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Abstract
This paper builds a model to predict US stock market returns over the next 50 years. The results of the model are an expected real rate of return after inflation, taxes, and overheads of 2.7% per year. Before taxes and overheads the rate of return is 4.0%. This rate of return is compared to other models and to the historical rate of return of the stock market, and after making certain adjustments is found to be broadly in agreement.Shortcut to the Bottom Line
Rather than read this paper it is possible to bypass the model
constructed, and take a shortcut to an approximate bottom line.
Shiller 1946-2006 shortcut
Shiller
reports 3.60% dividends, 3.33% real capital gains for a total
6.93% real return for equity for the period 1946-2006. We can use
this to project future returns assuming no change in the P/E ratio:
projected return = historical + changing + payout + GDP
before tax return P/E10 correction correction
= 6.93% + -0.98% + -0.82% + -1.0%
= 4.1% (approximate estimate)
Where "changing P/E10" accounts for the difference in P/E ratios based
on 10 years of earnings at the beginning and end of the historical
period, "payout correction" accounts for the difference in payout in
the present period and the historical period and is computed as:
payout total 1 1
correction = payout x ( ------------------ - --------------------- )
ratio P/E present period P/E historical period
= 53% x ( 1 / 17.4 - 1 / 13.7 )
= -0.82%
where 53% is the historical total payout ratio for this period (based
on 0.30% net share repurchases), 13.7 is the 1/(geometic mean of (1 +
E/P) - 1), and 17.4 is the current P/E ratio.
In computing P/E present period it is assumed earnings are at their normal level, and not subject to a short term drop or increase.
Shiller 1946-2001 shortcut
Shiller reports 3.77% dividends, and 3.48% real capital gains for a total 7.25% real return for equity for the period 1946-2001. We can use this to project future returns assuming no change in the P/E ratio:
projected return = historical + changing + payout + GDP
before tax return P/E10 correction correction
= 7.25% + -1.27% + -0.94% + -1.0%
= 4.0% (approximate estimate)
Where "changing P/E10" accounts for the difference in P/E ratios based
on 10 years of earnings at the beginning and end of the historical
period, "payout correction" accounts for the difference in payout in
the present period and the historical period and is computed as:
payout total 1 1
correction = payout x ( ------------------ - --------------------- )
ratio P/E present period P/E historical period
= 53% x ( 1 / 17.4 - 1 / 13.3 )
= -0.94%
where 53% is the historical total payout ratio for this period (based
on 0.22% net share repurchases), 13.3 is the 1/(geometic mean of (1 +
E/P) - 1), and 17.4 is the current P/E ratio.
Siegel 1946-2001 shortcut
Siegel (2002) reports a historical 7.1% real return for equity for the period 1946-2001. Factoring in how the future is likely to be different than the past, we can use this to project future returns:
projected return = historical + changing + payout + GDP
before tax return P/E10 correction correction
= 7.1% + -1.3% + -0.7% + -1.0%
= 4.1% (approximate estimate)
Where "changing P/E10" accounts for the difference in P/E ratios based
on 10 years of earnings at the beginning and end of the historical
period (based on Shiller's data), "payout correction" accounts for the
difference in payout in the present period and the historical period
and is computed as:
payout total 1 1
correction = payout x ( ------------------ - --------------------- )
ratio P/E present period P/E historical period
= 58% x ( 1 / 17.4 - 1 / 14.5 )
= -0.7%
where 58% is the historical total payout ratio for this period (or
rather 1960-2001 where there is data), and the historical P/E of 14.5
has been imputed to give the claimed historical total payout of 3.8%
dividends plus 0.2% net share repurchases. Other approaches to
estimating the historical P/E ratio involve measurement of the NIPA
and Flow of Funds data and are 1 / (geometric mean of (1 + E/P) - 1)
which is 11.9; a harmonic mean for the historical P/E is 11.8; an
arithmetic mean for the historical P/E is 13.6; and a geometric mean
for the historical P/E is 12.6.
