How and why is the Aggregate Equity Index= GDP*E/GDP*P/E ratio? And why is GDP ratio and GDP of P/E equal to zero in the long run?
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The value of the aggregate equity index is the sum of the prices of all the securities in the index. Let this figure be P. So, Aggregate Equity Index = P
Or, AEI = E*P/E = GDP * E/GDP * P/E
Hence, the equation.
Now, AEI has three components GDP, Earnings share of GDP (E/GDP) and P/E ratio.
It is clear that P/E cannot consistently grow. This means growth rate of P/E in the long run cannot be a positive or negative figure say 3% because this would mean that the price of the securities continuously rise in the long run and that they never go both up and down over the years. This can also mean that assuming a long term growth for P/E implies that the movement of stock prices is not random and rather is constantly growing. This is untrue and thus for the long term it is safe to say that P/E ratio’s growth is 0.
Similarly, Earnings cannot consistently rise in the long run. There will be periods of positive earnings and periods of negative earnings such that in the long run we cannot say that earnings consistently rise or fall. Thus, growth rate of earnings share of GDP is also assumed to be 0 in the long run.
This leaves us with just one component i.e., GDP. Growth on GDP in the long run. So, we can say that growth in aggregate equity index in the long run is equal to the growth rate in GDP.
By this logic, GDP also does not grow consistently. It can also go up and down?
Here, we are not talking about the short term ups and downs. We are talking about the long term movement. In the case of the other two in the long term there is no growth rate assumed because that would mean that in the long term they keep growing, which is absurd. However, long term GDP does have a growth rate. GDP is not constant. Even developed economies have a certain positive growth rate. In fact, we call this long term GDP growth rate as the trend rate.