1. The first one asked whether the cost of "electricity" would go down too since I had sold a fractional share of a machine. Good question and perceptive. I maybe wrote my "metaphor" wrong. The electricity is a proxy for my spending which wouldn't change with the selling of shares.
2. Here is part of response two: "...Making an equivalence leap of faith for these two companies--as an investor I can own X shares of Company D, receive annual dividends, and my X shares will not grow in value. Or I can own Y shares of Company G, whose shares are growing in value, and sell enough shares each year so that my total investment in Company G remains level. The annual proceeds from selling shares will equal the dividends from Company D. If these amounts (dividends and share sale proceeds) were not equal, relative market prices of the shares of the these companies would adjust to make them equal."
Yep. That's my question. Econ theory says equal and I agree, but I failed, in the money machine example, to clearly distinguish between the instruments and the strategy that uses the instruments. The instruments are the machines or, more accurately, the dividend payer/retainer pair and I agree with the theory of equivalence up to a point and accept arb theory as a possible influence too. It is in the area of life-cycle strategies and execution over time where I am confused. And by "strategy" I mean funding a spending program with instrument 1 (retainer) or instrument 2 (payer), neither of which strategy should have an impact in market arbitrage/pricing, I think. I agree that in year 1: a) collecting a div and using it to fund expenses and b) liquidating shares to fund expenses looks equivalent (all else equal). But in year 2 it gets more interesting assuming I have not mis-modeled or misunderstood which is entirely possible. Let's look at it in more detail....
Assumptions:
Two instruments, one pays a div, one retains
No taxes, inflation, or ill treatment of retained dividend
Zero growth except dividend retained, so no extra compounding in paid div
2 x $1M portfolios, one funded with retainer one with payer
1% dividend
$10,000 in spending
Share liquidation is after change in value and before consumption
Instrument "price end" is used to value portfolios
N is 10 which is arbitrary
Here are two instruments, 1 and 2:
So far so good (maybe, if I did not miss something here). And now here are the two strategies. First the "$1M/$10k spend" funded with instrument 1, the retainer:
And here is strategy B that funds 10k consumption with the div from instrument 2, the payer:
Ok, so instrument 1 and 2 are equivalent in this overly simple model in all years. And year 1 of the 2 "strategies" is equivalent across the two but then in years 2-N there is a degradation in strategy A due to the dilution of the claim on the dividend. Since I am not an economist or a financial academic I humbly presume that I have mid-modeled or made a naive error (and now in full public view). I just don't know whom to ask. On the other hand, if I am correct, I presume also that this is in some textbook or paper somewhere, I just don't know where to look and Google does not help. In real life this difference would probably be swamped by other things but now I'm curious.
3. Here is response 3 which is the most convincing so far.
"...the issue is NOT having the retained dividend compound. If it did compound you would continue to earn $10,000 even if you have less shares. In strategy B you spend the dividends and continue to retain $1m in an income generating portfolio producing $10k. In strategy A you spend a portion of your income producing portfolio but retain a portion of your non-income producing dividend. After year 1 these strategies are not the same as the non income producing portion is worth less. Said even more clearly - After year one you own $1m worth of a company in both scenarios yet for some reason by design one generates 10k and the other less than 10k. That doesn't make sense to me."
I've been thinking about this one and it is possible that it is correct. I probably won't take it too much further than this because there is no real benefit to doing so other than satisfying some curiosity. My only thoughts are that the dividend does in fact compound (though in the example I have taken out any growth ) the way I thought it was supposed to. I may be misinterpreting the way it should be done which may be the problem. That, and I may have the timing of how things are paid and spent in some kind of mis-order. Either way the div does carry forward and compound and, in addition, I have a real compounding version, too, where there is real compounding growth (not shown) where it works the same. I'll go back to what I know: 1) the two instruments are, in a total return world, equivalent because the dividend in the absence of spending compounds either way, and 2) I am in fact selling down shares. In period 10 I clearly own less of something that has become more valuable but the way I have it compounding does not keep up. Error or no error? I could go either way.
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