sean.mcgrath wrote: ↑Wed Jun 17, 2020 1:59 pm
longinvest wrote: ↑Wed Jun 17, 2020 7:24 am
<There's unfortunately no clean way to isolate returns due to dividends from returns due to capital fluctuations over time. Both are inherently interlinked through total returns.
I can believe you are right, but at least as far as I can tell, it works.
Let's pick a hypothetical investment that gains 0.25% in value every month and also pays 0.50% of its monthly start value as a dividend at the end of the month.
If I buy $100 of this investment and keep it for one month, I'll get:
- a $0.25 capital gain as the investment will have grown to $100.25 in value by the end of the first month, and
- a $0.50 dividend at the end of the first month.
It's pretty obvious that this investment is making a 0.75%/month total return.
It would also seem pretty obvious that this investment has a 0.25%/month
capital return and a 0.50%/month
dividend return as
total return = capital return + dividend return.
But, if I continue holding the investment and look at the annual returns, this fundamental property breaks. Let's check this.
Let's continue with the second month. The now $100.25 investment will again make a 0.25% capital return (and also a 0.50% dividend return) and I'll get:
- a $0.250625 capital gain as the investment will have grown to $100.5000625 in value (and
- a $0.50125 dividend at the end of the second month).
And so on. At the end of the 12th month,
the capital (assuming dividends are withdrawn) will have grown by
(((1.0025)^12) - 1) = 3.041596%. Let's call this the
annual capital return of the investment.
Let's try again, but reinvest the dividend to calculate total returns. At the end of the first month, I had a total portfolio of $100.75 composed of $100.25 invested and $0.50 cash. If I buy $0.50 of the investment at the current price, my $100.75 portfolio will grow by 0.75%, that's $0.755625. At the end of the second month, my portfolio is worth $101.505625.
And so on. At the end of the 12th month, the portfolio will have grown by
(((1.0075)^12) - 1) = 9.380690%. That's the
annual total return of the investment.
So, if the total return is 9.380690% and the capital return is 3.041596%, it seems pretty obvious that the dividend return should be
(9.380690% - 3.041596%) = 6.339364%. Right?
Yet, we know the monthly capital and dividend returns. Let's check if all these monthly returns are coherent with the annual returns we calculated:
- Capital return: 0.25%/month ⇒ (((1 + 0.25%)^12) - 1) = 3.041596%/year. This matches.
- Dividend return: 0.50%/month ⇒ (((1 + 0.50%)^12) - 1) = 6.167781%/year. This doesn't match!
- Capital return: 0.75%/month ⇒ (((1 + 0.75%)^12) - 1) = 9.380690%/year. This matches.
So, we have just found that there are
two possible annual dividend returns: either 6.339364% or 6.167781%. They obviously
can't both be right. It follows that there doesn't exist such a thing as a coherently-defined
dividend return. QED.
What's the problem? The problem is compounding. When we annualize the monthly returns, we get an isolated annual capital return (3.041596%) and an isolated annual dividend return (6.167781%) as well as an annual total return (9.380690%). The sum of the isolated returns is
(3.041596% + 6.167781%) = 9.209377%. That's less than the annual total return. The difference
(9.380690% - 9.209377%) = 0.171313% is caused by compounding. It's due to both capital and dividend monthly returns.
Attributing the extra 0.171313% return to dividends is incorrect and misleading. This extra return isn't due solely to dividends. Had the investment experienced a 0% capital return, there wouldn't have been such an extra return. (I leave the detailed calculations to check this as an exercise).
Hint: I remind readers about high school maths:
(a + b)² = a² + b² + 2ab. Yes, right, some people seem to always forget about that annoying last term (2ab).
In summary, compounding inherently links capital gains and dividends within total returns and generates an extra return. This makes it
impossible to express coherent dividend and capital returns such that (dividend return + capital return = total return) consistently across different measuring periods.
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