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01 April 2010

Equity

Global Quantitative Research

www.sgresearch.com

Global Quantitative Strategy

Dow to 40,000 by 2030? US pension funds certainly seem to think so

London Andrew Lapthorne (44) 20 7762 5762

[email protected]

Rui Antunes (44) 20 7762 5875

[email protected]

John Carson (44) 20 7762 4979

[email protected]

Georgios Oikonomou (44) 20 7762 5261

[email protected]

New-York Andy Kim (1) 212 278 5455

[email protected]

‘Dow 40,000’ sounds like a crazy forecast and it is. But this is what many investors seem to

implicitly expect, particularly in the US. Our models point to long-term equity returns being

significantly lower.

Storing up problems for the next generation seems to be a recurring global theme these

days. One such problem is the overly optimistic returns expectations embedded within

many corporate and state pension funds. We estimate US pension funds are factoring in

a nominal 9% equity return in the long-term. In the UK it is some 100bp lower.

How realistic are these expectations? Well if history repeats itself, following such a poor

10-year return period as we�ve experienced, on average the S&P 500 has delivered 11%

real over the next ten years. However, given the sharp rebound in equity prices since March

2009, half of that gain is already behind us. An analysis of Shiller PEs and future returns also

indicates average real returns of just 1.7% going forward!

A decomposition of historical returns into building blocks also indicates that with US

dividends yield below 2% and real dividend growth typically 100bps or more below trend

GDP growth, an implied real return of 3% from US equities is a realistic assumption. But this

is before deducting fees and trading costs.

So why do investors expect so much more? Well in part the higher volatility of earnings

growth relative to GDP and dividend growth gives the impression that higher growth is

possible; optimistic consensus sell-side profit expectations don�t help either. Our

calculations reveal that consensus 12-month forward earnings forecasts have over-

estimated S&P reported profits by $2.3 trillion dollar during the last 20 years. To put that

number in context, during the same period the S&P paid out roughly $3 trillion in dividends.

The reality is that current valuations still imply returns which are far below many investors

expectations. This should clearly be a concern for both companies and governments going

forward. It should however be no surprise to Warren Buffett, who said back in 2007: �What is

no puzzle, however, is why CEOs opt for a high investment assumption: It lets them report

higher earnings. And if they are wrong, as I believe they are, the chickens won’t come home

to roost until long after they retire’.


01 April 2010 2

Be wary of high equity return assumptions

UK pension fund return assumptions A quick scan through a selection of the latest UK reports and accounts indicates pension fund

return assumptions near 6.8% with equities expected to return around 8% -see below. This is

similar to 2008 when according to Mercer�s FTSE 100 survey the median return assumption

from equities was 7.8%1.

UK report and account pension fund return assumptions

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Overal return Equities Bonds Property

Source: SG Cross Asset Research, Various pension fund reports and accounts)

Pension fund consultant return assumptions These expected long-term equity return assumptions unsurprisingly are similar to those

produced by consultants. The chart below shows median expected real return for equities to

be around 5.5%, which when added to current inflation expectations of 2.5-3.0% implies 8-

8.5% norminal.

Range of expected real returns over 10 years according to Watson Wyatt

-1.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0

Global ex-UK equities

UK equities

Property

Private Equity

Hedge Funds

AA UK long corporate bonds

Index-linked gilts

long-term UK gilts

Upper quartile Median Lower quartile

Source: Actuarial valuation - our approach, Watson Wyatt, available at WatsonWyatt.com

1 See Mercer Quarterly briefing on Pension Accounting available on http://uk.mercer.com


01 April 2010 3

US pension fund return assumptions In the US we have only be able to find overall asset return assumptions � these average c. 8%

for the Dow Jones 30 companies. However if we use the asset allocations of pension funds

shown in Tower Watson�s latest Global Pension Asset Study 2010, which shows 61% of

assets are held in equities, 19% in bonds and 20% in �other�, we can approximate an

expected equity return of around 9% if we assume a generous return of 8% on �other� assets

and a 5% return on bonds. Not only is 9% high, but how come US pension companies

systematically have higher return assumptions than those in Europe? Indeed some even

assume diffierent returns rates for different regions.

As Warren Buffet described in his 2007 letter to shareholders:

‘Some companies have pension plans in Europe as well as in the U.S. and, in their accounting

almost all assume that the U.S. plans will earn more than the non-U.S. plans. This discrepancy

is puzzling: Why should these companies not put their U.S. managers in charge of the non-

U.S. pension assets and let them work their magic on these assets as well? I’ve never seen this

puzzle explained. But the auditors and actuaries who are charged with vetting the return

assumptions seem to have no problem with it.

