PART 2: VALUATION, RISK AND RETURN
A second flaw in applying this approach broadly is that most shares in the market do not have as long
a history as Oroton’s do to forecast the expected return. In the 10 years to mid-2012, around 1,400 new
companies listed their shares on the Australian Securities Exchange (ASX).^4 Over the same timeframe,
over 745 companies were delisted from the ASX, and over 200 of the companies that were delisted had
been listed for less than 10 years. These companies have no long-run track record to learn from – only a
few years of rather volatile recent history.^57-1b THE PROBABILISTIC APPROACH
A second method for estimating expected returns uses statistical concepts. When statisticians want to
estimate the expected value of some unknown quantity, they first list all possible values that the variable
of interest might take, as well as the probability that each outcome will occur. In principle, analysts can
use the same approach to calculate the expected return on shares and other financial assets. A potential
advantage of this approach is that it does not require an analyst to assume that the future will look just
like the past. Professional judgement plays a larger role here.
OrotonGroup Limited falls into a category of shares that traders call cyclicals, because these shares’
fortunes rise and fall dramatically with the business cycle. To project the expected return on Oroton
shares, an analyst can estimate the probabilities associated with different states of the overall economy.
The table below illustrates how this can work. The analyst assumes that the economy will be in one of
three possible states next year: boom, expansion or recession. The current climate presents a 20% chance
that the economy will experience a recession, and the probabilities of a normal expansion or a boom are
70% and 10%, respectively. Next, the analyst projects that if the economy slips into recession, Oroton
shareholders will experience a 30% loss. If the economy continues to expand normally, then Oroton’s
share return will be 15%. If the economy booms, Oroton shares will do very well, earning a total return
of 55%.Outcome Probability Oroton return
Recession 20% –30%
Expansion 70% 15%
Boom 10% 55%To calculate the expected return on Oroton shares, multiply each possible return times the probability
that it will occur and then add up the returns across all three possible outcomes:Oroton expected return = 0.20(–30%) + 0.70(15%) + 0.10(55%) = 10%^6
With an estimate of the expected return in place, the analyst can estimate the variance and standard
deviation of Oroton shares. To do so, subtract the 10% expected return from the actual return on Oroton
shares in each state of the economy. Then, square that difference and multiply it by the probability of
recession, expansion or boom. The accompanying table illustrates the calculation.4 MorningStar DatAnalysis, http://datanalysis.morningstar.com.au/af/dathome?xtm-licensee=dat. Subscription database.
5 Ibid.
6 It is easy to generalise this equation. Rather than assuming that there are just three possible outcomes for Oroton shares, suppose that there
are n distinct states, where n can be any number. Each state occurs with a particular probability (P 1 + P 2 +... Pn = 1.0) and results in a specific
return on Oroton shares (r 1 , r 2 , r 3 , ...). In this case, the expected return equals:
E (r) = P 1 r 1 + P 2 r 2 + P 3 r 3 +... + Pn rn