312  Estimating the Cost of Capital 
refer to this phenomenon as survivorship bias. Zvi Bodie writes, “There were 
36 active stock markets in 1900, so why do we only look at two [the UK and 
U.S. markets]? I can tell you—because many of the others don’t have a 100-
year history, for a variety of reasons.”11
Since it is unlikely that the U.S. stock market will replicate its performance 
over the next century, we adjust downward the historical market risk pre-
mium. Dimson, Marsh, and Staunton find that the U.S. arithmetic annual re-
turn exceeded a 17-country composite return by 0.8 percent in real terms.12 If 
we subtract a 0.8 percent survivorship premium from our range of 5.5 percent 
to 6.2 percent U.S. excess returns reported in Exhibit 15.2, the difference im-
plies that the U.S. market risk premium, as measured by excess returns, is in 
the range of 4.7 to 5.4 percent, which we round to 5 percent. It’s interesting 
that this number matches the average risk premium measured by reverse en-
gineering the expected market return using the key value driver formula.
Estimating the Risk-Free Rate  With an estimate of the historical market risk 
premium in hand, it is now possible to estimate the expected market return 
by adding the market risk premium to the current risk-free rate. Adding the 
historical risk premium to the current Treasury yield worked well until the 
financial crisis of 2007–2009. With interest rates at unprecedented lows, how-
ever, further analysis is required.
To combat the financial crisis, the U.S. Federal Reserve reduced short-term 
rates to almost zero, pulling down long-term rates as a by-product. It also began 
a policy of repurchasing bonds in the open market (known as quantitative eas-
ing), further pushing up prices and driving down yields. At the same time, 
U.S. government bonds became a haven for investors around the world, lead-
ing to high prices and lower yields for government bonds. As the crisis and 
11 Z. Bodie, “Longer Time Horizon ‘Does Not Reduce Risk,’” Financial Times, January 26, 2002.
12 Dimson, Marsh, and Staunton, “The Worldwide Equity Premium.”
EXHIBIT 15.3  Cumulative Returns for Various Intervals, 1900–2018
Arithmetic mean, %
Average cumulative returns
Annualized returns
Holding period
U.S. 
stocks
U.S. government 
bonds
U.S. excess 
returns1
U.S. excess 
returns
Blume estimate of 
market risk premium
1 year
11.3
5.4
6.3
6.3
6.3
2 years
23.8
11.0
12.6
6.1
6.3
4 years
51.2
23.3
25.0
5.7
6.3
5 years
67.4
30.2
32.2
5.7
6.2
10 years
172.6
72.1
71.3
5.5
6.2
1 Measured by averaging year-by-year excess returns, not as the difference between cumulative stock and bond returns.
Source: Data for 1900–2002 from E. Dimson, P. Marsh, and M. Staunton, “The Worldwide Equity Premium: A Smaller Puzzle,” in Handbook of Investments: Equity Risk 
Premium, ed. R. Mehra (Amsterdam: Elsevier Science, 2007); data for 2003–2017 from R. G. Ibbotson, 2018 SBBI Yearbook: Stocks, Bonds, Bills, and Inflation (New 
York: Duff & Phelps, 2018); data from 2018 from Bloomberg.