Portfolio Spending - simple model with and without Dividends

wksel

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Nov 11, 2016
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I was trying to create a very simple model today and got a little hung up. Here is the basic idea or question:

How much does the outcome vary (if at all) after N years if the sequence of returns is non random (i.e., worse returns are loaded into early years but with the same average return as if it was random) in two scenarios: A) the spending/consumption is funded by selling shares in something that retains dividends, and B) the consumption is funded by dividends alone from an equivalent instrument that pays dividends out. Let's say the portfolio is $1M and spending is 4%. Let's also say that there are no taxes, no inflation, and dividends aren't treated any better retained or not.​

Step 1. This has probably been done elsewhere but I was trying to do it myself. I started here. This is my attempt at creating two fake instruments, one with the div retained (#1) and one with the div paid out but compounded separately (#2). This may be flawed but bear with me. I was trying to create two instruments where i would be indifferent between them with respect to the div being in or out. If this is, in fact, flawed we can stop here. Here I was merely trying to create a price mechanism for the next step where I do a portfolio spend using these two. The 10 year duration is arbitrary. The return assumption is 2% only because it was a placeholder for later steps. The PriceEnd is what I use in the next step to value a portfolio.
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Step 2. Now create a $1M portfolio that has 40k in consumption each year. Run it once over N years with instrument#1 above and again with #2 above. The image below is what I came up with. This is where I got hung up. I was naively assuming when I started that with that placeholder assumption you see above of 2% constant return (later to be replaced in a subsequent step) that the two scenario's outcomes would be the same and that i would then move to step 3 where I would tilt the returns a bit. But the results came out different and now I can't convince myself either way if I did it right or wrong or if a whole other method is a better way to do this. I've been looking at it too long and wanted a fresh set of eyes to point out something that can nudge me along. Note that here that I let the return in scenario A occur before the spend.

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3. My hypothesis was originally that with randomly distributed returns that I would be more or less indifferent to whether I took a dividend or self rolled one by selling shares (in the absence of taxes and inflation) and that in the presence of an adverse sequence of returns early in the timeframe that I might have an advantage with using the dividend paying instrument. I just wanted a simple "back of the napkin" model that gave me the basic sense of this. Any thoughts would be appreciated even if it is "give up" or "there are other ways to do this" or whatever. The model does not have to be solved or corrected. Mostly I am looking for a pointer to a place to look something up online or perhaps a suggestion of "try this."

Regards
 

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Easier than it looks, I guess

The answer is fairly simple it seems thus illustrating the dangers of doing finance during or after happy hour (joke, I wasn't really drinking and financing...that would be irresponsible, kind of like doing finance while driving). If you look closely the difference between year 2 A and year 2 B the difference is 1509. That 1509 is 100% attributable to the fact that the dividend is no longer 40k on a 1M portfolio but is now 9623/10000 * 40k as compared to scenario B with the full div of 40 when no shares have to be sold. So 40k - (9622.64/10000)*40k = 1509. On the question of whether this is modeled correctly or whether the question is even the right question...that is another problem for another day...
 
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