What is no puzzle, however, is why CEOs opt for a high investment assumption: It lets them

report higher earnings. And if they are wrong, as I believe they are, the chickens won’t come

home to roost until long after they retire.’

Of course many of these return assumptions are often based on historical return patterns or

the returns of indices rather than actual returns generated, so exclude intermediary costs such

as management fees and trading costs. However small errors in long-term return assumptions

lead to outsized liability mismatches 30 years down the line.

History is littered with investors being promised high returns to help justify high level of current

spending. A case in point is the heavy pushing of endowment mortgages in the UK in the late

1980s, which promised £100,000 in 25 years based on £50 per week savings- a near 14%

annual return. Many of these policies matured 25 years late 70% below the expected

£100,000 target.

Return short-fall after 30 years versus a 6% nominal return

0

500

1000

1500

2000

2500

2010

2012

2014

2016

2018

2020

2022

2024

2026

2028

2030

2032

2034

2036

2038

2040

6% 7% 9% 11%

75%

sho

rt-fa

ll

57%

25%

Source: SG Cross Asset Research

http://www.towerswatson.com/assets/pdf/966/GPAS2010.pdf


01 April 2010 4

It’s been so bad that things can only get better – really? The argument for some expecting a prolonged period of equity market strength seems largely

based on the fact that equity returns during the last 10 years have been absolutely terrible (see

below). Using data from Robert Shiller�s extremely useful website, S&P 10 year real returns

from March 1999 to March 2009 were minus 5.8% annualised, worse than any 10 year period

since 1881.

S&P 10 year compound real returns from 1881 to current day (annualised rate)

-10

-5

0

5

10

15

20

1881

1885

1889

1893

1897

1901

1905

1909

1913

1917

1921

1925

1929

1933

1937

1941

1945

1949

1953

1957

1961

1965

1969

1973

1977

1981

1985

1989

1993

1997

2001

2005

2009

Nominal returns Real returns

Source: Robert Shiller

So does a dreadful recent period for equities imply an improved outlook going forward? Given

the data above, this would indeed appear to be the case. Grouping historical 10 year returns

into deciles shows a negative relationship between historical 10 year returns and future 10

year returns. This correlation is driven by extreme deciles where the strongest 10 year returns

lead to the worst 10 year periods and vice-versa. We assumed (arbitrarily) that the investor

had the choice to buy and hold the index for ten years either in February or August � however

switching to an annual purchase or other starting months did little to change the overall result.

Relationship between historical 10 year returns of the S&P and future 10 year returns

R2 = 0.67

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

1 2 3 4 5 6 7 8 9 10

Ranked historical 10 year real returns (decile 10 = strongest returns)

Futu

re 1

0 ye

ar re

al re

turn

s (%

)


http://www.econ.yale.edu/~shiller/


01 April 2010 5

This relationship is detailed in the table below, which shows the breakdown of future 10 year

returns based on prior 10 year returns. After the worst period of 10 year returns (decile 1), 10

year real returns averaged 10% annualised - with no negative periods - and only a 4%

instance of a real gain of 5% (or less).

Breakdown of future 10-year returns based on prior 10-year returns (by decile, real total returns)

Deciles based on prior 10 year returns (1 = weakest)

1 2 3 4 5 6 7 8 9 10

Average gains 10.7 7.3 7.8 7.1 6.1 5.9 4.5 6.3 6.5 3.2

Maximum gain (%) 18.8 17.0 17.2 12.4 14.4 14.2 15.4 14.7 14.1 9.5

Minimum loss (%) 3.0 1.9 -3.5 -3.5 -3.7 -2.8 -2.5 -2.5 -3.4 -5.0

Percentage of loss (%) 0.0 0.0 16.7 25.0 20.8 4.2 25.0 4.2 8.3 12.5

Percentage of gain 5%+ (%) 4.3 29.2 45.8 37.5 37.5 25.0 54.2 29.2 29.2 70.8


Therefore, given that historical returns are amongst the worst seen then this surely bodes well

for equity returns going forward. However, US equities have already made gains of 68% since

the trough in March 2009. Spread over 10 years this equates to a 5.3% gain per annum

already. Yes, it can be said that periods of extremely weak equity markets subsequently lead

to stronger future equity market performance, but it must also be said that a decent chunk of

those expected returns may have already been made.

The lost decade in Japan simply led to another lost decade Assuming that equity markets will put in a strong 10 year performance simply because the last

10 years were poor is, in our view, a fairly weak investment case. After all, there are plenty of

precedents where this clearly has not happened - Japan being the most obvious.

