How HYP1 might have grown with dividend reinvestment

[Gengulphus]

It is of course impossible to answer the question of how HYP1 would have grown with dividend reinvestment without knowing which shares it would have reinvested the income in, and that raises the hindsight issue - how on earth can we fairly decide which shares it would have picked now that we know so much about which shares did well and which didn't? That issue is IMHO essentially unsolvable.

And the question of how it might have grown with dividend reinvestment has a large variety of answers, depending on the reinvestment method one chooses - and most methods involve getting hold of a large amount of past data and exercising some human judgement about it (which inevitably raises the hindsight issue again). But there is one reinvestment method whose results can be worked out with only limited data about the portfolio as a whole, which I'll call the "more of the same" method: just buy all of the shares already in the portfolio in proportion to the existing holdings. It's not by any means a HYP reinvestment method I would recommend: it's liable to reinvest parts of the dividend income in non-high-yielding shares (either because they've cut their dividends or because their share price growth has outstripped their dividend growth), it's liable to make purchases of the HYP's smaller holdings that are too small to be cost-effective, and it does nothing to restore lost diversification. But it does have the advantage that it can be worked out for a non-reinvesting HYP like HYP1 long after the event and with no risk of using hindsight knowledge.

Assuming that reinvestment is done once per year on the portfolio anniversaries, that results in every holding being larger after the year 1 reinvestment by a factor of (V1+I1*cf)/V1, where V1 is the portfolio's capital value at the end of year 1, I1 is the year 1 income, and cf is the factor by which the reinvested income is reduced by trading costs. With the total income over the 20 years having been £101k, the average sum reinvested per year is about £5k, and the costs of reinvesting it would therefore average 0.5% stamp duty = £25, maybe 0.1% bid/offer spread = £5, and 15 or 16 buying commissions. With normal buying commissions, that will produce total costs of around £200-£250, i.e. costs of about 4-5% of the sum reinvested, or cf = 0.95-0.96. With low-cost buying commissions, that can be reduced to be in the range £50-£75 (cf = 0.985-0.99). If I remember correctly, low-cost buying commissions were brought in a few years after HYP1 was started, but have been available for most of the years; I think it's fair to assume that the effect of cf averages out as about the same as if cf were about 0.98 for all 20 years.

Anyway, with every holding bigger by that factor of G1 = (V1+I1*cf)/V1 from the start of year 2, the portfolio's income during year 2 and its capital value at the end of year 2 will both be greater by a factor of G1, so the corresponding calculation for year 2 says that the end-of-year-2 reinvestment increases all holdings by a factor of G2 = (G1*V2+G1*I2*cf)/(G1*V2) = (V2+I2*cf)/V2. And that argument cascades through the years, saying that the 'accumulation unit version' of HYP1 is larger than HYP1 by the product of all the factors Gy = (Vy+Iy*cf)/Vy for the years y = 1, 2, 3, ..., 20, where Vy is the capital value at the end of year y and Iy is the income earned during year y. I can get all the Iy values from pyad's year 20 report, and all the Vy values except V8 from his past reports. He didn't produce a year 8 report as far as I am aware, so V8 has to be estimated - I've based the estimate on the figure of £79,984 in kool4kats's report, but rounded it to £80,000 to try to avoid a spurious appearance of accuracy (it's not accurate because it's actually about CHYP1, not HYP1 - but it's not grossly inaccurate because HYP1 and CHYP1 had only had about 6 months to diverge from each other at that point).


Italics in this table indicate estimated and corrected figures. The V8 figure is estimated as described above; the V10, V11, V12 and V13 figures are corrected for an error caused by the Dixons share count having been inadvertently reset to its previous value of 5,841 after being increased to 8,008 by dealing with a rights issue in 2009. This wasn't detected and corrected until 2014, and was only corrected in the 2014 and later capital values - but I am correcting the affected earlier capital values because leaving the error uncorrected would lead to growth factors for reinvestments being overestimated. I should add that the corrections are individually pretty small - they each affect their year's growth factor by less than 1%. Their cumulative effect is still pretty small, at something of the order of 2%, but I felt it was just about worth the small amount of effort needed to correct the figures to remove that source of error.