S&P 500 P/E ratio data: Earnings
and Historical
P/E. S&P 500 P/E (1946-2001) 13.3, (1937-2007Q2) 13.4 computed as
1 / (geometric mean of (1 + E/P) - 1).
Introduction
Nobody knows what stock market returns might be tomorrow, next week, or even next year. In the short term stock market returns contain a lot of noise. However, over longer periods of time it is possible to make reasonable predictions about the stock market. The stock market is part of the larger economy, and reasonably accurate predictions can be made regarding growth of the larger economy. The larger economy defines boundaries within which the stock market must grow.It would be a fallacy to predict stock market returns in the future by looking at the past. The future will be different than the past. An aging population is expected to depress GDP, dividend yields are at historically low levels, and stock buy backs and employee stock options are new phenomena that are likely to affect stock prices. The significant impact of income taxes on returns is also all to often ignored. To predict US stock market returns over the next 50 years it is necessary to build a model that takes into account all of these factors.
This study considers the future returns of the stock market as a whole, such as returns for the Vanguard Total Stock Market Index Fund which attempts to mirror the MSCI US Broad Market Index or the Dow Jones Wilshire 5000 Index.
Abbreviations:
- CPI = Consumer price index
- D = dividends
- E = earnings
- GDP = Gross domestic product
- P = market capitalization
Equity returns and GDP
It would be expected that since corporations are part of the economy, corporate profits will over the long run have to grow at the same rate as GDP. In the short run this is roughly true, as can be seen by in the following graph of corporate profits relative to nominal GDP (BEA NIPA tables 1.1.5, 1.12):
Ignoring the Great Depression in the 1930s, the ratio of corporate profits to nominal GDP can be seen to be roughly a constant indicating they are both growing at the same rate. In the long run the relationship between these two variables is even stronger as is born out by data from the BEA (NIPA tables 1.1.6, 1.1.9, 1.12) and the Fed. (Z.1 table L.213, line 1):
1930 1950 2000 2005 30-00 50-05
real growth per year
Real GDP ($b) 790.7 1777.3 9817.0 11048.6 3.7% 3.4%
GDP deflator (2000 base) 11.5 16.5 100.0 112.7
Corporate profits with IVA and CCAdj ($b) 7.5 36.0 817.9 1330.7 3.7% 3.1%
Profits after tax with IVA and CCAdj ($b) 6.6 18.1 552.7 931.4 3.3% 3.7%
Corporate equities market value ($b) n/a 142.7 17627.0 18177.7 n/a 5.5%
P/E (after tax) - 7.9 31.9 19.5
NIPA dividends not shown because they include interest payments
by investment companies and other items that make them
inapplicable to the understanding of the corporate space. NIPA
dividends / market value are much greater than the stock markets
reported dividend yield.
Real growth per year in profits before tax (with Inventory Valuation
Adjustment and Capital Consumption Adjustment) has exactly matched GDP
growth in the 30-00 time period. In the 50-05 period profit growth
lagged GDP growth slightly by 0.3% per year or an aggregate 18% lag.
This lag will be discussed later when equity returns are compared to
historical data.
Real growth in profits after tax has also matched GDP growth apart from differences due to changes in the corporate tax rate. (The increase in after tax rates for 50-05 is primarily on account of the relaxation of the 50% corporate tax rate of 1950).
Dividends and net share repurchases are paid out of profits after tax, and have historically represented a semi-stable proportion of profits after tax of roughly 50-60% as reported by Liang and Sharp (1999). Consequently the total pay out, comprising dividends and net share repurchases, is expected to grow at the rate of GDP.
Corporate equities market value has grown faster than GDP on account of changing P/E ratios.
