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I'm researching time-weighted rate of return calculations as a performance metric to use with individual stock security holdings. I've read multiple sources of information to include but not limited to:

Regarding the treatment of income such as dividends or interest, DailyVest provides the most details (emphasis added):

…where EMV is the market value of the portfolio at the end of the sub-period, before any cash flows in the period, but including accrued income for the period. BMV is the market value at the end of the previous sub-period (i.e., the beginning of the current sub-period), including any cash flows at the end of the previous sub-period and including accrued income up to the end of the previous period.

This paragraph is a bit confusing because it doesn't define accrued income (which I understand to mean it has not yet be received, so are they just emphasizing unrealized gains?), they seem to be counting it twice (both as part of ending market value (EMV) and beginning market value (BMV)), and their example doesn't include dividend income.

However, Wikipedia's article seems to specifically state they should not be included:

The time-weighted return is a measure of the historical performance of an investment portfolio which compensates for external flows. External flows are net movements of value that result from transfers of cash, securities, or other instruments into or out of the portfolio, with no simultaneous equal and opposite movement of value in the opposite direction, as in the case of a purchase or sale, and that are not income from the investments in the portfolio, such as interest, coupons, or dividends.

...however, in this case I believe, because they're probably talking about a managed portfolio or a fun, they are referring to internal transactions such as when the manager receives a dividend payout from one of the invested securities.

I also recall reading that, specifically, reinvested dividends should not be counted in a TWRR calculation because their effect is already included in the market value (i.e., the increased number of shares). But nothing I could find was clear about dividends paid out.

So, how should non-reinvested dividends paid by a single security be counted in a TWRR calculations covering just that security?

Option 1 Treat it as an external cash outflow. That was my first thought, and then later I saw someone on Reddit suggest a similar thing, although the example there was for a mutual fund.

Option 2 Treat it as income and include it in the ending market value for the sub period being calculated.

Other options? What is the correct way to handle them?

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A dividend that is not reinvested is more or less equivalent to selling off a portion of your holdings for cash, so you would treat it as a "sell" or "outflow" from your investment's perspective. It is not "income" since the value of the investment drops by an equivalent amount. In other words, having a stock that pays a 5% dividend is equivalent to selling off 5% of your holdings. You have 5% in cash and 95% in stock.

As an example, if you bought a stock at $100, it rose to $120, had a $5 dividend that was not reinvested, and subsequently dropped to $115, then rose to $130, your TWR would be:

R1 = 120/100 = 20%   before the dividend
R2 = 130/115 = 13%   after the dividend

TWRR = [(1.20)(1.13)]^(1/2) -1 =  16.4%
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  • “It is not ‘income’ since the value of the investment drops by an equivalent amount.” I believe this is the reason I am/was having a hard time getting to option 1. I get the theory, not sure of the reality because of the number of factors that drive a share price. I suppose it is related to enterprise value. In my re-reading of the Wiki link this morning, I see it agrees with your answer but it also says “[TWR] always matches the share price performance (including dividends, etc.).” This makes sense if reinvested, but not if taken out. Correct?
    – tim.rohrer
    Commented Aug 20, 2022 at 14:36
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    That's how I would do it. If you had a stock that was worth $100 and it paid a $5 dividend, but you did not reinvest it, you have two different periods, one before the dividend and one after the dividend. The stock should drop by $5 because money was only transferred, not created, so it doesn't increase your "wealth". If you reinvest the dividend then the dividend doesn't really matter because you have the same amount (value-wise) before and after the dividend.
    – D Stanley
    Commented Aug 20, 2022 at 23:00
  • @DStanley I think your last sentence in that comment should be added to the answer; it hits the nail on the head. In most simplistic fashion, comparing original price to current value, if you bought for $100 and sold for $120 after 5 years, any reinvested dividends along the way all form part of the final sale value. Given cost of $100 and ending sale price of $120, your net return is the same whether you got $0 in dividends or $300 in [reinvested] dividends. Likewise counting the value of dividends received along the way [but not reinvested] as additional 'sales value' nets to final return.
    – Grade 'Eh' Bacon
    Commented Jan 17, 2023 at 17:14

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