Pension recovery performance 2020

[Deleted User]

Apart from private  and listed companies, GDP depends on the public sector. Which is huge. And none of it is related to valuation. 

Another_Saver

I think what happened was you got stuck at assuming that what I was saying needed annual correlation to be true, even though there is no reason for this to be true anymore than if you took quarterly, monthly or even daily GDP measurements. Nothing I said has anything to do with correlation. From then on, even though everything else I was saying was either correct mathematically, or a discussion of various papers including hard evidence that national stock index prices lag GDP,  you didn't even engage with any of it because you wrongly believed that correlation was a necessary premise. If you take much longer time periods of at least decades, you would expect to start seeing a correlation.

Secondly you asserted that comparing nominal GDP growth with nominal stock index price/capital growth without dividends is not a fair comparison, even meaningless. That is obviously untrue. In an economy, everyone has an income. Nominal GDP growth is a measure of change. You could have an economy with no growth in which GDP was say £2tn, and the stock market hovered around say an arbitrary index value of 7000. If the dividend yield of that index was 5%, capital owners would still receive an income that would not grow. Growth and income are clearly different. So to compare a measure of GDP growth with a sum of measures of a stock index's growth and income is manifestly not a fair or valid comparison. And the papers I offered show that in almost all markets and globally over sufficiently long periods this is borne out. Thanks to @itwasntme001 for this source showing the dramatic differences since 1985 (https://voxeu.org/article/big-bang-stock-market-capitalisation-long-run) post "big bang" and Dot Com. I think the additional capital supplied is explained mainly by widening market participation, uptake of DC retirement schemes, and boomer demographics increasing the wealth/GDP ratio.

As for index market caps growing faster than the index price, I have shown this to be true in respect of the FTSE 100. If my data or calculations are wrong please correct me.
 All you did was refute it and say it can't be true even though the two are not equivalent. The index price is computed on a per-share basis, the market cap is just a sum of market caps. Over time, new IPOs, stock options, new rights issues should cause this dilution effect that I measured at 2.23% for the FTSE 100, from 31/12/1985-31/12/2019.

Edit: also stock index prices tend to be forward looking and precede recessions or booms, so to isolate periods of one continuously measured time series and one quarterly/annually measured time series and assume they should be synchronised is, again, invalid.

[Deleted User]

“ you got stuck at assuming that what I was saying needed annual correlation to be true”.
No.  Correlation does not have to be “annual”, nor did I say it.   The fact is the two parameters you mentioned are not correlated at all. That means there is no relationship between the two variables.  And in fact, market returns have been higher, at least in the US since the 1930s.  As one can clearly see. https://www.bloomberg.com/opinion/articles/2020-06-09/stock-market-has-almost-always-ignored-the-economy. 

Another_Saver

Deleted_User said:

“ you got stuck at assuming that what I was saying needed annual correlation to be true”.
No.  Correlation does not have to be “annual”, nor did I say it.   The fact is the two parameters you mentioned are not correlated at all. That means there is no relationship between the two variables.  And in fact, market returns have been higher, at least in the US since the 1930s.  As one can clearly see. https://www.bloomberg.com/opinion/articles/2020-06-09/stock-market-has-almost-always-ignored-the-economy. 

...
I have now fully explained everything about your misunderstandings about correlation as best I can. A lack of or weak correlation does not imply a lack of relationship, however the debate continues to evolve.
That is not how correlation works. The two variables ought to be out of sync for a variety of reasons so again it is not a valid to imply a lack of correlation over the same time periods implies a lack of relationship.

All the sources I have referred to support my assertions. All the sources you have referred to do not support your assertions as explained in numerous posts above or by actually thinking.

 That is not how mathematics works. That is not how logic works.

Your second point, again, is wrong, obviously, as I explained above because you are comparing the total return (income + growth) with a measure of growth. You have also ignored the effect of rerating over the period and "big bang" in stock markets since the mid 80s. I do not know how else to explain this, it is one of those so obvious I take it for granted.

Placeholder for edit, I'm going to calculate correlation manually using multpl.com, ONS and Barclays UK equity index data.

[Deleted User]

“That is not how mathematics works. That is not how logic works.“

You know, as a farmer, in my past life, I used to occasionally lecture on the subject of nuclear physics at one of the universities in Canada.  You probably don’t know it, but my specialization requires a LOT of statistics.  I have come across students who lack knowledge of things they should have known.  I have never come across students who stubbornly refuse to learn basic concepts. 

Another_Saver

@Deleted_User
Re: correlation
I used ONS GDP at current market prices data, and the Barclays UK equity index, from 1948-2019. I use the CORREL function in Excel.

