Modern “Efficient Markets” J. Bradford DeLong Professor of Economics, U.C. Berkeley Research Associate, NBER delong@econ.berkeley.edu January 19, 2009 DRAFT
Introduction The real value P of a stock market index can be written: (1)
Pt =
Dt rt − gt
where D are the dividends paid on the index, and r and g are the suitablydefined required expected real rates of return and expected rates of real € dividend growth, respectively. We can divide the price by a ten-year moving-average of earnings to obtain the Graham Ratio: (2)
Pt D t / E 10 t = E 10 r − g t t t
Taking logs:
€ (3)
P D ln 10t = ln 10t − ln(rt − gt ) Et Et
and approximating the last term by: €
(4)
ln(rt − gt ) = ln(r0 − g0 ) +
Δrt Δgt − r0 − g0 r0 − g0
€
1
we get: (5)
P D Δgt Δrt ln 10t = − ln(r0 − g0 ) + ln 10t + − Et E t r0 − g0 r0 − g0
Fluctuations in the log Graham Ratio of prices to a ten-year movingaverage of earnings are therefore attributable to (a) fluctuations in the € value of current and expected future dividends: (6)
D Δgt ln 10t + E t r0 − g0
(b) fluctuations in required expected rates of return: €
(7)
−
Δrt r0 − g0
and, (c) their covariance. € t's very puzzling. Fama believes that the market is very "efficient." He also
believes (or at least John Cochrane believes, and Fama has written a bunch of papers with French in which he finds evidence that) a major source of risk in short-term stock market investments is "time-varying required expected rates of return." What that means is that a big source of short-term stock market risk is that the market will suddenly go up--and then afterwards expected returns will be low--or that the stock market will go down--and then afterwards expected returns will be high. As long as your personal rate of discount does not fluctuate with the stock market's expected return, there are lots and lots of opportunities for value investors whenever marketwide price-earnings ratios are low (and not so many when price-earnings ratios are high). And as long as the horizon of your investments is long, stock markets are much less risky to you than to
2
the agents who drive prices--and that opens up further opportunities for patient value investors. But Fama would still say that the market is "efficient," although in what sense I cannot determine...
References John Boehner, ed. (2009), “Stimulus Spending Skeptics: Economists Express Doubts About Trillion Dollar Spending Plan” <http://republicanleader.house.gov/UploadedFiles/stimulusskeptics.pdf>. Michael Cannon (2009), “Contribution” to John Boehner, ed. (2009), “Stimulus Spending Skeptics: Economists Express Doubts About Trillion Dollar Spending Plan” <http://republicanleader.house.gov/UploadedFiles/stimulusskeptics.pdf>. John Cochrane (2001), Asset Pricing (Princeton: 0691121370). John Cochrane (2009), “Fiscal Silliness” (University of Chicago) <http://faculty.chicagogsb.edu/john.cochrane/research/Papers/fiscal2.htm> . Eugene Fama (2009), “Bailouts and Stimulus Plans” (University of Chicago) <http://www.dimensional.com/famafrench/2009/01/bailoutsand-stimulus-plans.html>. Milton Friedman (1972), "Comment on the Critics," Journal of Political Economy 80:5 (September-October), pp. 914-5 <http://www.jstor.org/stable/pdfplus/1830418.pdf>. R. G. Hawtrey (1925), “Public Expenditure and the Demand for Labour,” Economica 13 (March), pp. 38-48. Friedrich A. von Hayek (1931) [1967], Prices and Production (Augustus Kelley).
3
John Hicks (1937), “Mr. Keynes and the ‘Classics’: A Suggested Interpretation,” Econometrica 5:2 (April), pp. 147-59. John Maynard Keynes (1932), Essays in Persuasion (Macmillan). Paul Krugman (2008), “Keynes’s Difficult Idea,” New York Times (December 24) <http://krugman.blogs.nytimes.com/2008/12/24/keynessdifficult-idea/?apage=2>. Frederick Leith-Ross (1929), “Memorandum to Sir Richard Hopkins and P.J. Grigg.” N. Gregory Mankiw (2009), “Fama on Fiscal Stimulus” (Harvard) <http://gregmankiw.blogspot.com/2009/01/fama-on-fiscal-stimulus.html>. N. Gregory Mankiw (2002), Macroeconomics 5e (Worth: 0716752379). Allan Meltzer (1989), Keynes’s Monetary Theory: A Different Interpretation (Cambridge University: 0521306159). Roger Middleton (2005), Toward the Managed Economy (Routledge: 9780-415-37977-9). G. C. Peden (1988), Keynes, the Treasury, and British Economic Policy (MacMillan: 0333362721). G. C. Peden (2005), Keynes and His Critics: Treasury Responses to the Keynesian Revolution, 1925-1946 (British Academy: 0197263224). Tim Peterson (2009), “I Have Thought About the Fama Article a Bit More…” <http://delong.typepad.com/sdj/2009/01/famas-fallacy-v-arethere-ever-any-wrong-answers-in-economics.html#comment6a00e551f080038834010536d0b4f8970b>. R. S. Sayers (1976), The Bank of England 1891-1944 (Cambridge University: 0521214750).
4
Joseph Schumpeter (1934), â&#x20AC;&#x153;Depressions,â&#x20AC;? in D.V. Brown et al. (1934), Economics of the Recovery Program (Macmillan).
5