Japan’s terrible decade (1990-2000) was followed by… another terrible decade

-10

-5

0

5

10

15

20

Q4

1979

Q4

1980

Q4

1981

Q4

1982

Q4

1983

Q4

1984

Q4

1985

Q4

1986

Q4

1987

Q4

1988

Q4

1989

Q4

1990

Q4

1991

Q4

1992

Q4

1993

Q4

1994

Q4

1995

Q4

1996

Q4

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

2007

Q4

2008

Q4

2009

Ann

ualis

ed 1

0-ye

ar re

al re

turn

(%)

Source: Thomson Financial Datastream, MSCI


01 April 2010 6

Price/Earnings as forecaster of long-term returns In a recent edition of Popular Delusions

2, Dylan Grice performed a similar exercise using the

Shiller PE multiple as a valuation starting point. As the chart below shows, current S&P 500

valuations are in the highest historic quintile (i.e. most expensive) and this starting point of

valuation has historically led to average real returns of 1.7% (see chart below) with a standard

deviation of 3.7%.

Shiller PE close to top quartile valuation (S&P relative to 10 year earnings, both deflated by CPI)

5

10

15

20

25

30

35

40

45

1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 1981 1991 2001

1st quintile (most expensive)2nd quintile3rd quintile4th quintile5th quintile (cheapest)

Source: SG Cross Asset Research, Robert Shiller

An important question when performing such analysis is just how relevant are historical US

stock market returns, when it could be argued that the US has been perhaps the most

successful and prosperous economy during the last 100 years. Surely there is a classic case

of survivorship bias. Why not, for example, use Russian stock market returns from 1881? 3

10 year real S&P returns by valuation quintile

1.7%

5.3%

6.4%

7.2%

11.0%

0% 2% 4% 6% 8% 10% 12

1

2

3

4

5

Current valuation quintile

Source: SG Cross Asset Research, Robert Shiller

2 What to do when there�s nothing to do? � Popular Delusions, 31 March 2010

3 For an interesting discussion on the relevance of historical long-term returns see �The Myth of 1926:

How much do We Know about Long-Term Returns on US stocks�, Journal of Investing Winter 2009.


01 April 2010 7

What assumptions drive decomposing historical returns? There have been numerous studies that have examined historical returns of equities and their

relationship to bond yields. For us, whilst these studies are useful references, the resulting

equity risk premium was not an active choice but rather it was something that the investor

received passively. However, we do find decomposing historical returns into underlying

components extremely useful and regular readers will be aware that we have a long history of

decomposing historical equity returns into dividend yield, real dividend growth and the change

in dividend yield.

Roger Ibbotson and Peng Chen in the Financial Analysts Journal4 decomposed historical

equity returns using six different methods:-

1. Building Blocks = Real Risk Free Rate + Inflation + Equity Risk Premium;

2. Capital Gain and Income = Inflation + Real Capital Gains + Real Dividends;

3. Earnings = Inflation + Real EPS growth + change in P/E + Real Dividends;

4. Dividends = Inflation + Real EPS growth + change in Payout Ratio + Real Dividends;

5. Return on Book Equity = Inflation + growth in Real Book Value + growth in Real ROE +

change in P/E + Real Dividends; and

6. GDP per Capita = Inflation + Real growth in GDP per Capita + increase in equity

markets relative to overall economic productivity + Real Dividends.

The above is a useful starting point for any discussion on equity returns. Using methods one

to five above, we decompose US MSCI data from 1980. We use data from this point simply

because it is readily available for illustration purposes.

Decomposition of US equity returns (nominal, since 1980)

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

1 2 3 4 5

Decompostion method

% to

tal n

omin

al re

turn

ERP

Risk free rate

Real ROE growth

Real book growth

Real dividend growth

Payout ratio

Real EPS growth

Real Capital gains

Change in P/E

Dividend yield

Inflation

Source: SG Cross Asset Research, MSCI

What can we realistically (and accurately) forecast? Looking down the six methods of decomposition above, the question we have to ask is how

many of these factors can realistically (or more accurately) be forecast?

4 See Financial Analysts Journal � volume 59, No 1. Jan/Feb 2003, p88-98


01 April 2010 8

Inflation – does it provide a natural hedge? Let�s start with inflation. The assumption is that via a growth in earnings, dividends or book

value, equity holdings will exhibit some form of inflation - hence the view that equity markets

provide an inflation hedge. We could therefore say that we do not need to concern ourselves

on forecasting inflation or indeed nominal returns. However, in each example above, there is

also a capital gain or multiple change component to account for. So, if inflation rises rapidly,

the key is how that might affect your exit price - and in a diversified asset portfolio, how much

higher inflation might impact the performance of your other assets, notably bonds. Not only do

we not know what inflation will be but neither do we know how that unknown might affect

terminal values.

