_ LOS 13.b: Relation between long-run rate of stock market appreciation and sustainable growth rate of economy _

I do not quite understand the equation that:-

Change in price = change in GDP + change in (E/GDP) + change in P/E

The text states that in the long run, change in E/GDP will be zero. Change in P/E will be zero as investors will not continue to pay ever increasing price for same level of earnings…

Why is the level or earnings the same? Is it an assumption?

E/GDP is a ratio between 0 and 1, this means that the sum of all earnings of all companies in a country (aggregate earnings) can not exceed the whole GDP of the country, it always will be a portion of it. That portion (ratio) will mantain a determined level, because if aggregate earnings rise, the GDP also does.

P/E is a ratio too, in this equation we have the P/E ratio of the whole economy. Investors would never pay an indefinitely increasing price for a company that eventually will achieve a certain level of earnings (earnings never growth indefinitely), so the price level of a stock will always stay in a reasonable relation with the earnings its generates. For example, a company gives 5 dollars earnings per share, you know that paying 50 dollars for the stock is ok. Would you pay for a 6-dollar-earnings-per-share stock a price of 250 dollars? The relation of P and E is not reasonable. This is why in the long run the variation of P/E ratio will be zero, despite of P and E can grow up, but they will mantain a reasonable relation (ratio).

Summing up, company earnings of the whole economy can only grow with the growth of the GDP only. Aaaaand GDP grows with the growth of company earnings…

You’re getting hung up on the wrong point. All they are saying is there is a max price investors are willing to pay for a given level of earnings, so a P/E ratio can’t be constantly increasing, otherwise their yield (E/P) would approach zero. So in the long run, P/E remains relatively unchanged.

E/GDP is corporate profit share of GDP. This too cannot be constantly increasing because workers will not accept less and less pay while corporate earnings grow. People won’t work all the way down to slavery/free while E/GDP = ~1.

So in the extreme long run, the only thing that truly grows a stock price is the growth in the economy, because the other factors are mean-reverting at 0 on a net-change basis.

Using this idea, one could conclude that stock markets are overpriced today due to stagnant wage growth compared to corporate earnings, relatively high P/E ratios, and very low real GDP growth. Thus only the short term factors have provided corporate earnings growth recently.

That said, alot of people have called into questions whether the current higher multiples are sustainable given the low inlation/interest rate environment we are in. If this is the case, markets might not be as overvalued as many people think, but this is more theoretical than anything. Important point to remember is that aggregate profit margins and P/E are not expetced to change over the long term.