Useful discussion on measuring portfolio growth rates

[tjh290633]

Forgive me for pouring cold water on this discussion.

The debate about how to get precision on measuring portfolio returns is completely spurious, as it is ignoring an element that has much greater impact on real return, namely inflation.
Any tracking of annual returns should be inflation adjusted to be meaningful.

What I do is to compare my figures for unit price versus inflation. For this purpose I would use the income unit version, and compare both unit price and dividend per unit with the RPI. If the figures are ahead of the RPI, then I have won, if they lag, then I have lost.

.            Income Units              Accumulation   Rebased   Rebased   April   Rebased
Year to      Unit Value     Div/Unit   Unit Value     FT30      FT100     RPI     RPI    
21-Apr-87            1.00       0.00           1.00      1.00      1.00   1.018      1.00
05-Apr-88            0.91       2.86           0.94      0.92      0.91   1.058      1.04
05-Apr-89            1.18       2.72           1.28      1.10      1.05   1.143      1.12
05-Apr-90            1.21       4.24           1.40      1.13      1.14   1.251      1.23
05-Apr-91            1.34       5.42           1.69      1.28      1.26   1.331      1.31
05-Apr-92            1.30       7.52           1.75      1.24      1.26   1.388      1.36
05-Apr-93            1.51       6.91           2.13      1.44      1.46   1.406      1.38
05-Apr-94            1.70       6.27           2.50      1.65      1.65   1.442      1.42
05-Apr-95            1.66       7.48           2.55      1.57      1.62   1.490      1.46
05-Apr-96            1.95       7.38           3.13      1.80      1.90   1.526      1.50
05-Apr-97            2.16       8.40           3.62      1.85      2.21   1.563      1.54
05-Apr-98            3.31      10.00           5.72      2.45      3.05   1.626      1.60
05-Apr-99            3.44       8.46           6.12      2.47      3.21   1.652      1.62
05-Apr-00            3.32      11.33           6.13      2.42      3.35   1.701      1.67
05-Apr-01            3.29      12.42           6.32      2.05      2.89   1.731      1.70
05-Apr-02            3.37      13.02           6.76      1.65      2.69   1.757      1.73
05-Apr-03            2.29      12.10           4.85      0.85      1.85   1.812      1.78
05-Apr-04            2.92      13.38           6.56      1.22      2.25   1.857      1.82
05-Apr-05            3.46      13.06           8.10      1.33      2.51   1.916      1.88
05-Apr-06            4.30      17.42          10.57      1.68      3.06   1.965      1.93
05-Apr-07            4.91      19.42          12.63      1.90      3.31   2.054      2.02
05-Apr-08            4.14      24.32          11.21      1.58      2.93   2.140      2.10
05-Apr-09            2.28      21.17           6.46      0.87      2.01   2.115      2.08
05-Apr-10            3.69      11.06          10.86      1.33      2.91   2.228      2.19
05-Apr-11            4.16      16.71          12.76      1.43      3.03   2.344      2.30
05-Apr-12            4.40      17.73          14.19      1.33      2.96   2.408      2.37
05-Apr-13            5.27      21.83          17.01      1.54      3.29   2.476      2.43
05-Apr-14            5.34      23.05          18.88      1.75      3.38   2.557      2.51
05-Apr-15            5.91      24.98          21.84      1.91      3.47   2.580      2.53
05-Apr-16            5.92      22.67          21.72      1.79      3.17   2.614      2.57
05-Apr-17            6.62      26.21          25.47      2.10      3.76   2.706      2.66
05-Apr-18            6.12      33.19          24.66      1.79      3.62   2.797      2.75
05-Apr-19            6.35      31.25          27.04      1.95      3.82   2.856      2.81
05-Apr-20            4.60      31.57          26.64      1.44      2.77   2.926      2.87
05-Apr-21            5.99      22.54          29.07      1.76      3.46   2.960      2.89
05-Apr-22            6.70      24.68          34.29      1.69      3.86   3.236      3.18

So there you can compare the figures directly. Also those for the two indices that I have followed. I have other tables which compare the annual change in the various figures. Some will be lagging the RPI but most are ahead of it.

TJH

[tjh290633]

Here is that table, which shows the effect of special dividends.