We get very little information from market prices to tell us what growth or inflation might be

going forward. For example, nominal bond yields (see below) tell us more about what has

occurred rather than what is likely to happen in the future and whilst inflation-linked bonds will

provide the bond investor with an inflation hedge, no such mechanism exists in the equity

market.

US 10 year bond yields, trailing year-on-year real GDP growth and inflation (%)

-4

-2

0

2

4

6

8

10

12

14

16

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

Inflation GDP growth Bond yields



01 April 2010 9

What about growth? Whilst long-term inflation is highly unpredictable, making forecasting nominal quantities next

to impossible, real GDP growth (as we show in the table) is far more stable. US real GDP has

risen on average by 2.7% since 1980 with a standard deviation of just 0.8%.

US Real GDP growth (1980-1999)

(%) Compound Average Minimum Maximum Standard Deviation

Real GDP growth 2.7 1.1 4.9 0.8

Real Dividend growth 1.1 -1.7 8.6 2.5

Real Earnings growth 0.3 -10.8 18.2 6.9

Source: SG Cross Asset Research * Simple average and maximum and minimum are based on annualised 5-year compound averages

Our analysis also confirms what many other studies have shown, namely that quoted sector

compounded earnings and dividend growth does not exceed real GDP growth in the long-run.

Robert Shiller�s much quoted data shows real dividend growth to have been around 1.1%

during the last 139 years, whilst earnings have grown by 1.4%.

One reason for a disappointing profit performance versus GDP growth is that the quoted

equity market is continually diluted by new issuance. For example, an investor in the S&P 500

would have had to sell existing positions to fund, say, the purchase of Google when it listed in

2004. Over time, this equity dilution mounts up. In an excellent paper, Bernstein & Arnott5

discussed this topic in detail and come up with a very simple way of measuring dilution by

comparing the change in market capitalisation versus the change in index price level.

Below we show two such series for the MSCI US index since 1969. The gap is significant and

equates roughly to two percent dilution per annum. Coincidently, this is similar to the

conclusion reached by Bernstein & Arnott with a completely different dataset and time period.

Equity dilution: comparing the rise in US equity market capitalisation against the index

0

5

10

15

20

25

30

35

40

Dec

-69

Dec

-71

Dec

-73

Dec

-75

Dec

-77

Dec

-79

Dec

-81

Dec

-83

Dec

-85

Dec

-87

Dec

-89

Dec

-91

Dec

-93

Dec

-95

Dec

-97

Dec

-99

Dec

-01

Dec

-03

Dec

-05

Dec

-07

Dec

-09

Equity prices Equity market cap


5 Bernstein, William J. and Arnott, Robert D., Earnings Growth: The Two Percent Dilution. Financial

Analysts Journal, Vol. 59, No. 5, pp. 47-55, September/October 2003. Available at SSRN:

http://ssrn.com/abstract=489602


01 April 2010 10

So why do investors expect so much more? Volatility in earnings growth (see below) no doubt

helps create the impression that higher growth is indeed possible and bottom-up consensus

forecasts do little to dispel the idea that double-digit earnings growth is possible.

Real GDP, earnings and dividend growth (5 year averages, annualised)

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

Q4

1984

Q4

1985

Q4

1986

Q4

1987

Q4

1988

Q4

1989

Q4

1990

Q4

1991

Q4

1992

Q4

1993

Q4

1994

Q4

1995

Q4

1996

Q4

1997

Q4

1998

Q4

1999

Q4

2000

Q4

2001

Q4

2002

Q4

2003

Q4

2004

Q4

2005

Q4

2006

Q4

2007

Q4

2008

Q4

2009

Real Dividend growth Real Earnings growth Real GDP


Consensus IBES long-term EPS growth expectations (typically defined as five years) are

perennially optimistic (see chart below). We plot the series against the actual realised growth

in earnings five years later. So how seriously should we take these estimates? Well some,

most notably Alan Greenspan6, often quote such numbers as justification for higher equity

market valuation. Sadly, we find that these numbers over-estimate long-term earnings growth

by between 500 and 750 bps depending on whether you compare them to operating or

reported profits. Using them to predict long-term equity returns will therefore lead to a

massive over-estimation of profits.

