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					   How Large is the
Equity Premium Today?
   Warwick Finance Lecture
     Warwick in London
       March 28, 2007

       John Y. Campbell
    Harvard University and
    Arrowstreet Capital, LP
Defining Terms
• The equity premium is the expected excess return on a
  broad stock index over a safe bond market investment

• To measure it, we need to make choices:
   – What stock index? (I will emphasize the World index but also
     show results for the US and UK)
   – What safe investment? (I will use long-term inflation-indexed
     bonds)
   – What starting point? (I will use current conditions)
   – What investment horizon? (I will discuss forecasting methods
     suitable for a 5-10 year holding period)
   – What kind of expectation? (I will use a geometric average)


                                                                     1
Geometric vs. arithmetic average
• This sounds like a technical issue but is first-order
  important in practice
• Simple stock returns have fat right tails and truncated left
  tails (limited liability)
• So the arithmetic average is pulled to the right and
  exceeds the median (the value you beat half the time)
• The geometric average is close to the median
• The difference between the two is about one-half the
  variance of returns, or about 1.5% for short-term returns
• To the extent that stocks are mean-reverting, variance
  and arithmetic average decline with the horizon
• I will report geometric average returns as a useful
  benchmark for long-term investors
                                                                 2
The fat right tail of stock returns




                                      3
Alternative ways to estimate the equity premium


Two extreme approaches:
1. Take an average of historically realized excess returns.
2. Estimate the historical relationship between realized
   excess returns and initial conditions (yields)

Two compromise approaches:
3. Adjust historically realized excess returns for conditions
   that are unlikely to repeat in the future.
4. Infer the equity premium from steady-state valuation
   models, using current yields and historical averages for
   other inputs.
                                                                4
1. Historical average excess returns
• This gives you a high number
   – Dimson, Marsh, and Staunton (DMS, 2006) report geometric
     averages of 4.7% for the world, 5.5% for the US, and 4.4% for
     the UK over the period 1900-2005
   – The numbers are even higher in the late 20th Century
• You need a long historical sample because stock returns
  are noisy
   – With 100 years of data and 15% standard deviation of returns
     per year, the standard error of the estimate is 1.5%
• But over a long period, it is plausible that the equity
  premium changes
   – This invalidates the method
• Since stock prices rise when the equity premium falls, a
  decline in the equity premium leads you to increase your
  estimate just when the true number is falling
                                                                     5
2. Historical impact of yields
• I will use US data to illustrate this method
• In the US, the dividend-price ratio (dividend yield) is
  close to a historic low, and the smoothed earnings-price
  ratio (smoothed earnings yield) is also low relative to its
  20th Century average
• Historically, these ratios have returned to normal through
  price adjustments, not adjustments in dividends or
  earnings (Campbell and Shiller 2005)




                                                                6
                                           S&P 500 10-Year Average Dividend/ Price

                       18.00%


                       16.00%


                       14.00%


                       12.00%
Dividend-Price Ratio




                       10.00%

                                                                ``
                       8.00%


                       6.00%
                                                                                     Average D/P = 4.4%

                       4.00%


                       2.00%
                                                                                                          D/P in 1/06 = 1.69%

                       0.00%
                            1881   1901   1921                1941                   1961                       1981            2001
                                                                 Year




                                                                                                                                 7
1.7% in 2006   Historical average



                                    8
2. Historical impact of yields
• Extrapolating the linear relationship gives a very gloomy
  view (a negative equity premium)
• But is this too extreme?
   – It’s always dangerous to extrapolate a linear relationship beyond
     the range of the historical data
   – There may have been a permanent shift in valuations, so that we
     may never return to the historical norm of the 20th Century