Gengulphus

[tjh290633]

I think that is a reasonable estimate. My method would probably have been to reinvest income in the lower value shares, to provide some sort of rebalancing towards equal weight. The picture is complicated by the extreme unbalance created when all the proceeds of a take-over went into a single share. However my approach was later modified to couple this with the higher yields, and resulted in my subsequent method to give a top-up ranking. Probably impossible to recreate either approach at this time, and yours is the best that we could achieve without a vast amount of research.

TJH

[moorfield]

Very interesting work Gengulphus.

If you don't mind some feedback, I think it would be useful to have an additional column on that table detailing the income produced each year as a result of dividend reinvestment. Happy to have a stab at that myself but it may take me a few days, as I'm interested in looking at how income grows as a result of the combined effect of dividend reinvestment, rises and cuts.

[pyad]

Interesting results G.

Moderator Message:
Unnecessary provocation deleted. - Chris

[dealtn]

Interesting results G.

[Deleted.]

I'm waiting to see how much less or more concentrated the portfolio would look.

[moorfield]

I'm waiting to see how much less or more concentrated the portfolio would look.

It wouldn't, because:

But there is one reinvestment method whose results can be worked out with only limited data about the portfolio as a whole, which I'll call the "more of the same" method: just buy all of the shares already in the portfolio in proportion to the existing holdings.

[dealtn]

I'm waiting to see how much less or more concentrated the portfolio would look.

It wouldn't, because:

But there is one reinvestment method whose results can be worked out with only limited data about the portfolio as a whole, which I'll call the "more of the same" method: just buy all of the shares already in the portfolio in proportion to the existing holdings.

Understood (now)

[Gengulphus]

If you don't mind some feedback, I think it would be useful to have an additional column on that table detailing the income produced each year as a result of dividend reinvestment. Happy to have a stab at that myself but it may take me a few days, as I'm interested in looking at how income grows as a result of the combined effect of dividend reinvestment, rises and cuts.

Easy enough - each year's income from the portfolio with dividend reinvestment is produced by the portfolio produced by the previous years' reinvestments, which is the actual HYP1 scaled up by the previous year's cumulative growth factor. So it's the original income on the same row times the cumulative growth factor on the previous row, which expands the table to:


Gengulphus

[moorfield]

Easy enough - each year's income from the portfolio with dividend reinvestment is produced by the portfolio produced by the previous years' reinvestments, which is the actual HYP1 scaled up by the previous year's cumulative growth factor.

Thanks Gengulphus, your model has generated some interesting data which can be explored further.

I've taken the liberty of testing those income figures against a compound annual growth rate (CAGR) of 7.2% - see the red curve below. That's not a curve of best fit, rather a "black box" test which isn't interested in portfolio constituents, relative weights, or top up method, just the overall income produced year on year through the combined effect of dividend raises, cuts and reinvestment.

Why 7.2%? That is the rate I chose to measure my own progress of income building by dividend reinvestment, which was a semi-arbitrary choice based on the initial amount I had to invest, the ftse yield at the time, how much I thought I might be able to save regularly, when I thought I might retire, and my target retirement income. I estimated somewhere between 6-8%, and read something (in Moneyweek I think) suggesting 5-7% was conservative. So I settled on the rule of 72 because the idea of "doubling income in a decade" had a nice ring to it, and was easy to understand and communicate.

Such a curve has two practical uses for a HYP builder here that I can think of:

Firstly, it helps the builder peer beyond the short term - a decade or two further on, say - and plan for their retirement. With a guesstimate of inflation, a target retirement income can also be expressed in "today's money" to help put that in some context.

Secondly, it serves as a useful "hands-off/hands-on" switch. In years of surplus income (eg. 13-19) the builder can remain "hands-off", there is no need to tinker, and that surplus can be reinvested or alternatively used to build a cash reserve. In years of shortfall (eg. 9-12) the builder might choose to be "hands-on" and do some tinkering of poor performers or reinvest any cash reserve.

Your model raises an interesting question about the frequency of top ups. My test here does not suggest that once a year is inadequate, which is food for thought.

[88V8]

[Your model raises an interesting question about the frequency of top ups. My test here does not suggest that once a year is inadequate, which is food for thought.

Yes, the whole exercise is interesting.
In a way, a variation on the automated system that Luni cherished.

As regards topping up, annually would make sense in the early years while income is modest, especially if one is splitting not much money between rather a lot of purchases.

V8

[Gengulphus]

[Your model raises an interesting question about the frequency of top ups. My test here does not suggest that once a year is inadequate, which is food for thought.