Consensus long-term EPS growth expectations are way off the mark – US S&P500

-40

-30

-20

-10

0

10

20

30

Mar

-85

Mar

-86

Mar

-87

Mar

-88

Mar

-89

Mar

-90

Mar

-91

Mar

-92

Mar

-93

Mar

-94

Mar

-95

Mar

-96

Mar

-97

Mar

-98

Mar

-99

Mar

-00

Mar

-01

Mar

-02

Mar

-03

Mar

-04

Mar

-05

Mar

-06

Mar

-07

Mar

-08

Mar

-09

Mar

-10

5-ye

ar g

rwot

h ra

te (a

nnua

lised

, %)

I/B/E/S long-term EPS growth expectations

Realised I/B/E/S EPS growth (lagged 5 years)

S&P reported profit growth (lagged 5 years)

Source: SG Cross Asset Research, I/B/E/S, Standard & Poor

6 http://www.federalreserve.gov/boarddocs/hh/2000/february/testimony.htm

http://www.federalreserve.gov/boarddocs/hh/2000/february/testimony.htm


01 April 2010 11

It is not just long-term growth expectations which contribute to exaggerated profit growth.

Nearer term forecasts also create the impression that equities deliver more in terms of

earnings than they actually do. The chart below shows the difference between year 1 forecast

earnings and three measures of actual reported profit: S&P reported profit (which includes

most things such as write-downs and other exceptional items); MSCI profit (which is defined

as pre-exceptional EPS from operations); and IBES actual profit (which is pretty much

anything you like).

Year-ahead profit forecasts over-estimated actual earnings by 26% on average through 1990-

2009 when compared to S&P reported profits or 7% when compared to the rather more liberal

IBES reported profit number. The numbers shown below are massive in economic terms. For

example, based on forecast IBES data, cumulative earnings on the S&P 500 during the last 20

years was US$8,800bn however, using S&P data gives just US$6,500bn of earnings. That�s a

twenty year short fall of US$2.3 trillion dollars. To put that number into context, roughly

US$3 trillion has been paid out in dividends over the same period!

Weighted average annual (Year 1) forecast error in the US (1990-2009)

0.0

5.0

10.0

15.0

20.0

25.0

30.0

vs S&P reported profits vs MSCI reported profits vs I/B/E/S reported profits

Ave

rage

ann

ual o

ver-e

stim

atio

n (%

)



01 April 2010 12

So valuation must surely provide the key? So far we have discussed two major elements of historical nominal returns: inflation (which we

can�t forecast) and dividend/earnings growth (which has historically been less than trend real

GDP growth), having averaged somewhere between 1-2% historically (depending on the data

series used).

A substantial part of a long-term equity return comes from the initial price you pay, in other

words, the spot valuation, which is encouraging as at least we can measure valuation. For

example, one of our most popular charts - particularly amongst income fund managers -

shows that since the 1970�s, the bulk of real equity returns has come from dividend yield (see

chart below), with additional returns coming through dividend growth and then valuation

change - essentially the classic Gordon growth model.

Decomposition of real equity returns since 1970

3.0

5.75.55.0

6.1

4.6

4.3

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

UK US France Germany Australia Canada Japan

Dividend Yield Dividend growth Multiple expansion Total annualised returns

Source: SG Cross Asset Research, MSCI, Thomson Financial

As we have already discussed, stock market earnings and dividends have historically failed to

match growth in the real economy7. So, looking forward, real GDP growth should represent

the upper bounds on any long-term earnings growth assumptions, with a more realistic

estimate some 100bps lower to take account of equity market dilution.

Using these basic inputs we can then create a very simple long-term equity return forecasting

model, which consists of the current dividend yield plus trend real GDP growth (for which

we�ve used 10 year averages).

7 For an interesting look at the relationship between economic growth and equities see Cornell, Bradford ,

Economic Growth and Equity Investing (February 16, 2010). Financial Analysts Journal, Vol. 66, No. 1,

2010. Available at SSRN: http://ssrn.com/abstract=1553823


01 April 2010 13

US long-term estimates of future real equity returns: based on dividend yield plus trend real GDP (minus 100bps for equity market dilution)

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

Mar

-70

Mar

-72

Mar

-74

Mar

-76

Mar

-78

Mar

-80

Mar

-82

Mar

-84

Mar

-86

Mar

-88

Mar

-90

Mar

-92

Mar

-94

Mar

-96

Mar

-98

Mar

-00

Mar

-02

Mar

-04

Mar

-06

Mar

-08

Mar

-10

Impl

ied

equi

ty re

turn

s (%

)

Dividend yield + Real GDP - 100bps


We can then take such forecasts and deduce an implicit forward looking equity risk premium

by subtracting a real bond yield. Index-linked bond yields have a more limited history, so by

means of example we show data for the US from 1997. As shown below, the movement in the

long-term equity risk premium has largely been dictated by a decline in real yields and has

been in the range of 1.5-3% during the last eight years. Note the recent break-down in this

relationship, with real yields going much lower whilst the implied equity risk premium (courtesy

of weak equity) prices stayed put at around the 1.8-2.0% range.