.        .   Change                                                         Corrected   Change             Unit 
Year to      Unit Value   Div/Unit   FT30      FTSE      RPI      Sp Divs   Ord divs    Ord divs   Yield   /FTSE
21-Apr-87                                                                                                   1.00
05-Apr-88        -8.60%               -8.09%    -4.82%    3.93%                  2.86              3.13%    0.96
05-Apr-89        28.62%     -5.19%    19.45%    11.73%    8.03%                  2.72     -5.19%   2.31%    1.11
05-Apr-90         2.89%     56.05%     2.96%     7.78%    9.45%                  4.24     56.05%   3.50%    1.06
05-Apr-91        10.39%     27.92%    12.92%    10.31%    6.39%                  5.42     27.92%   4.06%    1.06
05-Apr-92        -2.44%     38.62%    -2.59%    -0.68%    4.28%                  7.52     38.62%   5.77%    1.04
05-Apr-93        15.82%     -8.01%    15.65%    16.51%    1.30%                  6.91     -8.01%   4.58%    1.03
05-Apr-94        12.90%     -9.31%    14.78%    12.84%    2.56%                  6.27     -9.31%   3.68%    1.03
05-Apr-95        -2.82%     19.29%    -5.07%    -2.01%    3.33%                  7.48     19.29%   4.52%    1.02
05-Apr-96        17.83%     -1.38%    14.71%    17.32%    2.42%                  7.38     -1.38%   3.78%    1.03
05-Apr-97        10.87%     13.93%     3.01%    16.57%    2.42%                  8.40     13.93%   3.89%    0.98
05-Apr-98        52.96%     18.99%    32.17%    37.71%    4.03%    11.18%        8.88      5.69%   2.69%    1.09
05-Apr-99         4.05%    -15.39%     0.91%     5.47%    1.60%                  8.46     -4.74%   2.46%    1.07
05-Apr-00        -3.42%     33.92%    -2.12%     4.41%    2.97%                 11.33     33.92%   3.41%    0.99
05-Apr-01        -1.05%      9.66%   -15.07%   -13.86%    1.76%     5.55%       11.73      3.57%   3.57%    1.14
05-Apr-02         2.39%      4.79%   -19.85%    -6.79%    1.50%                 13.02     10.95%   3.87%    1.25
05-Apr-03       -32.00%     -7.09%   -48.58%   -31.17%    3.13%                 12.10     -7.09%   5.28%    1.23
05-Apr-04        27.74%     10.62%    44.80%    21.34%    2.48%    13.16%       11.62     -3.94%   3.97%    1.30
05-Apr-05        18.43%     -2.39%     8.32%    11.60%    3.18%     7.57%       12.07      3.89%   3.49%    1.38
05-Apr-06        24.22%     33.38%    26.86%    21.87%    2.56%    24.66%       13.12      8.71%   3.05%    1.41
05-Apr-07        14.17%     11.48%    12.92%     5.76%    4.53%    27.69%       14.04      7.00%   2.86%    1.52
05-Apr-08       -15.78%     25.25%   -16.84%    -9.61%    4.19%                 24.32     73.21%   5.88%    1.41
05-Apr-09       -44.87%    -12.95%   -45.08%   -31.15%   -1.17%                 21.17    -12.95%   9.28%    1.13
05-Apr-10        61.85%    -47.75%    52.75%    44.66%    5.34%                 11.06    -47.75%   3.00%    1.27
05-Apr-11        12.78%     51.07%     8.14%     4.03%    5.21%                 16.71     51.07%   4.01%    1.37
05-Apr-12         5.70%      6.10%    -7.50%    -3.13%    2.73%     1.57%       17.46      4.44%   3.97%    1.50
05-Apr-13        19.81%     23.08%    16.44%     9.19%    2.82%     8.79%       19.91     14.05%   3.78%    1.64
05-Apr-14         1.36%      5.59%    13.14%     5.58%    3.27%    11.19%       20.47      2.81%   3.83%    1.58
05-Apr-15        10.57%      8.37%     9.28%     2.65%    0.90%    14.60%       21.33      4.22%   3.61%    1.70
05-Apr-16         0.27%     -9.24%    -6.28%    -8.83%    1.32%     4.38%       21.67      1.61%   3.66%    1.87
05-Apr-17        11.72%     15.63%    17.57%    18.59%    3.52%     4.67%       24.99     15.28%   3.78%    1.76
05-Apr-18        -7.56%     26.61%   -14.95%    -3.64%    3.36%    11.91%       29.23     37.06%   4.78%    1.69
05-Apr-19         3.79%     -5.83%     9.09%     5.53%    2.11%     6.41%       29.25     34.94%   4.61%    1.65
05-Apr-20       -27.56%      1.03%   -26.26%   -23.83%    2.45%     7.16%       29.31     17.31%   6.37%    1.17
01-Apr-21        30.22%    -28.61%    22.26%    18.78%    1.16%    15.99%       18.93    -35.24%   3.16%    1.53
05-Apr-22        11.85%      9.52%    -3.90%    13.01%    9.32%     3.92%       23.71    -18.92%   3.54%    1.69

A bit wide, but you get the gist.