GDP growth rate
GDP is the aggregate economic output of a country. It is reported by the BEA (NIPA table 1.1.6):
real annual real
GDP increase
($2000/b)
1930 791 -
1940 1034 2.7%
1950 1777 5.6%
1960 2502 3.5%
1970 3772 4.2%
1980 5162 3.2%
1990 7113 3.3%
2000 9817 3.3%
1930-2000 3.7%
1950-2000 3.5%
2001 9891 0.8%
2002 10049 1.6%
2003 10301 2.5%
2004 10704 3.9%
2005 11049 3.2%
2006 11415 3.3%
GDP is analyzed based on its individual components:
"The real growth rate in gross domestic product (GDP) equals the combined growth rates for total employment, productivity, and average hours worked. Total employment is the sum of the U.S. Armed Forces and total civilian employment, which is based on the projected total civilian labor force and unemployment rates."In previous versions of this paper we estimated each of the individual components of GDP. Productivity growth was predicted to be constant. We now realize this is wrong. As the rate of employment growth declines lowering GDP in the future, the amount of capital per worker should increase, increasing productivity, and this should boost GDP. Additionally capital can move overseas, either US firms can operate overseas, or capital can invest directly in foreign corporations. In sum, a GDP drop associated with declining employment growth rates will have a lesser effect on returns to capital.--- Social Security Administration 2006 OASDI Trustees Report (2006)
According to "market timer" on the diehards.org forum: "It is a common assumption in macroeconomics models that GDP will grow at a rate of (1/3)*(percent change in capital) + (2/3)*(percent change in labor) + change in technology." In their 2007 report the SSA Trustees project productivity unchanged at 1.7%, labor dropping from 1.7% to 0.3% and hours worked rising from -0.3% to 0.0% compared to the 1965-2005 time period. So the net change in labor is -1.1%, and the resulting net change in GDP is -0.7%.
GDP projection
In the 1965-2005 time period real GDP has grown 3.1% per year. However, a declining labor force will reduce the GDP:
projected historical effect of change
GDP growth = GDP growth + in labor force
= 3.1% + -0.7%
= 2.4%
The Philadelphia
Fed. Survey of Professional Forecasters (1st quarter surveys)
projects the growth rate for real GDP over the next 10 years:
10 year GDP projection
2000Q1 3.05%
2005Q1 3.3%
2006Q1 3.2%
2007Q1 3.0%
The GDP estimate we have made thus seems reasonable, if a little low.
It agrees with the 2007 projection made by the SSA Trustees of 2.4%.
| Projected real GDP growth rate = 2.4% |
Equity returns
The Gordon formula says:
real return = adjusted dividend yield + real dividend growth rate
Where adjusted dividend yield is defined to include all forms of
dividend paid by corporations to investors including net share
repurchases, and real dividend growth rate is defined to include all
forms of dividend growth including new issue slippage.
Thus:
projected real return = (D/P + net repurchases/P) + (GDP growth rate - slippage)
D/P
An estimate of D/P can be gained by looking at stocks directly (Vanguard Research VTSAX fund -> overview, holdings):
P/E E growth D/P
5 years
Jan 2005 22 7.5% 1.4% + 0.09% = 1.49%
Jun 2005 19 11.0% 1.7% + 0.09% = 1.79%
Aug 2006 17.2 15.8% 1.76% + 0.09% = 1.85%
Dec 2006 17.9 18.5% 1.60% + 0.09% = 1.69%
Sep 2007 17.4 21.4% 1.75% + 0.09% = 1.84%
The reported D/P reported by Vanguard is net of expenses. Expenses
are added back to find out the behavior of the idealized stock market.
Expenses are subtracted out again later when considering overheads and
taxation in order to get real world estimates of returns.
| Projected D/P = 1.8% [2007 Aug.] |
Net repurchases/P
Estimating net repurchases/P is more difficult. Liang and Sharp (1999) report:"We estimate the effects of share repurchases and employee stock option exercises on net share retirements for large S&P 500 companies. We find that, over the past five years, gross repurchases have reduced shares outstanding 2 percent annually; but, owing to the exercise of employee stock options, only about half of those shares were actually retired. Given the recent pace of employee stock option grants, and assuming that equities continue to be priced at about 30 times earnings, our analysis suggests that the pace of net share retirements will fall well below the pace of the last few years, unless corporations use nearly all their earnings to fund shareholder payouts. Moreover, over the long haul, assuming corporations need to retain 40 to 50 percent of their earnings to invest and grow at historical rates, the long-run average pace of net share retirements is likely to fall to 1/2 percent or less."Liang and Sharp estimate a sustainable rate of share repurchases as:
net repurchases/P = repurchases/P - net options exercised/P
= 0.57% [1999 looking forward]
The above value was for when the P/E ratio was approximately 30.
