The Aggregate Change in Shares and the Level of Stock Prices
Abstract
The average change in shares of equity is negatively correlated with estimates of the equity premium calculated using the dividend-ratio model of Campbell and Shiller, as well as with a variant of the model written in terms of the earnings-price ratio. This correlation is consistent with corporations issuing equity when it is a relatively inexpensive source of finance and repurchasing equity when it is a relatively good investment. However, when the retirement of shares resulting from mergers are included, the average change in shares is no longer significantly correlated with the equity premium.
Figure 1 Stock Market Data Log Earnings Price Ratio -1.8 -2.0 -2.2 -2.4 -2.6 -2.8 -3.0 -3.2 -3.4 1926 1934 1942 1950 1958 1966 1974 1982 1990 Growth in Earnings Minus T-Bill Return 28 .stP egatnecreP 60 40 20 0 -20 -40 -60 1926 1934 1942 1950 1958 1966 1974 1982 1990 Log Payout Ratio 0.4 0.2 -0.0 -0.2 -0.4 -0.6 -0.8 -1.0 1926 1934 1942 1950 1958 1966 1974 1982 1990
Figure 1 (cont.) Stock Market Data Change in Shares 29 tnecreP 8 7 6 5 4 3 2 1 0 -1 1926 1934 1942 1950 1958 1966 1974 1982 1990 Log Dividend Price Ratio -2.25 -2.50 -2.75 -3.00 -3.25 -3.50 -3.75 -4.00 -4.25 1926 1935 1944 1953 1962 1971 1980 1989 Growth in Dividends Minus T-Bill Return .stP egatnecreP 48 32 16 0 -16 -32 -48 -64 1926 1934 1942 1950 1958 1966 1974 1982 1990
Figure 2 FOF v. CRSP Change in Shares No Mergers Included in CRSP Change CRSP, All Corporations 30 tnecreP 5.0 2.5 0.0 -2.5 -5.0 CRSP FOF -7.5 1956 1961 1966 1971 1976 1981 1986 1991 1996 Mergers Included in CRSP Change CRSP, All Corporations tnecreP 3.2 1.6 -0.0 -1.6 -3.2 -4.8 -6.4 CRSP FOF -8.0 1956 1961 1966 1971 1976 1981 1986 1991 1996 Mergers Included in CRSP Change CRSP, Nonfinancial Corps. tnecreP 3.2 1.6 -0.0 -1.6 -3.2 -4.8 -6.4 CRSP FOF -8.0 1956 1961 1966 1971 1976 1981 1986 1991 1996
Figure 3 Equity Premium(t) and Change in Shares(t-5) No Mergers <-Shares Spread-> 31 tnecreP Percentage Pts. 8 40 7 30 6 5 20 4 10 3 2 0 1 -10 0 -1 -20 1931 1939 1947 1955 1963 1971 1979 1987 1995 With Mergers <-Shares Spread-> tnecreP Percentage Pts. 7.5 40 30 5.0 20 2.5 10 0.0 0 -2.5 -10 -5.0 -20 1931 1940 1949 1958 1967 1976 1985 1994
Figure 4 Earnings-Ratio v. Dividend-Ratio Model Log Earnings-Price Ratio 32 tnecreP -1.8 Actual Const. Prem. -2.0 -2.2 -2.4 -2.6 -2.8 -3.0 -3.2 -3.4 1927 1935 1943 1951 1959 1967 1975 1983 1991 Log Dividend-Price Ratio tnecreP -2.25 Actual Const. Prem. -2.50 -2.75 -3.00 -3.25 -3.50 -3.75 -4.00 -4.25 1927 1936 1945 1954 1963 1972 1981 1990 Implied Expected Equity Premium .stp egatnecreP 8.8 8.0 7.2 6.4 5.6 4.8 4.0 E-R Model D-R Model Mean 3.2 1927 1935 1943 1951 1959 1967 1975 1983 1991 Difference Between The Expected Premia Earnings-Ratio minus Dividend-Ratio .stp egatnecreP 0.42 0.28 0.14 0.00 -0.14 -0.28 -0.42 -0.56 1927 1936 1945 1954 1963 1972 1981 1990
Figure 5 Ex-Ante Premium v. Realized Spread No Post Sample Data 33 .stp egatnecreP 10 D-R Model Realized 9 8 7 6 5 4 3 1927 1935 1943 1951 1959 1967 1975 1983 1991 Post Sample Data=Mean .stp egatnecreP 10 D-R Model Realized 9 8 7 6 5 4 3 1927 1935 1943 1951 1959 1967 1975 1983 1991
Figure 6 Change in Shares and The Equity Premium Dividend-Ratio Model <--Shares Premium--> 34 tnecreP Percentage pts. 8 8.8 7 8.0 6 7.2 5 4 6.4 3 5.6 2 4.8 1 4.0 0 -1 3.2 1927 1936 1945 1954 1963 1972 1981 1990 Earnings-Ratio Model <--Shares Premium--> tnecreP Percentage pts. 8 8.5 7 8.0 6 7.5 5 7.0 4 6.5 3 6.0 2 5.5 1 5.0 0 4.5 -1 4.0 1927 1936 1945 1954 1963 1972 1981 1990
Cite this document
William R. Nelson (1999). The Aggregate Change in Shares and the Level of Stock Prices (FEDS 1999-08). Board of Governors of the Federal Reserve System, Finance and Economics Discussion Series. https://whenthefedspeaks.com/doc/feds_1999-08
@techreport{wtfs_feds_1999_08,
author = {William R. Nelson},
title = {The Aggregate Change in Shares and the Level of Stock Prices},
type = {Finance and Economics Discussion Series},
number = {1999-08},
institution = {Board of Governors of the Federal Reserve System},
year = {1999},
url = {https://whenthefedspeaks.com/doc/feds_1999-08},
abstract = {The average change in shares of equity is negatively correlated with estimates of the equity premium calculated using the dividend-ratio model of Campbell and Shiller, as well as with a variant of the model written in terms of the earnings-price ratio. This correlation is consistent with corporations issuing equity when it is a relatively inexpensive source of finance and repurchasing equity when it is a relatively good investment. However, when the retirement of shares resulting from mergers are included, the average change in shares is no longer significantly correlated with the equity premium.},
}