TJH

[XFool]

Let’s get this sorted.

What TJH is calculating is NOT the portfolio XIRR , it is just using the XIRR formula ( which is perfectly valid for just a data pair, instead of using other usual mathematical formulae) to calculate the rate at which his acc units have compounded.

Yes. Which is exactly what I did - by not using XIRR.

Should indeed give the same answer - if there are no cash inflows or outflows. But, if there are...

(For those of you, like me, who unitise, be very careful that if a special is attached to a consolidation, then this portfolio event is NOT a unitisation event. If you count it as such you distort your acc data and badly overstate it. I fear that many unitisers on theses boards make that fundamental mistake repeatedly. Likewise, a rights issue is NOT a unitisation event, another common error I frequently spot from unitisers, having run many workshops on unitising in the past).

I am not into unitisation so cannot really comment. However... this sounds a bit to me like how some XIRRers sometimes get muddled up over the portfolio XIRR and include dividends and cash flows inside the portfolio - which are irrelevant.

[XFool]

Forgive me for pouring cold water on this discussion.

The debate about how to get precision on measuring portfolio returns is completely spurious, as it is ignoring an element that has much greater impact on real return, namely inflation.
Any tracking of annual returns should be inflation adjusted to be meaningful.

I don't agree. I'm not saying inflation doesn't matter, but surely you need to get the correct return calculation sorted out first? Inflation is then just a simple matter of an adjustment factor to the end result.

[doug2500]

Let’s get this sorted.

What TJH is calculating is NOT the portfolio XIRR , it is just using the XIRR formula ( which is perfectly valid for just a data pair, instead of using other usual mathematical formulae) to calculate the rate at which his acc units have compounded.

Yes. Which is exactly what I did - by not using XIRR.

Should indeed give the same answer - if there are no cash inflows or outflows. But, if there are...

(For those of you, like me, who unitise, be very careful that if a special is attached to a consolidation, then this portfolio event is NOT a unitisation event. If you count it as such you distort your acc data and badly overstate it. I fear that many unitisers on theses boards make that fundamental mistake repeatedly. Likewise, a rights issue is NOT a unitisation event, another common error I frequently spot from unitisers, having run many workshops on unitising in the past).

I am not into unitisation so cannot really comment. However... this sounds a bit to me like how some XIRRers sometimes get muddled up over the portfolio XIRR and include dividends and cash flows inside the portfolio - which are irrelevant.

For unitisation they are irrelevant for an Acc portfolio but not inc. I do Acc and the only thing included is cash added or withdrawn, which shows up as an increase or decrease in number of units. Dividends are all included in the total value of pf and show up as part of the price per unit (the cash from divi's is all held in broker accounts, or a dedicated bank account)......but we digress.

[XFool]

I am baffled as to how we get two different results for the IRR, using the same data.

Regarding cash flow results, I get 9.75% to date for the portfolio, which of course allows for money in and out.

My formula is =-XIRR(BF597:BF598,BF594:BF595) in cell BF600, and the cells are:

21-Apr-87
31-Mar-22

33.41
-1.00

9.55%

BF597-BF600 in my spreadsheet.

Hold on. I have found the answer. If I transpose the values, to be 1.00 in BF597 and -33.41 in BF598, I get 10.56%. Remove the - sign from the formula. Back to square 1.

Are you sure? (I haven't checked) As I noticed when I started using XIRR - and as Gengulphus once pointed out - XIRR gives exactly the same result if you consistently reverse all the signs. I prefer though to stick with the officially 'correct' procedure.

Possibly just a matter of using actual dates for the XIRR calculation, rather than a simple year to year calculation with the original figures?

[TUK020]

Forgive me for pouring cold water on this discussion.

The debate about how to get precision on measuring portfolio returns is completely spurious, as it is ignoring an element that has much greater impact on real return, namely inflation.
Any tracking of annual returns should be inflation adjusted to be meaningful.

I don't agree. I'm not saying inflation doesn't matter, but surely you need to get the correct return calculation sorted out first? Inflation is then just a simple matter of an adjustment factor to the end result.

