The most important number in finance is the equity risk premium - the return that investors can expect from holding the market portfolio of common stocks in excess of the return on 20-year government securities. Unfortunately, the number is unknown. As a result, hundreds of articles have been written on the subject offering estimates of what it might be. Below I offer my take on what the literature has to say and what a reasonable estimate of the risk premium is likely to be.

With regard
to the equity risk premium, there is now widespread support for the view
expressed that expected stock returns vary over time. John Cochrane (2011), began his Presidential
Address to the American Finance Association with the statement that “Discount
rates (

*i.e. expected eturns*) vary
over time.”

[1] Recent finance Nobel Prize winner, Eugene
Fama, citing various leading scholars as well as himself, stated as early as
1990 that, “There is also evidence that expected returns (and thus the discount
rates that price expected cash flows) vary through time (for example, Fama and
Schwert (1977), Keim and Stambaugh (1986), Campbell and Shiller (1998) and Fama
and French (1988, 1989).”

[2]^{,[3]} In his Nobel lecture in 2013, Fama returned
to this theme stating that, “As noted above, early work on market efficiency
generally assumes that equilibrium expected stock returns are constant through
time. This is unlikely to be true. The expected return on a stock contains
compensation for bearing the risk of the return. Both the risk and the
willingness of investors to bear the risk are likely to change over time,
leading to a time-varying expected return.”

[4]

Given that
expected stock returns (and, therefore, equity risk premiums) vary through
time, it would be pure serendipity if a long-run historical average (currently
about 6.7% measured with respect to 20-year Treasury securities over the period
from 1926 to 2015) happened to be a good estimate of the risk premium at the
end of 2015. But the argument for using
an historical average is even weaker than that because there are host of
reasons why the equity risk premium is likely to have

*declined* over time. As
discussed by Cornell (2013), those reasons include, in no particular order:

[5]
1. Increases
in market liquidity along with improvements in trading technology and record
keeping.

2. Innovations
in capital market regulation and oversight to protect investors including the
establishment of the Securities Exchange Commission.

3. Advances
in economic theory and policy leading to increased stabilization of the
economy.

4. Advances
in asset pricing and portfolio theory leading to improved risk measurement and
investment management.

5. The
expansion of stock market participation via the invention of mutual funds and
the creation of the modern retirement savings system.

6. The
collection and dispersion of data on the financial performance of equity
investments leading to, among other things, investor appreciation that equities
are not exotic investments with an unacceptable level of risk.

7. A
decline in the volatility of the return on the market portfolio.

8. An
aging of the U.S. population that will likely sell equities to fund retirement
reducing expected market returns.

Assuming that the risk premium has
declined over the last ninety years, an historical average will be an upward
biased average of the current risk premium.
That bias can be reduced somewhat by using the so called supply side
risk premium (currently about 6.1% measured with respect to 20-year Treasury
securities) which deducts from the historical average the portion of the return
attributable to expansion of price-earnings ratios on the grounds that such
expansion will not be repeated. There is
no reason to assume, however, that this somewhat ad hoc deduction is sufficient
to account for all the factors listed above.

All of the
foregoing consideration apply to U.S. data.
It is common for analysts to rely on U.S. because it is the most
complete and the most accurate. But that
itself is a problem. The U.S data is so
clean because during the last century, the United States became the world’s
leading economy, it was politically stable, it did not lose a war, and it had
the most rapidly growing financial markets.
For all of those reasons, the historical U.S. data are likely to be
biased. From the perspective of 1900, investors
would that the U.S. would be blessed over the next 115 years. To overcome this bias, Dimson, Marsh and
Staunton (2002) look at stock market returns on a global basis throughout the
20

^{th} century.

[6] They conclude that historical averages based
on U.S. data likely overstate the forward looking equity risk premium.

Aware of the
potential biases inherent in the use of historical averages, particularly those
based exclusively on U.S. data, academics and practitioners have turned to
other approaches for estimating the equity risk premium. One of the most widely accepted is the
discounted cash flow model applied to the market as a whole. Given the current observable price index for
the market and predictions regarding either future cash flows to equity or future
dividends, one can calculate the discount rate that equates the present value
of the predicted cash flows (or dividends) to the index. This discount rate is by definition the
average future expected rate of return over the long run.

[7] Prof. Aswath Damodaran publishes on his
website a monthly time series of the forward looking equity risk premiums
calculated using his measure of expected future cash flow. His most current estimate for November 2015
is approximately 5.6% calculated with respect to the yield on 20-year
government bonds. He also estimates the
ERP using projected dividends instead of his measure of cash flow to equity. In November, his dividend based model yielded
an ERP of less than 4.0%.

Another
alternative is to survey experts including academics, financial officers, and
investment managers as to what they expect the ERP to be in the futures. The problem with surveys, of course, is that
it depends on who you ask, when you ask them, and even how you phrase the question. Nonetheless, most surveys result in ERPs
below the long-run average and even below the supply side estimate. An extensive survey of CFOs by Graham and
Harvey reported an average risk premium of 3.11% - more than 3 percentage
points below the historical average.

[8] Based on survey of 150 valuation and finance
textbooks, Fernandez reports and an average ERP of 4.80%, well below the
historical average and the supply side estimates.