                                                                         9
Is there middle ground?
Is there middle ground between the bull and the bear?




                                                        10
3. Adjusted historical average excess returns
• Stock prices cannot increase forever in relation to
  dividends and earnings
   – To the extent that historical average returns have been
     generated by such increases, this component should be
     subtracted out to reflect static valuation ratios going forward
   – DMS and Fama-French (2002) propose this approach
   – DMS find that the adjustment is about 0.7% in the US and
     globally, but only 0.2% in the UK
• Valuation ratios represent initial conditions for an
  investor
   – The dividend yield has fallen below the historical average by
     over 2.5% in the US
   – Some of this reflects a shift to share repurchases, but even with
     a 1% adjustment for this effect, the decline is 1.5%
   – This can be subtracted from historical average return to estimate
     the equity premium for an investor buying at today’s prices
                                                                         11
3. Adjusted historical average excess returns
• The first adjustment to the 1900-2005 average returns
  would give us a geometric equity premium of 4.0% for
  the world, 4.8% for the US, 4.2% for the UK
• If we also make the second adjustment, we get a
  geometric equity premium of 2.5% for the world, 3.3%
  for the US, 2.7% for the UK




                                                          12
4. Steady-state valuation models
• The simplest steady-state model is the Gordon growth
  model: R = D/P + G
• That is, returns come from income and capital gains,
  which in steady state must equal dividend growth
• Use current D/P and an estimate of G to infer R
• The problem with this is that US firms have shifted from
  dividends to share repurchases, which has altered G in a
  way that is hard to estimate
• Campbell and Thompson (2006) find that an earnings-
  based approach works better



                                                             13
4. Steady-state valuation models
• Use two facts:
   – D/P = (D/E)(E/P)
   – G = (1-D/E) ROE, where ROE is accounting return on
     equity
• Get an earnings-based formula:
   – R = (D/E)(E/P) + (1-D/E) ROE
• The rate of return is a weighted average of the earnings
  yield and profitability, where the payout ratio is the
  weight on the earnings yield
• In practice, you need to smooth earnings, ROE, and
  payout ratio to eliminate short-run cyclical noise
• Finally, to get an equity premium number you must
  subtract an estimate of the real interest rate
                                                             14
Earnings yield
    .2
                   3-Year Smoothed Earnings / Current Price
  .15
    .1
  .05
        0




            1982   1986    1990      1994        1998   2002   2006

                             World          US          UK


                                                                      15
Profitability
                                    Smoothed Real ROE
                    (3-Year Smoothed Earnings / Current Book Value) - Inflation
     .2
   .15
     .1
   .05
         0




             1982      1986       1990       1994         1998     2002       2006

                                    World            US             UK


                                                                                     16
Payout ratio
                       Smoothed Dividend Payout Ratio
                  Current Dividend / 3-Year Smoothed Earnings
    .8
    .7
    .6
    .5
    .4
    .3




         1982   1986       1990     1994        1998    2002    2006

                            World          US            UK


                                                                       17
Real interest rate
                 Inflation-Indexed Government Bond Yields
    .05
    .04
    .03
    .02
    .01




          1982   1986    1990     1994    1998    2002      2006

                                 UK         US


                                                                   18
The equity premium today
  •Point estimates
 Implied equity premium, 1/31/2007
  • Method 1: Assume constant real ROE of 6%, dividend payout ratio of 50%
  • Method 2: Use 3-year smoothed ROE and dividend payout ratio
  • Weighted average: 75% weight on Method 1, 25% weight on Method 2


                                                      Weighted
                      Method 1        Method 2
                                                      Average

       World            3.0%            5.7%            3.7%


         US             2.9%            6.8%            3.9%


         UK             3.8%            7.3%            4.7%

                                                                         19
Implied world equity premium
                             Equity Premium -- World
   .08
   .06
   .04
   .02
         0
  -.02




             1982   1986     1990       1994       1998       2002      2006

                     Assume Constant Real ROE 6%, Dividend Payout Ratio 50%
                     Use 3-Year Smoothed ROE and Dividend Payout Ratio


                                                                               20
Implied US equity premium
                               Equity Premium -- US
   .08
   .06
   .04
   .02
         0
  -.02




             1982   1986     1990       1994       1998       2002      2006

                     Assume Constant Real ROE 6%, Dividend Payout Ratio 50%
                     Use 3-Year Smoothed ROE and Dividend Payout Ratio

                                                                               21
Implied UK equity premium
                               Equity Premium -- UK
   .08
   .06
   .04
   .02
         0
  -.02




             1982   1986     1990       1994       1998       2002      2006

                     Assume Constant Real ROE 6%, Dividend Payout Ratio 50%
                     Use 3-Year Smoothed ROE and Dividend Payout Ratio