Implied equity risk premium and index-linked bond yields in the US (%)

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Q1

1997

Q3

1997

Q1

1998

Q3

1998

Q1

1999

Q3

1999

Q1

2000

Q3

2000

Q1

2001

Q3

2001

Q1

2002

Q3

2002

Q1

2003

Q3

2003

Q1

2004

Q3

2004

Q1

2005

Q3

2005

Q1

2006

Q3

2006

Q1

2007

Q3

2007

Q1

2008

Q3

2008

Q1

2009

Q3

2009

Q1

2010

Impl

ied

Ris

k Pr

emiu

m (%

)

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Rea

l bon

d yi

elds

(%)

Implied ERP (%) Index-linked bond yields (rh scale%, inverted)



01 April 2010 14

How does this tie in with equity risk premium expectations? Duke University and CFO Magazine

8 regularly conducted a survey of chief financial officers.

The survey asks CFO�s about their long-term (10-year) return expectations for the S&P 500

and by subtracting the nominal bond yield they extract an implied equity risk premium (ERP)9,

a time series of which is given below. As we show, long-term equity return expectations since

2002 have remained anchored around 7-8%. However, the equity risk premium remains at an

elevated level. Does this stem from the view that equities have become more risky? No, it�s

simply a residual of their return expectations, i.e. it is the lower bond yield driving ERP higher.

US Duke CFO Survey: Implied Equity Risk Premium (%)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2000Q3 2001Q3 2002Q3 2003Q3 2004Q3 2005Q3 2006Q3 2007Q3 2008Q3 2009Q3

Impl

ed E

RP

(%)

5

6

7

8

9

10

11

Expe

ct 1

0 ye

ar re

turn

(%)

Average 10 year return expectations

Source: Duke CFO Magazine Global Survey

We have asked our clients for their opinions on the equity risk premium on a number of

occasions. The last such survey was carried out in November 2008 which gave us similar

results to one we conducted in 2002. Around 50% of respondents in the US and Europe

provided an answer of between 4-5%10

. When I first started in this job (many moons ago), my

then boss told me to inform anybody that rang him asking for an equity risk premium number

to plug into their spreadsheets that �the answer is four�! Quite frankly, I hadn�t a clue what he

was talking about back then but certainly everyone seemed more than happy with the

confident answer I gave. As far as I can tell, return expectations (and with it the equity risk

premium) seem to be firmly anchored on past nominal returns and it is this anchoring that is

driving valuation models rather than any sensible analysis of actually what might be possible.

SG investor equity risk premium survey results –November 2008

Europe US Japan Emerging markets

Average 4.7% 4.6% 4.4% 6.8%

Median 4.5% 4.3% 4.0% 6.0%

Most common response 5.0% 5.0% 4.0% 5.0%

Standard deviation 1.6% 1.6% 1.6% 2.7%

Responses 210 207 175 165


8 see http://www.cfosurvey.org/index.htm

9 see Graham, John R. and Harvey, Campbell R., The Equity Risk Premium amid a Global Financial Crisis

(May 14, 2009). Available at SSRN: http://ssrn.com/abstract=1405459

10 Also see Fernandez, Pablo, Market Risk Premium Used in 2008 by Professors: A Survey with 1,400

Answers). Available at SSRN: http://ssrn.com/abstract=1344209


01 April 2010 15

Dividend yield proves a solid forecaster of long-term returns Another possibility is to back-test future 10 year returns given a starting level of valuation. We

performed such an exercise using dividend yield in the latest edition of our Global Income

Investor (�Quality income scarce as low yields narrow the focus�, 28 January 2010); as we

show below, during the past 40 years there has been a strong relationship between the

starting level of dividend yield and long-term real returns.

UK: Dividend yield as a predictor of 10 year total real returns US: Dividend yield as a predictor of 10 year total real returns

y = 0.20x + 3.25R2 = 0.58

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

-5.0 0.0 5.0 10.0 15.0 20.010 year total real return (%)

Star

ting

DY

(%)

y = 0.13x + 2.63R2 = 0.31

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

-10.0 -5.0 0.0 5.0 10.0 15.0 20.010 year total real return (%)

Star

ting

DY

(%)

Source: SG Cross Asset Research, MSCI Source: SG Cross Asset Research, MSCI

Using data since 1970, we show below that the higher starting dividend yield, the greater the

10 year real returns. This relationship also holds if we use five year returns but is less marked.