[9]

Turning back
to historical averages, Fama and French (2012) demonstrate that if dividend and
earnings growth rates rather than stock price changes are used to measure the
expected rate of capital gain more accurate estimates of the ERP can be
produced. Using this procedure, the
authors conclude that “Our estimates for 1951 to 2000, 2.55 percent and 4.32
percent, are much lower than the equity premium produced by the average stock
return, 7.43 percent. . . Our main conclusion is that the average stock return
of the last half-century is a lot higher than expected.”

[10] Updates of the Fama-French study using more
current data report similar results.

[11]

These
findings are also consistent with very long-run historical data. For example, Levi and Welch report, based on
reconstruction of U.S. data over the last two centuries, that the average
premium of equities over long-term government bonds has been on the order of
4%.

[12]

Finally,
there is a conceptual question as to whether the historical arithmetic average
is the proper number in the first place.
To begin, McKinsey & Company (2010) observes that the arithmetic
average is the best predictor of the risk premium for next year

*if* the data are stationary and not
correlated over time. But the McKinsey
book goes on to note that “A one-period risk premium, however, can’t value a
company with many years of cash flow.
Instead, long-dated cash flows must be discounted using a compound rate
of return.” This is not a problem for
forward looking models that explicitly solve for a compound rate of
return. But it is as reason not to rely
on the historical arithmetic average. In
light of this problem, and other considerations they discuss, McKinsey
concludes that the appropriate equity risk premium is in a range of 4.5 to 5.5
percent.

[13]

The research
cited here is a small subset of the papers that have been written on the equity
risk premium. The literature largely
agrees on two propositions: 1) That risk premiums vary over time and 2) That
past averages are unlikely to an appropriate estimate of the risk premium to
use in the context of corporate valuation.
However, there is less agreement on precisely how to estimate the
premium and on its current level. Based
on my reading of this extensive literature, and for the reasons discussed
above, I conclude that a reasonable estimate of the equity risk premium is no
more than 5.50 percent.

As a final
note of support for my conclusion, Duff & Phelps, the firm that has taken
over the commercial task of producing data on the historical and supply side
equity risk premiums also reports its own recommended equity risk premium. In the most recent update to the firm’s
Valuation Handbook, Duff & Phelps recommended an equity risk premium over
20-year Treasury securities of 5.0 percent.

[14]
Like my choice, the Duff & Phelps
recommendation is not based on any one piece of evidence, but instead on the
firm’s review of what it believes are all the relevant materials.

[1] Cochrane, John H., 2011, Discount rates, *Journal
of Finance*, 66, 1047-1108.
[2] Fama, Eugene F., 1990,
Stock returns, expected returns and real activity, *Journal of Finance*, 45, 1089-1108.
[3] Fama, Eugene F. and G. William
Schwert, 1997, Asset returns and inflation, *Journal
of Financial Economics*, 5, 115-146.
Campbell, John Y. and Robert Shiller, 1988, The dividend price ratio and
expectations of future dividends and discount factors, *Review of Financial Studies*, 1, 195-228. Fama, Eugene F. and Kenneth R. French, 1988,
Dividend yields and expected stock returns, *Journal
of Financial Economics*, 22, 3-25.
Fama, Eugene F. and Kenneth R. French, 1989, Business conditions and
expected returns on stocks and bonds, *Journal
of Financial Economics*, 25, 23-49.
Keim, Donald B. and Robert F. Stambaugh, 1986, *Journal of Financial Economics*, 17, 357-390.
[4] Fama, Eugene F., 2013, Two
pillars of asset pricing, Nobel Prize Lecture.
[5] Cornell, Bradford, 2013,
Dividend-price ratios and stock returns: Another look at the history,” *Journal of Investing*, 22, 2, 15–22.
[6] Dimson, Elroy, Paul Marsh
and Mike Staunton, 2002, *Triumph of the
optimists: 101 years of global investment returns*, Princeton University
Press, Princeton, NJ.
[7] Damodaran, Aswath, 2015,
Equity risk premiums (ERP): Determinants, estimation and implications – The
2015 edition,” unpublished working paper, New York University.
[8] Graham, John R. and
Campbell R. Harvey, 2015, The equity risk premium in 2014, unpublished working
paper, Fuqua School of Business, Duke University.
[9] Fernandez, Pablo, 2015, The
equity premium in 150 textbooks, unpublished working paper, IESE Business
School.
[10] Fama, Eugene F. and Kenneth
R. French, 2002, The equity risk premium, *Journal
of Finance*, 57, 637-659.
[11] Cornell, Bradford and Max
Moroz, 2009, The equity risk premium revisited, unpublished working paper,
Research Affiliates LLC.
[12] Levi, Yaron and Ivo Welch,
2015, Assessing cost-of-capital inputs, unpublished working paper, Anderson
School of Management, UCLA.
[13] Koller, Tim, Marc Goedhart
and David Wessels, 2010, *Valuation:
Measuring and managing the value of companies 5*^{th} edition,
McKinsey & Company, New York,
[14] Duff & Phelps, 2015, *Valuation Handbook: Quarterly update*,
New York.