                                                                               22
The world equity premium today
• The steady-state approach gives results that are highly
  sensitive to one’s beliefs about corporate profitability
• If recent profitability is sustainable, with a high
  reinvestment rate, then the world equity premium is
  5.7%
• If profitability and reinvestment rates return to their late
  20th Century averages, then the world equity premium is
  only 3.0%
• A reasonable compromise number is 3.7%
• This is one percentage point lower than the 1900-2005
  historical average reported by DMS
• Note that the equity premium is this high only because
  long-term real interest rates are low
                                                                 23
The equity premium in the US and UK
• The US and UK numbers are even more sensitive to the
  assumption about profitability
• In the US, the compromise number of 3.9% is 1.5%
  below the 1900-2005 historical average
• In the UK, the compromise number of 4.7% is actually
  slightly higher than the 1900-2005 historical average
• Thus in the US, we should not expect the future to be as
  good as the past
• But in the UK, the future and the past appear roughly
  comparable
• Again, the equity premium numbers are this high in part
  because real interest rates are low
                                                             24
What do institutional investors believe?
• Graham and Harvey (2007) survey CFO’s of US
  corporations and report that the median US equity
  premium forecast in November 2006 was 3.4%
• This suggests that many institutional investors have
  conservative expectations for stock returns
• Consistent with such a belief, many institutions have
  aggressively sought other types of risk with
   – High average return
   – Low correlation with equities
• Example: Harvard Management Company



                                                          25
Harvard policy portfolio
105                                                                                                                105

 95                                                                                                                95

 85                                                                                                                85

 75   Domestic Bonds                                                                                               75

 65                                                                                                                65

 55                                                                                                                55

 45                                                                                                                45

 35                                                                                                                35

 25                                                                                                                25
      Domestic Equities
 15                                                                                                                15

 5                                                                                                                 5

 -5                                                                                                                -5
  1992    1993     1994       1995    1996         1997   1998    1999        2000   2001     2002       2003   2004

           Cash                      Domestic Equities       Private Equity           Foreign Equities
           Emerging Markets          Domestic Bonds          Foreign Bond             High Yield Bonds
           Inflation-indexed Bonds   Real Estate             Commodities              Absolute Return

                                                                                                                        26
Harvard investment beliefs in 2004 (1)

                           7


                           6                                                      Timber                      Private Equity
  Expected Excess Return




                           5
                                                                                                              Emerging Markets

                           4                                       Real Estate          Domestic   Foreign
                                                                                        Equity     Equity
                           3                                 High Yield
                                                                               Absolute Return
                           2
                                                                          Domestic Bonds              Commodities
                           1                                              Foreign Bonds
                                   Inflation-indexed Bonds

                           0
                               0                   5                      10                 15          20                    25
                                                                          Standard Deviation




                                                                                                                                27
Harvard investment beliefs in 2004 (2)

                           7

                                      Timber                                        Private Equity
                           6

                                                                                        Emerging Markets
  Expected Excess Return




                           5


                           4               Real Estate                                      Foreign Equity
                                                                                                   Domestic Equity
                                                               High Yield
                           3
                                                           Absolute Return
                           2
                               Commodities
                                    Foreign Bonds          Domestic Bonds
                           1
                                  Inflation-indexed Bonds

                           0
                           0.00         0.20        0.40          0.60       0.80           1.00      1.20       1.40

                                       Beta with Portfolio of 60% Domestic Equity/40% Domestic Bonds


                                                                                                                        28
The limits of diversification
• Many alternative asset classes have been revalued
  recently in response to these strategies
   – Timberland
   – Emerging markets
• One should have moderate return expectations for these
  asset classes
• But even with lower returns, they can still enhance
  overall portfolio performance by diversifying risk




                                                           29
Conclusion
• Sensible methods for estimating the equity premium give
   – positive numbers
   – lower than historical excess stock returns in most countries
   – comparable to the historical average in the UK
• These numbers are measured relative to a long-term
  real interest rate of about 2%, as compared to 3.5% in
  the 1990’s
• In response to lower real returns, many investors have
  diversified aggressively across asset classes
• Real returns in these asset classes have likely fallen as
  a result
• But there are still rewards to intelligent diversification.

                                                                    30

				
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Description: International Equities Premium