Pension recovery performance 2020

Another_Saver

You can find a 2016 version of the Barclays Equity gilt study here (https://www.google.com/url?sa=t&source=web&rct=j&url=https://www.allocationblog.com/content/uploads/sites/3/2016/07/Equity-Gilt-Study-2016.compressed.pdf&ved=2ahUKEwj8kYOWib_tAhVmQEEAHacxC0UQFjAHegQICRAB&usg=AOvVaw09xOHJaiaGRAvInLXPGE_R).
I used the UK equity index, not the total return index. From 2015 onwards you would just multiply the 2015 Barclays index value by the 2016 FTSE all share year end value, divided by the 2015 year-end FTSE all value (you can get these from a Yahoo! Finance chart or any number of sources). Or you could stop at 2015 to save time.

ONS GDP at current prices (https://www.ons.gov.uk/economy/grossdomesticproductgdp/timeseries/ybha/qna). Link doesn't seem to work, either go to ONS/economy/GDP and select "GDP at market prices: current price" or just Google "ONS GDP at current market prices" 🤷‍♂️

All the US data came from multpl.com (because lazy). S&P 500 historic prices here (https://www.multpl.com/s-p-500-historical-prices/table/by-year), nominal GDP here (https://www.multpl.com/us-gdp/table/by-year).

Of course, any conclusions drawn from these data are endpoint sensitive.

LHW99

When do we get on to diffrential equations?

Another_Saver

Deleted_User said:

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

I'll explain it with a model, but this is theoretical.

If you model a stock index total return r over a period as the growth g of the index plus the dividend yield y (park the maths for a minute and let's just use arithmetic)
r = g + y

Then you can breakdown g into economic measures:

Inflation i

Population growth p

Real GDP per capita growth e

And three non-economic variables to mediate the difference:

Valuation change v - which must be a constant measure and relevant to the economic measures, I and the MSCI Barra paper use change in the PE multiple, Arnott and Bernstein use change in the dividend yield, I assume this data was easier to find but it has a flaw of not accounting for payout ratio changes. Accounting standards have no doubt changed, but so too perhaps have economic methodologies. Structural economic changes have also taken place (women at work, Empire to Commonwealth, Hawaii etc.). This is a random variable and over the long term you would expect this to average 0 c.p., in reality valuations since 1990 are far higher than prior historic norms (easy to see in the Barclays study back to 1900 for the UK, and multpl.com back to 1870 ish for the US).1825-1870 the geo average UK index dividend yield was 7.6% (https://www.google.com/url?sa=t&source=web&rct=j&url=https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.959.5232&rep=rep1&type=pdf&ved=2ahUKEwiK4rqJo7_tAhXBolwKHTQiCdYQFjACegQIDBAB&usg=AOvVaw2I7GgawMPVxIXBjbVdFOZY) and that includes Rail Mania.

Change in the number of shares per unit of market capitalisation, capital dilution (or "concentration"), d - a random variable that historic samples suggest averages -2% a year

Change in the size of the stock market relative to GDP (expansion or contraction), c, also a random variable which intuitively should average 0 long term.

Then g = [nominal GDP growth] i + p + e + [mediators] v + d + c

Where it gets more complicated, past the point I care to think about is how the latter 3 variables and the economy interact. All 3 have economic causes and economic consequences. Globalisation doesn't help either.

[Deleted User]

OK, mate.  I looked at what you did. I admit: it is a great discovery. Well impressed. 

You are looking at gross rather than real GDP figures and gross market cap (index). Both of these datasets include inflation. Then you took a dataset starting in 1948.  This period included high inflation, in some years over 20% (1975).  

In other words you compared two variables, which both included inflation. Surprise! You found that inflation is correlated to inflation. And its a linear dependence!  Very cool. Might not get a Nobel, but discovery it is.  We often get this phenomenon with graduates coming up with similar discoveries when they use computer codes for modelling, there is even a special term: s..t in, s..t out. 

Now, for a change, try to compare something slightly more meaningful. Like real GDP growth vs real return.  Not that finding that inflation is correlated to inflation wasn’t fruitful but still... 

Another_Saver

Another_Saver said:

Deleted_User said:

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

I'll explain it with a model, but this is theoretical.