Correlation, lining up GDP year with start of year index is 97.74%, with end of year index is 97.79%.

I used S&P 500 index prices and US nominal GDP from multpl.com back to 1929. Correlation between GDP and start of year S&P 500 is 96.24%, end of year 95.75%.

As these datasets grow exponentially I then used the LN function to get the natural log and repeated to get the following correlations.
UK GDP with start of year index price 97.81%
UK GDP with end of year index price 98.11%
US GDP with start of year index price 97.04%
Us GDP with start of year index price 97.45%

Re: stock indices lagging GDP

UK GDP 1948 11425, index year start 170, year-end 157
UK GDP 2019 2214362 index year start 15185 year-end 17339.
GDP grew 7.70%, stock index year start to hear start 6.53%, year-end to year-end 6.85%

US GDP 1929 0.1tn, S&P 500 year start 24.86, year-end 21.71.
US GDP 2019 21.75tn, S&P 500 year start 2607.39, year end 3278.2
GDP grew 6.16%, index year start to hear start 5.31%, year-end to year-end 5.73%.

This does not include that both valuations, and the size of the stock market relative to GDP have both expanded significantly since the mid 1980s as covered in the voxeu and other sources above, including multpl.com for S&P PE data and my own calculations showing for example the FTSE 100 mkt cap/GDP ratio has increased from 39.6% to 85.3% from the end of 1985 to the end of 2019 (see the 1st half of my 3rd post on page 15 of the thread).

I rest my case.

[Deleted User]

Before I look at this, are we now aligned on the basics? That is if the two variables are related to each other, they are correlated.  I am still a little confused because you claimed 2% delta between the two variables, that Index can’t outperform the GDP and that it does not translate to correlation.  You also said things (in all caps) like:
” HAVE NEVER SAID THAT IF YOU COMPARE NOMINAL GDP, OR ANNUAL NOMINAL GDP GROWTH, WITH A STOCK INDEX, OR ITS ANNUAL CHANGES, THAT THERE SHOULD BE ANY SIGNIFICANT CORRELATION.”
Now you appear to claim an almost perfect linear correlation and we agree that a relationship does mean correlation.  Right? 

Another_Saver

Deleted_User said:

Before I look at this, are we now aligned on the basics? That is if the two variables are related to each other, they are correlated.  I am still a little confused because you claimed 2% delta between the two variables, that Index can’t outperform the GDP and that it does not translate to correlation.  You also said things (in all caps) like:
” HAVE NEVER SAID THAT IF YOU COMPARE NOMINAL GDP, OR ANNUAL NOMINAL GDP GROWTH, WITH A STOCK INDEX, OR ITS ANNUAL CHANGES, THAT THERE SHOULD BE ANY SIGNIFICANT CORRELATION.”
Now you appear to claim an almost perfect linear correlation and we agree that a relationship does mean correlation.  Right? 

Two quantitative variables can be related without necessarily being correlated just as they can be correlated without necessarily being related. 
I did not assert that GDP and national stock indices are not correlated, you did, and unless I've made an error I think I've disproven your assertions.

I have done the maths you suggested and these are the outputs. I've never worked this out before so I'm as surprised by the numbers as anyone. And I am not claiming anything, but all the r values are greater than 95% 

The sources I refer to, the evidence they refer to, and the calculations I have done suggest the opposite of your assertion that a stock index can outgrow GDP, that growth of GDP acts as a cap on growth of a stock market index, with the caveats that valuations can change materially even over very long periods and corporate profits are not a constant proportion of GDP but can fluctuate materially even over very long periods (S&P 500 PE data from multpl.com, US corporate profits as a % GDP from

https://fred.stlouisfed.org/graph/?g=1Pik). Caveat: the latter source I understand to include private enterprises so I don't use that figure in any calculations, it's just helpful to illustrate.

And to be clear, I have never said that 2% is an absolute, constant or rule, it just appears to be an average (https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.msci.com/documents/10199/a134c5d5-dca0-420d-875d-06adb948f578&ved=2ahUKEwj85r6d_b7tAhWAQUEAHTLaDhwQFjALegQICRAB&usg=AOvVaw2yECfSMHHAykx8dJz6Mt-K, https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.researchaffiliates.com/documents/FAJ-2003-Two-Percent-Dilution.pdf&ved=2ahUKEwj-7oS-_b7tAhWPZMAKHYD4DAMQFjAAegQIAhAB&usg=AOvVaw3k73yZYUiPErU7pmTxLLQD).

[Deleted User]

Alright, please give me an example of two variables related to each other that are not correlated. 

[Deleted User]

P.S. there is no way on earth your calculation of the correlation coefficient is correct.   Too busy now but will look into it later.