However, it fails when it comes to short holding periods such as one year returns. If we use

nominal returns the relationship is even stronger.

Dividend yields and their relationship with long-term real returns (since 1970, %)

US UK Average Dividend yield 5.5 4.2 3.4 2.9 1.7 Average Dividend yield 6.4 5.2 4.6 4.0 2.9

Yield low 5.0 3.8 3.2 2.8 1.1 Yield low 5.7 5.0 4.5 3.8 2.2

Yield high 6.5 4.9 3.7 3.1 2.8 Yield high 11.6 5.6 4.9 4.4 3.8

Average 10 year real return (%) 11.1 10.2 12.1 4.9 3.0 Average 10 year real return (%) 12.4 10.9 9.8 4.5 0.2

Best 10 year real return (%) 14.5 17.4 17.1 12.0 9.1 Best 10 year real return (%) 16.5 15.0 13.6 9.2 7.2

Worst 10 year real return (%) 6.9 2.3 -0.3 -3.6 -5.6 Worst 10 year real return (%) 7.4 4.6 3.9 -1.6 -4.2

Probability of 10 year loss (%) 0 0 5 33 26 Probability of 10 year loss (%) 0 0 0 9 50

Japan Europe ex-UK Average Dividend yield 2.9 2.0 1.1 0.8 0.5 Average Dividend yield 5.8 4.4 3.6 2.9 2.0

Yield low 2.3 1.7 0.9 0.7 0.4 Yield low 5.3 4.1 3.4 2.8 1.5

Yield high 5.2 2.2 1.6 0.9 0.7 Yield high 6.6 5.1 4.0 3.2 2.7

Average 10 year real return (%) 4.1 12.3 13.1 -1.8 -7.0 Average 10 year real return (%) 13.7 10.4 7.9 9.2 5.6

Best 10 year real return (%) 9.7 33.0 28.8 7.4 1.4 Best 10 year real return (%) 17.0 15.6 17.1 14.5 10.4

Worst 10 year real return (%) -4.2 -12.3 -6.1 -8.4 -11.9 Worst 10 year real return (%) 8.8 0.4 -0.9 1.3 -3.2

Probability of 10 year loss (%) 13 21 23 78 96 Probability of 10 year loss (%) 0 0 12 0 21


The current �starting� dividend yield of 1.9% in the US suggests a performance going forward

in line with the lowest quintile, as indeed does a 3.5% dividend yield in the UK. In Japan, the

current dividend yield of 1.6% suggests mid-quintile returns, which is mildly encouraging. In

Europe ex-UK, the relationship is less solid than in other regions but perhaps this is because

we are carrying out the analysis on a regional rather than a country level, as is the case for the

US, Japan and the UK.


01 April 2010 16

Conclusion �Why deal with something today which you can put it off until tomorrow?� is the mantra of the

indebted world. Corporate managers have little incentive to put conservative assumptions into

their pension fund calculations when many of the liability mismatches will likely occur well

beyond their watch. For our work, 4% real growth is at the upper end of expectations with a

very real risk of yet more losses over the next ten years. Higher inflation may help, especially if

those in the pension scheme have their inflation tracking capped at lower levels. Pension

under funding is already proving to be a drag on growth, with several companies already

struggling to invest or expand due to their historical pension commitments.

Does this hamper equity in the short-term? For one those with lower return expectations can

continue to buy, those with higher expectations will simply have to make up the short-fall by

saving more or reducing benefits. Also during the last 10 years equities have happily ignored

over-valuation signals whenever cyclical momentum is positive. However once that

momentum fades, it may be a long way down until you start hearing that equities are �cheap�.


01 April 2010 17

Appendix I: The Wilkie Model The Wilkie investment model was introduced by actuary David Wilkie in 198611 to explain and

predict the behaviour of various economic variables. Originally, it only included models for

inflation, dividends, dividend yield and long-term interest rates and was applied to the UK

market. In 199512, Wilkie revised and extended his model to cover wages, short-term interest

rates, property yields and index-linked yields. He also introduced his model to other countries.

The Wilkie model and its extensions are widely used today in the actuarial world and

elsewhere to forecast the aforementioned economic series and predict market returns.

In the context of this model, inflation is the key driver of all economic series. The direction of

influence and cross dependencies in the original Wilkie model are shown below; notably share

dividends and long-term interest rates are influenced by both the dividend yield and inflation

levels, while the dividend yield is only dependant on inflation. On the other hand, inflation is

only described by its own previous values.

