around March 9th, the return of that money year-to-date would be over 50%.

I prefer to call this methodology the Personal Rate of Return because it is truly personal. It is unlikely that any people have the exact same transaction amounts and dates as you. However, while this number may seem more accurate, it’s harder to compare against a benchmark and use for future investment decisions. As seen above, luck in the timing of your investments can swing the numbers either way.

I have an older post on how to calculate this dollar-weighted rate of return, but the Zohosheets aren’t displaying ideally right now. You can click on “Full Screen View” or try this page instead if you have Excel and the XIRR function installed.

What method do major investment firms use?
When Fidelity first started including “personal rate of return” in people’s 401(k) statements, it was a time-weighted rate of return. According to this 2000 LA Times article, Fidelity thought it was more appropriate to allow comparisons to published mutual fund numbers. At that same time, a spokesperson from Vanguard thought investors would be too confused either way, so they published nothing:

“We have several reservations about such reporting,” says Vanguard Group spokesman John Woerth. “Among them: Personal returns and fund returns are likely to differ, and perhaps substantially, which could confuse–even mislead–investors.”

How about today? When I checked my statements, both Fidelity and Vanguard use the money-weighted method for their “personal rate of return”. Our other 401(k) provider did as well, so it seems like things are shifting. I guess Vanguard thinks we’re smart enough to see the number now. ;) In the end, as long as you understand the differences, I think both stats can be useful.

* This is mostly true, but actually my small allocation to an Emerging Markets fund (VEIEX) is up 60% YTD.

Comments

  1. I think you are oversimplifying time weighted return by saying it assumes no transactions at all. Actually time weighted return factors in the amount of time the specific amount of money was left to grow. For example, in your above example, you first calculate the holding period return of the first 10k for the first 3.5 months, then you calculate the holding period return for your next period (with whatever left of 10K+5k). Then you take the geometric mean of the returns. So as you can see, time weighted return does take into account the new money coming in (and out).
    Actually, if you are a money manager (mutual fund manager), time weighted return is the best one to use because you do not have control of inflows and outflows of cash. But individuals can control when to invest and when to take out money, so it’s ok to use money weighted return. I think time weighted return is a measure of manager’s performance.

  2. I think what you are saying is correct, but I think the following statement is also correct and is more of what I meant in regards to comparing the returns:

    If a mutual fund has a calculated (time-weighted) return of 20% for one year, an investor who had money in the fund for that entire year, would have realized that same 20% return. When there are no deposits or withdrawals, the time-weighted and money-weighted returns are the same.

  3. Thank you for the thorough follow-up post! :)

  4. Good article. I always thought that Personal Rate of Return always meant IRR.

  5. I’m still confused. I could be wrong, but I think the terms rate of return and return are different. You noted in the monthly update that your return year to date (YTD) was 41%. Then above you say that your “rate of return” YTD was 41%. I don’t think of them as the same thing. The return of the market since it’s bottom has been about 50%, but it has done that in about 1/2 year; I would consider that a the rate of return be closer to 100% (50% divided by 1/2 year). I’d just like to get a clear understanding what your 41% represents.

  6. If you used XIRR without any adjustment and you got 41%, that number is an annualized number. To make it comparable with a YTD time-weighted return, you would adjust for the numbers of days to date. The return would be (1 + 0.41) ^ (263 / 365) – 1 = 28%.

  7. Robin Smith says:

    My rate of return (Fidelity 401 acct, fidelity managed for about $200 a quarter year.) LAST year at end was 39%.

    So far this year it is 13.7 I lost $1500 of whatever gains I made last year, plu the costs associaled with the management fees.

    When I was managing the fund, not fidelity, the years before last, I was making +3.00 – +6% , so it’s not 39%, but it wasn’t negative either.

    Any advice? Sit it out, wait til year end to judge the Fid managing?
    thanks… the fund holds $45K in 401, and $5K in 457 account.

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