Updating for the current value:
net repurchases/P = 1.0% [2006 Dec.]
Alternatively more recent data could be used. Weston and Siu
(2003) present share repurchase data:
repurchases/$b
1990 36.1
1991 20.4
1992 35.6
1993 38.3
1994 73.8
1995 99.5
1996 176.3
1997 181.8
1998 237.3
1999 164.6
2000 158.1
2001 177.4
Wilcox
(2003) reports employee stock options net gain on exercise:
options/$b
1995 11.3
1996 20.7
1997 36.8
1998 60.8
1999 95.0
2000 110.6
2001 57.3
2002 31.3
Taking the 2001 data on repurchases and options from both, and price
levels from the Fed. (Z.1
table L.213, line 1):
net repurchases/P = (repurchases - net options exercised) / P
= (177.4 - 57.3) / 15310.6
= 0.78% [2001]
Adjusting this for the P/E levels now versus those in 2001 (27.2):
net repurchases/P = 1.2% [2006 Dec.]
Alternatively, data from the Fed. (Z.1 table F.102 - line
38) for nonfarm nonfinancial corporate business could be combined with
data from the BEA (NIPA table 1.12):
net profits net repurchases /
repurchases/$b after tax/$b profits after tax
1946 -1.0 8.7 -11%
1947 -1.1 12.4 -9%
1948 -1.0 18.7 -5%
1949 -1.2 18.9 -6%
1950 -1.3 18.1 -7%
1951 -2.1 18.6 -11%
1952 -2.3 19.9 -12%
1953 -1.8 19.4 -9%
1954 -1.6 21.2 -8%
1955 -1.7 27.5 -6%
1956 -2.3 26.5 -9%
1957 -2.4 26.9 -9%
1958 -2.0 24.5 -8%
1959 -2.1 32.0 -7%
1960 -1.4 31.0 -5%
1961 -2.1 32.0 -7%
1962 -0.4 39.2 -1%
1963 0.3 42.6 1%
1964 -1.1 48.3 -2%
1965 0.0 56.4 0%
1966 -1.3 59.3 -2%
1967 -2.4 58.4 -4%
1968 0.2 59.2 0%
1969 -3.4 55.4 -6%
1970 -5.7 48.9 -11%
1971 -11.4 59.9 -19%
1972 -10.9 69.7 -16%
1973 -7.9 75.5 -10%
1974 -4.1 63.0 -7%
1975 -9.9 83.2 -12%
1976 -10.5 98.1 -11%
1977 -2.7 118.0 -2%
1978 0.1 131.8 0%
1979 7.8 133.2 6%
1980 -10.4 113.9 -9%
1981 13.5 141.8 10%
1982 -1.9 143.2 -1%
1983 -20.0 183.6 -11%
1984 79.0 221.1 36%
1985 84.5 230.9 37%
1986 85.0 209.8 41%
1987 75.5 238.4 32%
1988 129.5 291.0 45%
1989 124.2 280.5 44%
1990 63.0 292.4 22%
1991 -18.3 312.6 -6%
1992 -27.0 330.6 -8%
1993 -21.3 370.9 -6%
1994 44.9 406.5 11%
1995 58.3 478.0 12%
1996 47.3 554.5 9%
1997 77.4 622.4 12%
1998 215.5 553.3 39%
1999 110.4 592.6 19%
2000 118.2 552.7 21%
2001 48.1 563.2 9%
1946-2001 2.35%
2002 41.6 693.7 6%
2003 42.0 749.9 8%
2004 126.6 923.9 14%
2005 363.4 979.9 37%
1985-2005 18.95%
2006 614.1 1099.8 56%
1946-2006 4.14%
2007Q1 572.8 1095.2 52%
2007Q2 770.0 1152.2 67%
Where all of the above net repurchases / profits after tax values need
to be increased by around 28%, to capture farm and financial corporate
business. (According to Vanguard: VTSAX Fund Holdings, 22%
of the total US stock market is made up of the Financial sector as of
2007-08-31. So this alone would warrant a 28% increase, while data
from the Fed. suggests the farm corporate business sector is tiny,
perhaps a little short of 0.5%).
