Sunday, May 1, 2016

The Most Important Number in Finance

     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 20th 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 5th edition, McKinsey & Company, New York,
[14] Duff & Phelps, 2015, Valuation Handbook: Quarterly update, New York.

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