Oct

29

Using Robert Shiller's monthly data* (1900-2013 ), I constructed SP500 earnings yield:

E/P = (monthly earnings) / (SP500 price)

(Note this is conventional earnings yield, rather than his P/E adjusted with earnings smoothed over 10 years)

Shiller's data also contains contemporaneous "long interest rate"; GS10, which is 10 year Treasury Constant Maturity Interest Rate.

Used E/P and long interest rate to construct a "FED model": (E/P) - (long interest)

E/P - long interest is plotted monthly from 1910 - 2013 as the blue line.

For each month, mean monthly stock returns were calculated for the future 36 months (3 year mo avg return), plotted contemporaneously in red.

The FED model generated with this data is a great deal less stable than corresponding future stock market returns. This is in contrast to one of Shiller's main observations that stocks are too volatile compared to expected dividends (earnings, etc). It is an article of faith that investors and scientists are forced into stocks when bond yields are small compared to earnings yields. If this were true one would expect a more stable relationship than observed here.

Instead it appears the FED model changed around 1980; with E/P getting smaller than long interest rates - making the curve go negative. Recently it has trended back up as bond yields dropped and earnings stabilized. Perhaps we are headed back to an older religion.

anonymous writes: 

Please elaborate on your statement: "It is an article of faith that investors and scientists are forced into stocks when bond yields are small compared to earnings yields. If this were true one would expect a more stable relationship than observed here."

I don't understand your logic. Which are the independent variables? In the arbitrage-free model, isn't everything explained by the equity risk premium — which is yet another independent variable? And isn't the Fed model essentially a Cauchy (ratio) Distribution? I believe your comment therefore is to be expected. Please direct me to any academic papers (not popular press) where Shiller cites the Fed model. I thought his point is that stock prices move around a lot more than the underlying earnings/dividends. Is that incorrect? 


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