Note, this data set doesn't mesh well with the Weston and Siu, BEA measures.
The current high net repurchases may be due to the 2007 fad of leveraged buyout, paying cash to initiating firm, and refloating with more debt. Examining data from the Fed. (Z.1 table F.102 - line 39, 38, 37) for nonfarm nonfinancial corporate business
net credit market instruments/$b net repurchases/$b net funds raised in markets/$b
(bonds, commercial paper, loans, ...)
1985 182.9 84.5 98.4
1986 223.9 85.0 138.9
1987 162.7 75.5 87.2
1988 222.4 129.5 92.9
1989 160.0 124.2 35.8
1990 136.4 63.0 73.4
1991 -52.9 -18.3 -34.6
1992 24.3 -27.0 51.3
1993 32.5 -21.3 53.8
1994 126.3 44.9 81.4
1995 227.3 58.3 168.9
1996 183.7 47.3 136.4
1997 291.5 77.4 214.1
1998 396.9 215.5 181.4
1999 370.2 110.4 259.8
2000 341.8 118.2 223.6
2001 215.2 48.1 167.1
2002 12.9 41.6 -28.7
2003 88.6 42.0 46.6
2004 165.2 126.6 38.7
2005 245.0 363.4 -118.4
2006 436.9 602.1 -165.2
Some increased borrowing appears to be occuring concurrent with the
recent increased repurchases, and thus they might be unsubstainable.
It is not totally beyond historical bounds though. Recently, net
funds raised in markets is negative, thus companies are probably
depleting their treasury in order to pay out the substantial net
repurchases amounts. This is clearly not sustainable.
A sustainable level of net repurchases based on historical data is:
sustainable net repurchases = recent historical repurchase rate x recent profits after tax
= 18.95% x $931.4b
= $177b
As a rough estimate of recent history (adding in 28% or so for farm
and financial corporate business) estimate the projected level of
total repurchases at $227b, and take the price level from the Fed. (Z.1 table L.213, line
1). Also add back the $26b in venture capital related share issues in
order to approximate net repurchases for the public markets (National Venture Capital
Association 2006):
net repurchases/P = (227 + 26) / 19306.3
= 1.3% [2006 Dec.]
All three of these estimates for net repurchases/P are close to each
other. The Fed. estimate will be used:
| Projected net repurchases/P = 1.3% [2006 Dec.] |
As Liang and Sharp point out a given level of repurchases may be unachievable without companies going into debt or growth slowing due to the lack of the historical 40-50% reinvestment of earnings. This estimate is reasonable, giving a total pay out ratio in the expected 50-60% range.
total pay out ratio = (D/P + net repurchases/P) * P/E
= (1.8% + 1.3%) * 17.4
= 54%
For the S&P 500 dividend pay out ratio + NIPA non-financial net
repurchases / earnings, a 58% average total pay out was recorded for
the period 1960-2001 (data based on Wright 2004). The previous
relationship could also have been used to compute D/P + net
repurchases/P, or just net repurchases/P, as:
net repurchases/P = 58% / P/E - D/P
= 58% / 17.4 - 1.8%
= 1.5% (alternative estimate)
Strictly speaking existing company new share issues should be
subtracted from the Liang and Sharp, and Weston and Siu and BEA
estimates, but these are both small, below 0.1% in 1997 according to
Liang and Sharp, and captured in the methodology for estimating new
company slippage below.