Direction of influence in original Wilkie model

Source: SG Quantitative research, Wilkie (1986)

11 Wilkie(1986). �A stochastic investment model for actuarial use�:

www.soa.org/library/monographs/.../investment.../m-as99-2-06.pdf

12 Wilkie(1995). �More on a stochastic asset model for actuarial use�:

www.inqa.com/files/Conferences/MoreOnAStochasticAssetModel1995BAJ1.pdf

Inflation

Yield

Dividend Long-term interest rate


01 April 2010 18

The 4 equations describing the dynamics of the Wilkie original model are shown below:

(1) Inflation

∇logQ(t) = QMU + QA(∇logQ(t-1) - QMU) + QSD.QZ(t),

where Q(t) = Retail price index, ∇logQ(t)= logQ(t) - logQ(t-1), QZ(t)~iidN(0,1) and QMU,QA,QSD

constants13.

(2) Dividend Yield

logY(t) = YW.∇logQ(t) + YN(t)

where YN(t) = logYMU + YA(YN(t-1) - logYMU) + YSD.YZ(t),

Y(t) = Dividend yield, YZ(t)~iidN(0,1) and YW,YMU,YA,YSD constants14.

(3) Dividends

D(t) = D(t-1).exp{DW.DM(t) + DX.∇logQ(t) + DMU + DY.YSD.YZ(t-1) + DB.DSD.DZ(t-1) +

DSD.DZ(t)},

where DM(t) = DD.∇logQ(t) + (1-DD).DM(t-1),

D(t) = Dividend index, DZ(t)~iidN(0,1), DW,DX,DMU,DY,YSD constants15.

(4) Long-term interest rates

C(t) = CW.CM(t) + CMU.exp{CN(t)},

where CM(t) = CD.∇logQ(t) + (1 - CD).CM(t-1),

CN(t) = CA1.CN(t-1) + CA2.CN(t-2) + CA3.CN(t-3) + CY.YSD.YZ(t) + CSD.CZ(t),

C(t) = Long-term interest rate, CZ(t)~iidN(0,1) and CW,CD,CMU,CA1,CA2,CA3,CY,CSD

constants16.

According to the above equations, the inflation model is designed to depend only on its own

previous levels, the dividend yield on the current level of inflation and previous dividend yields,

the dividends index on the current level of inflation, the residuals of the yield model as well as

previous dividends, while the long term interest rates are dependant on the current and

previous level of inflation, the residuals of the yield model and previous interests rates. It is

also worth noticing the mean reverting properties of the above equations.

13 Wilkie(1995): QMU=0.047, QA=0.58, QSD=0.0425. 14 Wilkie(1995): YW=1.8, YA=0.55, YMU=0.0375, YSD=0.155.

15 Wilkie(1995): DW=0.58, DD=0.13, DMU=0.0016, DY=-0.175, DB=0.57, DSD=0.07.

16 Wilkie(1995): CW=1.0, CD=0.045, CMU=0.0305, CA1=0.9, CA2=0, CA3=0, CY=0.34, CSD=0.185.


01 April 2010 19

Predictions We have applied the Wilkie model in the UK market (FTSE All Share) using the 1995 revised

coefficients. Below we present the model�s prediction for inflation and dividend yields levels,

as well as capital and total returns over the next decade. Instead of using the 4.7% inflation

rate used in the 1995 edition of the model, we adjusted it downwards to 3%.

Wilkie model predictions over the next decade

Year Inflation Yield Dividend Price Index Price Return Total Return

2010 3.7% 3.2% 91.6 2898.4

2011 3.5% 3.6% 95.3 2681.1 -7.5% -3.9%

2012 3.2% 3.8% 99.4 2637.1 -1.6% 2.1%

2013 3.2% 3.9% 103.9 2666.0 1.1% 5.0%

2014 3.1% 4.0% 108.4 2740.6 2.8% 6.8%

2015 3.1% 4.0% 113.0 2827.0 3.2% 7.2%

2016 3.0% 4.0% 117.9 2942.6 4.1% 8.1%

2017 2.9% 4.0% 123.2 3073.4 4.5% 8.5%

2018 3.0% 4.0% 128.7 3200.9 4.2% 8.2%

2019 3.1% 4.0% 134.4 3336.3 4.2% 8.3%

2020 3.0% 4.0% 140.2 3473.0 4.1% 8.1%

Source: SG Quantitative Research, FTSE, Bloomberg


01 April 2010 20


01 April 2010 21

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MSCI, this information and any other MSCI intellectual property may not be reproduced, redisseminated or used to create any financial

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