Interesting contrast in perspectives!
I agree with the need to get the correct return calculation first, my take on which is the real, inflation adjusted, return for each year. How you then portray the averaging or compounding of several years return is my view of the subsequent adjustment...
Let's agree to disagree.

[Bagger46]

Let’s get this sorted.

What TJH is calculating is NOT the portfolio XIRR , it is just using the XIRR formula ( which is perfectly valid for just a data pair, instead of using other usual mathematical formulae) to calculate the rate at which his acc units have compounded.

Yes. Which is exactly what I did - by not using XIRR.

Should indeed give the same answer - if there are no cash inflows or outflows. But, if there are...

(For those of you, like me, who unitise, be very careful that if a special is attached to a consolidation, then this portfolio event is NOT a unitisation event. If you count it as such you distort your acc data and badly overstate it. I fear that many unitisers on theses boards make that fundamental mistake repeatedly. Likewise, a rights issue is NOT a unitisation event, another common error I frequently spot from unitisers, having run many workshops on unitising in the past).

I am not into unitisation so cannot really comment. However... this sounds a bit to me like how some XIRRers sometimes get muddled up over the portfolio XIRR and include dividends and cash flows inside the portfolio - which are irrelevant.

For unitisation they are irrelevant for an Acc portfolio but not inc. I do Acc and the only thing included is cash added or withdrawn, which shows up as an increase or decrease in number of units. Dividends are all included in the total value of pf and show up as part of the price per unit (the cash from divi's is all held in broker accounts, or a dedicated bank account)......but we digress.

You are not correct. A normal divi triggers a unitisation computation for both acc and inc units, (best done automatically on the nail as the divi hits the portfolio to maximise accuracy). A special attached to a consolidation (which is in fact just a rearragement of the capital base in you portfolio designed to be neutral at the outset) does not. If matters a great deal. In the 80's and 90's, we ran in our investment club about 75 workshops on unitising( and believe me these workshops were attended by beginners but also very sharp experienced cookies with massive skin in that game) , having been introduced to the subject at the outset by expert visiting speakers from the City, so I should know. I have always found the general understanding on the subject extremely poor on TMF.

I will leave it at that

Bagger

[OldPlodder]

I attended such a workshop in 1994 or 95. It started my wife and I off with unitising. Don't know if it was one of those mentioned by Bagger ( probable because it was run by a visitor from another investment club), but I must say that what he is posting is totally correct.

Plodder

[doug2500]

I'd appreciate it if Bagger didn't leave it there. If I'm wrong I want to know.

I based my approach on rules published on TMF, and now Lemon Fool, here:

http://lemonfoolfinancialsoftware.weebl ... folio.html

And I quote:

If dividends are kept within the portfolio, and either immediately or at a later point reinvested in shares, there is no change in the number of units. All that happens is that the value of the portfolio increases, therefore the price of each unit increases a little.

[doug2500]

And further:

So to summarise:
With accumulation units
adding money to the portfolio buys extra units but does not affect the price per unit
dividend income received and retained in the portfolio increases the price of each unit but has no effect on the number of units
withdrawing money (either capital or dividends received) reduces the number of units owned, but does not affect the price of each unit

[Newroad]

Hi Old Plodder et al.

The genesis of this was Terry listing the history of his accumulation units (and IRR in a separate column) to which I replied

So, based on the accumulation units, around 10.545% per annum cumulative?

I would be grateful if those who believe that is materially* wrong in terminology, calculation or both, illustrate the error by providing a corrected version as to what I could/should have written as the confirming question?

Like Doug, I think that there is some learning on this topic which may be incomplete for some.

Regards, Newroad

* e.g. not counting the 21 day start day discrepancy, which has already been noted

[MDW1954]

Hi Doug.

It could be wrong, but here's what I did



Each year multiplies the year before by cell C1.

Regards, Newroad

I think I understand where you're coming from, but the correct way (or at least my way) would be XIRR as explained.

Doug2500,

What Newroad has done is to calculate the compound annual growth rate that transforms 1 into 33.4094 over 35 years, ie 10.545%.

Compound growth (CAGR) delivers exactly the same result as the geometric mean, although the actual calculations vary.

As you may have seen on the HYP board (and recently the Financial Software board) I prefer to use logarithmic linear least squares to perform such growth estimates, for the reasons I explained on the latter board.