Slippage
Slippage is the difference between the growth in GDP and the growth of an initial investment in the stock market. Slippage results from investors not being able to invest in the full corporate space, but only public issues. New companies have a diluting effect on investor returns relative to GDP. Estimating slippage is hard.Bernstein (2002) estimates slippage as 2.15% for the period 1926-2001 comparing CRSP 1-10 capitalization to CRSP 1-10 price data. Bernstein fails to correct for changes in the P/E ratio between the start and end of the interval over which he measures slippage. Bernstein subsequently published his work in the Financial Analysts Journal with Arnott as a co-author. His findings have not changed substantially.
Bernstein measures slippage by comparing a capitalization index to a price index. A capitalization versus price index measure of slippage fails to account for the fact that the public corporate market now accounts for more of the business space than it did historically. An example of this increasing public corporatization can be seen by looking at the NIPA (table 1.12). Corporate income relative to proprietor's income has increased 80% from 1926 to 2005. Thus as proprietorships incorporate, the capitalization index increases, the price index remains constant, and measured slippage increases.
Johnson (2005) initially independently estimates slippage (termed the lag factor) at 1.0% for the period 1925-1995 comparing GDP to the S&P 500. After correcting for changing P/E ratios Johnson got slippage values of 1.4 and 1.5%.
There is no need to worry about share repurchases and option exercises significantly effecting Bernstein or Johnson's slippage estimates because although significant in magnitude, they have waxed and waned over history to largely cancel out. This is as the earlier data shows only averaging 2.35% of earnings after tax (plus around 25%) for the period 1946-2001.
Perhaps a more accurate estimate of slippage can be obtained by starting with Siegel (2002) which reports a historical 7.1% real return for equity on a 3.8% dividend yield for the period 1946-2001. As just mentioned net repurchases/E averaged 2.35% x 128% = 3.0% for the period, while the P/E ratio was 12.6 at the start of the period and 27.2 at the end of the period (data below). 13.7 is a reasonable estimate for the average P/E ratio over the period according to Shiller. If net repurchases/E is divided by this P/E it gives 0.2% as a rough estimate for net repurchases/P over the 1946-2001 time period. GDP growth for this time period was 3.4% (see calculation of GDP growth for 1946-2001 below). Earlier when comparing equity returns to GDP it was noted equity returns had lagged GDP by 0.3% in the 50-05 period. Doing the same mini-calculation for the 1946-2001 period using data from the BEA (NIPA tables 1.1.6, 1.1.9, 1.12) and the Fed. (Z.1 table L.213, line 1):
1946 2001 46-01
real growth per year
Real GDP ($b 2000) 1589.4 9890.7 3.38%
GDP deflator (2000 base) 14.0 102.4
Corporate profits with IVA and CCAdj ($b) 17.8 767.3 3.3%
Profits after tax with IVA and CCAdj ($b) 8.7 563.2 4.0%
Corporate equities market value ($b) 109.7 15310.6 5.5%
P/E (after tax) 12.6 27.2
P/E ratios changed during the 1946-2001 time period. The annual
growth in P of 5.5% exceeded the annual growth in E of 4.0% by 1.5%.
