PART 2: VAlUATION, RISK AND RETURN
Year 2007 2008 2009 2010
Return on shares (%) 5.6 –37.2 28.5 17.1
Return on bonds (%) 9.9 25.9 14.5 6.4
Risk premium (%)P6-15 The table below shows the average return on US shares and bonds for 25-year periods ending in
1925, 1950, 1975 and 2000. Calculate the equity risk premium for each quarter of a century. What
lesson emerges from your calculations?Ave. return 1925 1950 1975 2000
Shares 9.7% 10.2% 11.4% 16.2%
Bonds 3.5% 4.1% 2.4% 10.6%
Risk premium
Source: Dimson, Elroy, Triumph of the Optimists. © 2002 Elroy Dimson, Paul Marsh and Mike Staunton.
Published by Princeton University Press. Reprinted by permission of Princeton University Press.P6-16 The current YTM on a one-year Treasury bill is 4%. You believe that the expected risk premium on
shares versus bills equals 7.7%.
a Estimate the expected return on the share market next year.
b Explain why the estimate in part (a) may be better than simply assuming that next year’s share
market return will equal the long-term average return.VOLATILITY AND RISK
P6-17 Using Figure 6.5, how would you estimate the probability that the return on the share market will
exceed 30% in any given year?P6-18 In this problem, use Figure 6.5 to estimate the expected return on the share market. To estimate
the expected return, create a list of possible returns and assign a probability to each outcome. To
find the expected return, multiply each possible return by the probability that it will occur, and then
add up across outcomes. Notice that Figure 6.5 divides the range of possible returns into intervals
of 10% (except for very low or very high outcomes). Create a list of potential future equity returns
by taking the midpoint of the various ranges as follows:Possible equity returns (%)–35 –25 –15 –5 5 15 25 35 45 553
1114
111
3
111
2
111
Expectedreturn=3
111
( 35)+
4
111
(
− −−25)++
3
111
(45)+
2
111
⋅⋅⋅⋅ (55)=?
Figure 6.5 shows that four years out of 111 had returns of between –20% and –30%. Let us
capture this fact by assuming that, if returns do occur inside that interval, the typical return would
be –25% (in the middle of the interval). The probability associated with this outcome is 4/111, or
about 3.6%. Fill in the missing values in the table, then fill in the missing parts of the equation to
calculate the expected return.
P6-19 Below are the nominal returns on shares, bonds and bills for the 1920s and 1930s. For each decade,
calculate the standard deviation of returns for each asset class. How do those figures compare with
the more recent numbers for shares presented in Table 6.4 and the long-run figures for all three
asset types in Table 6.5?