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Thank you Michael Alexander for the interesting note. Three points.
R = ‘real’ cumulative retained earnings = cumulative (retained earnings / price index).
According to this definition, R is an aggregation of the ratio between two nominal series. I don’t know how this aggregation is a proxy of ‘real’ capital — first, because retained earnings are at best the consequence of ‘real’ capital; and second, because ‘real’ capital, understood as a material/productive entity, is unknowable to anyone and everyone, including economists. Yes, Marxists claim that the ‘capital stock’ is ploughed-back surplus value (incarnated as ‘real’ retained earnings), though you cannot operationalize this claim with historical summation when prices deviate from values (whatever they might be) and when technical change makes existing plant and equipment useless/worthless to an unknowable degree.
P/R = S&P 500 price index / R = S&P 500 price index / cumulative (retained earnings / price index).
This is a relationship between three nominal indices. It is bounded because the denominator R is a rising series with the same slope as the stock market trend. Take any other rising series with a similar slope — or the stock market trend for that matter — and you get the same result.
I’m not sure I understand your last chart and associated explanation.