This data is subject to instabilities in the profit after tax value,
so rather than use this data we use the annual change in the P/E10
ratio reported by Shiller for 1946-2001 of 1.27%. Combining all of
the above factors:
actual real return = changing P/E10 ratio + (D/P + net repurchases/P)
+ (GDP growth rate - slippage)
7.1% = 1.3% + (3.8% + 0.2%) + (3.4% - slippage)
slippage = 1.6%
Or performing the same calculation using data from Shiller 1946-2001:
actual real return = changing P/E10 ratio + (D/P + net repurchases/P)
+ (GDP growth rate - slippage)
7.25% = 1.27% + (3.77% + 0.22%) + (3.38% - slippage)
slippage = 1.39%
Or performing the same calculation using data from Shiller 1946-2006:
actual real return = changing P/E10 ratio + (D/P + net repurchases/P)
+ (GDP growth rate - slippage)
6.93% = 0.98% + (3.60% + 0.30%) + (3.27% - slippage)
slippage = 1.22%
Therefore:
unadjusted historical slippage = 1.4%
It is necessary to consider the impact of changes to the corporate tax rate on slippage. According to the Tax Policy Center the corporate tax rate went from 38% in 1946 to 35% in 2001. This creates a 3% / (1 - 38%) or 4.8% increase in earnings, or 0.1% per annum. Adjusting for this increases historical slippage 0.1%:
historical slippage = 1.5%
We predict future slippage based on the past:
| Projected slippage = 1.5% |
The different slippage estimates and projections are compared in the following table:
period slippage author data
estimate
1871-2000 ~2.2% Bernstein & Arnott GDP vs. unspecified price index
1900-2000 1.5%* Bernstein & Arnott GDP vs. Dimson dividend growth data
1926-2001 2.3%+ Bernstein & Arnott CRSP 1-10 cap. vs. CRSP 1-10 price index
1926-2001 2.2%+ Bernstein CRSP 1-10 cap. vs. CRSP 1-10 price index
1946-2001 1.7% Irlam GDP vs. Siegel price data
1946-2001 1.5% Irlam GDP vs. Shiller price data
1946-2006 1.4% Irlam GDP vs. Shiller price data
1954-1990 1.5% Johnson GDP vs. S&P 500
1965-1995 1.4% Johnson GDP vs. S&P 500
2010-2050 1.5% Irlam projection
* - dividend model; ignores share repurchases
+ - capitalization versus price index; sensitive to increasing corporatization
Resulting equity returns
Bringing everything together:
projected real return = (D/P + net repurchases/P) + (GDP growth rate - slippage)
= (1.8% + 1.3%) + (2.4% - 1.5%)
= 4.0% [2007 Sep.]
This return will fluctuate if asset prices fluctuate causing the
dividend yield to fluctuate.
For comparison the historical, Siegel 1946-2001, rate of return:
historical real return = changing P/E ratio + (D/P + net repurchases/P)
+ (GDP growth rate - slippage)
= 1.3% + (3.8% + 0.2%) + (3.4% - 1.6%)
= 7.1% [1946-2001]
In summary:
| Projected long term return on equity = 4.0% |
Comparison to other models
Johnson (2005) employs a slightly different methodology and comes up with a estimate for the long term return on equity of 4.1%. Differences between this estimate and the present model are a 1.1% difference in GDP growth, a 0.4% difference in slippage estimates, and a 0.6% difference in dividend yield.Ibbotson and Chen (2002) construct an earnings model and predict 6.09% return after inflation. However 2.28% of this return is attributed to a much higher P/E ratio (25.96) than the historical average, which they interpret as the market expectation of higher earnings growth. P/E ratios have dropped significantly since then. This suggests mis-pricing as an alternative explanation, which they at the time dismissed on market efficiency grounds. Whatever the explanation, this term can now be safely dispensed with. The first of the two other components of return they consider is D/P + net repurchases/P which they capture as "INC(00) + ADY" and estimate as 2.05%. After correcting for the current P/E ratio this comes out to 3.1%, which is 0.0% above that of the current study. The second component is the growth component GDP growth rate - slippage, which they capture as "g(DIV) - g(PO)" and which comes out to 1.74%, compared to 0.9% in the present study. In total a 4.8% return is anticipated, 0.8% above the current study.
Comparison to historical data
For the period 1802-2001, Siegel reports a historical 6.9% real return for equity on a 5.2% dividend yield. Adjusting Siegel's return for the total pay out ratio of 3.1%, reduces the real return to 4.8%. EH.Net provides historical GDP data (below) showing real GDP growth of 3.7% per annum is 0.2% higher in the 1802-2001 period than the 3.5% projected for the future. Adjusting for this lowers the return to 4.6%, 0.6% above the present study.
1802 2001 1802-2001
real growth per year
Real GDP ($b 2000) 7.09 9890.7 3.7%
There isn't the historical data to correct for equity to GDP growth
rate variance, or changing P/E ratios, but the time period involved
means their effects should be small.