I have tools available to perform such calculations within Excel spreadsheets (as well as statistical package R), and user modellingman (who I've known since the 1970s in real life) kindly uploaded a spreadsheet that also performs logarithmic linear least squares. Either my tools or his may be useful to others. I intend making mine publicly available shortly.

MDW1954

[MDW1954]

Moderator Message:
Several requests urged moderators to split the original thread in two. Hence this discussion. Feel free to continue it! It will probably be made "sticky". --MDW1954

[Newroad]

Hi All.

Thanks to all who contributed in this (now moved) sub-strand earlier.

I would still be interested in bottoming some of the stuff raised out - my guess is Doug would too. Any takers to help?

Regards, Newroad

[MDW1954]

Hi All.

Thanks to all who contributed in this (now moved) sub-strand earlier.

I would still be interested in bottoming some of the stuff raised out - my guess is Doug would too. Any takers to help?

Regards, Newroad

It might be useful if you summarised exactly what it is that you're trying to bottom out.

Or is it what you say in the post below?

https://www.lemonfool.co.uk/viewtopic.php?p=497020#p497020

MDW1954

[doug2500]

To summarise, for me at least, I'd like an answer to this query:

Bagger, who I believe is extremely experienced and knowledgeable on the subject, said this to me:

You are not correct. A normal divi triggers a unitisation computation for both acc and inc units,

Whereas the rules I follow (here: http://lemonfoolfinancialsoftware.weebl ... folio.html) say this:

dividend income received and retained in the portfolio increases the price of each unit but has no effect on the number of units

The two seem incompatible to me, and I really want to get this right.

Finally, apologies to those following the original thread for my contribution in it's drifting, all I can say is that although it was a minor query that triggered it, it was important to me to find out the correct answer.

[doug2500]

Additional thought...I would agree with Bagger if dividends we're paid into a bank account and not reinvested but he went on to say this:

best done automatically on the nail as the divi hits the portfolio

Which implies divis are being retained within the pf.

[tjh290633]

The corrected version of my earlier post, viewtopic.php?p=496991#p496991 is:

The rate of return for my accumulation units for the 35 periods, each starting on 21 Apr 1987 and finishing on the date shown, is as follows:

Year End    Acc Unit   IRR from start
                       to year end   
21-Apr-87       1.00                 
20-Apr-88       0.92           -8.00%
16-Apr-89       1.24           11.42%
11-Apr-90       1.39           11.70%
28-Mar-91       1.69           14.26%
28-Mar-92       1.75           12.00%
27-Mar-93       2.13           13.58%
22-Mar-94       2.50           14.15%
26-Mar-95       2.55           12.52%
01-Apr-96       3.13           13.59%
28-Mar-97       3.62           13.81%
28-Mar-98       5.72           17.28%
31-Mar-99       6.12           16.37%
31-Mar-00       6.13           15.02%
31-Mar-01       6.32           14.13%
31-Mar-02       6.76           13.63%
31-Mar-03       4.85           10.40%
31-Mar-04       6.56           11.73%
31-Mar-05       8.10           12.36%
01-Apr-06      10.57           13.24%
31-Mar-07      13.20           13.80%
31-Mar-08      11.21           12.22%
31-Mar-09       6.46            8.87%
31-Mar-10      10.86           10.95%
31-Mar-11      12.76           11.21%
30-Mar-12      14.19           11.21%
28-Mar-13      17.41           11.64%
31-Mar-14      18.88           11.51%
31-Mar-15      21.84           11.66%
31-Mar-16      21.91           11.25%
31-Mar-17      25.47           11.41%
30-Mar-18      24.66           10.91%
31-Mar-19      26.64           10.81%
31-Mar-20      21.64            9.77%
31-Mar-21      29.07           10.43%
31-Mar-22      33.41           10.64%

This accounts for much of the discussion above.

TJH

[Hariseldon58]

Interesting discussion, unitising can get complicated…I do not bother, but prefer to look at my portfolio growth rates over many different time periods, I prefer roughly right to precisely wrong.*

The problem with the CAGR is that you basically start at the beginning and look at the result at the end and calculate the number, but change the start and finish dates slightly and despite a long time period the numbers can move around a lot… it may not help you to compare with other investment possibilities, unless you are very careful in your comparison or to have a feeling for what may come next.

https://www.raynergobran.com/2017/07/hacking-compound-annual-growth-rate/

This is an interesting post on this subject.

* It’s not that I am unable to do the maths ( Oxford ) but the cash flows can get very complicated in the real world and subjective decisions can mean the answer is not that helpful !