Yes, the whole exercise is interesting.
In a way, a variation on the automated system that Luni cherished.

As regards topping up, annually would make sense in the early years while income is modest, especially if one is splitting not much money between rather a lot of purchases.

Just in case anyone is wondering, I wasn't recommending any particular frequency of topping up, just as I wasn't recommending the "more of the same" method of choosing which shares to top up and by how much. It's just that the data I have available about HYP1 is essentially pyad's annual reports, so trying to do anything else would have involved a lot more work gathering the data needed about past share prices and dividends! (And indeed, some of it would probably be unavailable, at least from free sources - e.g. past share prices for Gallaher, Associated British Ports and various other shares taken over in the 2000s.)

Gengulphus

[moorfield]

Just in case anyone is wondering, I wasn't recommending any particular frequency of topping up, just as I wasn't recommending the "more of the same" method of choosing which shares to top up and by how much.

Yes understood which is why I wrote in the double negative. I think had I written "My test here suggests that once a year is adequate" would have implied you were and that my cagr test is representative of a HYP builder's long term income growth - it isn't, it's just what works for me, but it's a technique that might work for others too.

[moorfield]

I've taken the liberty of updating Gengulphus's model which I've been meaning to do for a while.

Accumulation-HYP1's income was £25,272 in Year 21, which works out at a compound annual growth rate of 10.5% since Year 1.
(As mentioned previously, I have fixed this at 7.2% for my own long term forecasting.)

Overall value has multipled 5.08x.

[MDW1954]

I make that a logarithmic linear least squares growth rate of 8.521%, with an r-squared of 0.937.

(PS: I can add one of my logarithmic linear least squares growth rate plots, if anyone would like that? I have posted them before.)

MDW1954

[monabri]

I make that a logarithmic linear least squares growth rate of 8.521%, with an r-squared of 0.937.

(PS: I can add one of my logarithmic linear least squares growth rate plots, if anyone would like that? I have posted them before.)

MDW1954

Go for it!

[MDW1954]

I make that a logarithmic linear least squares growth rate of 8.521%, with an r-squared of 0.937.

(PS: I can add one of my logarithmic linear least squares growth rate plots, if anyone would like that? I have posted them before.)

MDW1954

Go for it!

Your wish is my command! The original calculation that I quoted above came from a custom Excel function -- here's a chart pulled from some R/ggplot2 code that I wrote.

MDW1954

[moorfield]

That looks like growth rate for the capital values? Can you do the same for the income figures? It's the rate of income growth due to the combined effects of dividend increases, cuts and reinvestments that interests me ...

[MDW1954]

That looks like growth rate for the capital values? Can you do the same for the income figures? It's the rate of income growth due to the combined effects of dividend increases, cuts and reinvestments that interests me ...

Here you go...

MDW1954

[moorfield]

Growth rate = 9.751 %

Thanks MDW. Amidst the panolpy of portfolio reviews I read here (that season starts again soon...) which tend to focus on capital gains or losses, I think that is the first empirical data I have seen that shows income growth through the combined effect of dividend increases, cuts, and reinvestment (plus a few corporate actions) in a LTBH portfolio over a long period of time. One may disagree with the premise of Gengulphus's model (ie. just buy all of the shares already in the portfolio in proportion to the existing holdings) and note he would not recommend it, but it is a simple and useful one if we are able to extract charts like yours from it.

[MDW1954]

Growth rate = 9.751 %

Thanks MDW. Amidst the panolpy of portfolio reviews I read here (that season starts again soon...) which tend to focus on capital gains or losses, I think that is the first empirical data I have seen that shows income growth through the combined effect of dividend increases, cuts, and reinvestment (plus a few corporate actions) in a LTBH portfolio over a long period of time. One may disagree with the premise of Gengulphus's model (ie. just buy all of the shares already in the portfolio in proportion to the existing holdings) and note he would not recommend it, but it is a simple and useful one if we are able to extract charts like yours from it.

Given the data, the charts take seconds to do. Calculating just the growth rates is even easier, as I have it as a custom-written function in Excel.

The beauty of logarithmic linear least squares is that it uses all the data points, unlike (say) CAGR, which just uses two. Geometric means are almost as poor, in my view, because they simply calculate the average growth rate that transforms the first data point into the last data point, thereby producing the same result as CAGR.

So feel free to ask, whenever relevant data is quoted here.

MDW1954