If you model a stock index total return r over a period as the growth g of the index plus the dividend yield y (park the maths for a minute and let's just use arithmetic)
r = g + y

Then you can breakdown g into economic measures:

Inflation i

Population growth p

Real GDP per capita growth e

And three non-economic variables to mediate the difference:

Valuation change v - which must be a constant measure and relevant to the economic measures, I and the MSCI Barra paper use change in the PE multiple, Arnott and Bernstein use change in the dividend yield, I assume this data was easier to find but it has a flaw of not accounting for payout ratio changes. Accounting standards have no doubt changed, but so too perhaps have economic methodologies. Structural economic changes have also taken place (women at work, Empire to Commonwealth, Hawaii etc.). This is a random variable and over the long term you would expect this to average 0 c.p., in reality valuations since 1990 are far higher than prior historic norms (easy to see in the Barclays study back to 1900 for the UK, and multpl.com back to 1870 ish for the US).1825-1870 the geo average UK index dividend yield was 7.6% (https://www.google.com/url?sa=t&source=web&rct=j&url=https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.959.5232&rep=rep1&type=pdf&ved=2ahUKEwiK4rqJo7_tAhXBolwKHTQiCdYQFjACegQIDBAB&usg=AOvVaw2I7GgawMPVxIXBjbVdFOZY) and that includes Rail Mania.

Change in the number of shares per unit of market capitalisation, capital dilution (or "concentration"), d - a random variable that historic samples suggest averages -2% a year

Change in the size of the stock market relative to GDP (expansion or contraction), c, also a random variable which intuitively should average 0 long term.

Then g = [nominal GDP growth] i + p + e + [mediators] v + d + c

Where it gets more complicated, past the point I care to think about is how the latter 3 variables and the economy interact. All 3 have economic causes and economic consequences. Globalisation doesn't help either.

Why thank you. I'm glad we aren't shouting at each anymore. And I have to admit I can't think of an obvious example of a not necessarily causative relationship without necessary correlation and I've forgotten almost all of my degree to replace it with tax knowledge. But I think the model I suggested, though I presented it as an arithmetic sum for convenience it ought to be geometric, the output variable being a sum of independent (ish) random variables should explain how the relationship need not correlate to exist.

Inflation is immaterial to my point as it is the same for both indices, and does not affect the magnitude of GDP lag. According to the BofE 1948-2019 averaged 5.2% pa. 
I'm happy to work it out though the only ONS data going back to 1948 is RPI, I could try instead to compute a price index from comparing real and nominal GDP, also the Barclays study provides a price index but I'm sceptical of its reliability, and there are academic sources like our world in data.

[Deleted User]

“ Inflation is immaterial to my point as it is the same for both indices”.

You are claiming that two variables are related. Then you add a large and same variable to each.  Then you run it through excel and find a linear relationship.  Quelle surprise. 

Look... I am too lazy to google but real GDP growth in the developed economies has averaged under 2% for decades.  Nobody even reports gross GDP growth, its a meaningless number.  Real return on index investing has averaged... I am guessing 6% annual over the last two decades (based on my portfolio and I subtracted guesstimated inflation of 2%).  

If you remove high inflation period in your correlation calcs, the numbers would not be right but a bit more meaningful.  

Another_Saver

UK same GDP and equity index data, I used the spliced consumer price index to 2015 from our world in data and ONS cpi thereafter. This only provides full year price index data which I assume is the mid year price evel.

I could have used ons real GDP and the UK equity index in real prices from the Barclays study, but they don't seem to have the same inflation data so for consistency that's what I did. E.g. my 1948 real GDP is £305bn in 2019 prices, ONS is £365bn seems to be in 2018 prices.
UK real GDP/year start real stock index correlation 89.62%, 90.00% with yearend. If I use LNs, it's 81.84% and 83.73% respectively.

US data all from multpl.com, same GDP and S&P with their CPI (they use year start cpi, I apply that to the previous years GDP and stock index, i.e. 1930 GDP is turned into 1930 real GDP by multiplying by 1/1/20 CPI and dividing by 1/1/31 CPI. Year start 1930 stock index is turned into real terms using year start CPI for 1930, year end stock index is turned into real terms using CPI for next year start)

US Real GDP with real year start S&P 500 correl 89.76%
With year end 89.48%

LN real GDP correl with LN real year start S&P 87.16%, with yearend 88.10%.

Nb I assume that any value on 31/12 year 1 is the same on 1/1 year two, I.e. year starts and ends at the same point in time.

Are you going to make me deduct population growth next too?

garmeg

Can we move on to Fermat's Last Theorem please?

IvanOpinion

I am just trying to work out how to apply all this maths to my morning bowl of porridge

TBC15

IvanOpinion said:

I am just trying to work out how to apply all this maths to my morning bowl of porridge

I’m just wondering if there is enough milk in the bowl to drown myself.