Equity overhead
It isn't possible to invest in equity directly. Holding shares involves transaction expenses as well as considerable time dealing with taxes and class action lawsuit claims. Investing in a mutual fund involves fund overheads. This study will only consider investing in an index based mutual fund or exchange traded index fund, since that is the only practical way to get the necessary diversification to match the returns of the broad stock market.For index funds, the annual overhead for Vanguard's Total Stock Market Index Fund Admiral shares is 0.09% per annum. This is one of the lowest expense ratios around. A typical index fund is around 0.5%. Rounding 0.09% to 0.1% reduces the long term return on equity 0.1%.
For exchange traded funds, Vanguard's Total Stock Market Index Fund VIPER shares expenses are slightly lower at 0.07% per annum, but this neglects the cost of buying and selling the shares, as well as the cost of holding cash while settlement of purchase takes place. Fees on S&P Depository Receipts (SPDRs) are $0.10 per $100 of market value per annum, or 0.1%. All in all, the overheads of exchange traded funds are probably similar to those of low cost index funds.
| Projected long term return on equity after overhead = 3.9% |
Inflation
Inflation is the rate at which the value of money decreases. The Consumer Price Index measures inflation.In the 1970's, and through to 1981, the CPI was extraordinarily high. It is now back to historic levels. CPI data is available from the BLS, including a CPI table:
Dec-Dec
1930-1940 -1.7%
1940-1950 5.6%
1950-1960 1.8%
1960-1970 2.9%
1970-1980 8.0%
1980-1990 4.5%
1990-2000 2.7%
1930-2000 3.4%
1950-2000 4.0%
2001 1.6%
2002 2.4%
2003 1.9%
2004 3.3%
2005 3.4%
2006 2.5%
The Philadelphia
Fed. Survey of Professional Forecasters (1st quarter surveys)
projects the inflation rate over the next 10 years.
10 year CPI projection
2000Q1 2.5%
2005Q1 2.5%
2006Q1 2.5%
2007Q1 2.4%
For the most part the inflation rate doesn't enter into the following
calculations. It only comes up when projecting after tax returns. A
high inflation rate increases the real amount of taxes.
| Projected inflation rate = 2.5% |
Equity taxation
It makes sense to hold assets as long as possible, so that capital gains will not suffer from repeated taxation.The expected return on equity after overhead is 3.9%, and the dividend yield is known to be 1.8%, so the real yield growth rate must be 3.9% - 1.8% = 2.1%. The tax rate for capital gains and qualified dividends is 15% federal, and effectively 8% state, depending upon the state and tax bracket, for a total tax rate of 23%. To simulate the effect of these taxes on returns a computer program was used, Irlam (2006):
Tax rate = 23.0%
Yield = 1.8%
Real yield growth rate = 2.1%
Inflation rate = 2.5%
yearly sale final year sale
real real real real
year increase rate increase rate
1 2.4% 2.4% 2.4% 2.4%
10 26.4% 2.4% 28.8% 2.6%
20 59.7% 2.4% 71.5% 2.7%
30 101.8% 2.4% 133.0% 2.9%
40 155.1% 2.4% 220.3% 3.0%
It may be necessary to buy or sell equity assets every 10 or 20 years.
Therefore:
| Projected long term return on equity after tax = 2.7% |
Conclusion
By considering how the future will be different than the past it was possible to construct a model for predicting future stock market returns. Factors considered included changing GDP, changing slippage, and changing share repurchase and employee stock option transactions. Based on this a 2.7% return after taxes and overheads is predicted for the long term, and a 4.0% return before taxes and overheads.Reframing how this result was derived:
projected return = historical + changing + D/P + GDP + net repurchases + other - taxes
after tax return P/E correction correction correction factors
= 7.1% + -1.3% + -2.0% + -1.0% + 1.1% + 0.0% - 1.2%
= 2.7%
This estimate assumes there isn't a significant difference between P/E
ratios when the stock is bought and when it is sold. It is hard to
predict future P/E ratios, but the current P/E ratio is the best
predictor of the P/E future ratios. The impact on long term returns
of unexpected capital gains or losses due to changing P/E ratios will
lesson as the time span over which the stock is held increases.