PART 2: VAlUATION, RISK AND RETURN
TABlE 6.3 AUSTRALIAN ASSET CLASS RETURNS (AFTER INFLATION) TO 30 JUNE 20153 months (%) 1 year (%) 5 years (%) 10 years (%) 20 years (%) Since 31 December 1981 (%)
Cash –0.1 1.1 1.3 2.0 4.2 4.0
Australian shares –7.1 4.0 7.0 4.2 7.2 7.0
International shares –0.8 23.3 12.8 3.5 6.9 6.4
Property –3.0 18.4 11.6 –0.3 6.1 6.1
Source: Wealth Foundations. Used with permission. Data taken from ‘Graphical Finance,’ Wealth Foundations: http://www.wealthfoundations.com.au/graphical-finance.html.
Accessed 6 October 2015.6-3 VOlATIlITY AND RISK
6-3a THE DISTRIBUTION OF HISTORICAl SHARE RETURNS
We begin our analysis of risk with one more historical illustration. Figure 6.5 shows a histogram of
stock returns since 1900. The shape of this histogram is probably familiar to you because it is somewhat
reminiscent of a bell curve, also known as a normal distribution. In most years, US stocks earned a
return not far from the historical average of 11.4%. Of the 111 annual returns shown in the figure, more
than half (64, to be exact) fall in a range between 0 and 30%. Extremely high or low returns occur less
frequently. The only years that showed losses of 30% or more were 1931, 1937 and 2008, while 1933
and 1954 were the only two years in which stocks rose more than 50%. Collectively, these years with very
high or very low returns represent about 4.5% of the data from the 111 years.
Figure 6.5 gives us a sense that equity returns can be quite volatile, and it tells us something
about the relative frequencies of different outcomes in the US stock market. We are interested in these
frequencies not only for their historical significance but also for what they may tell us about future stock
market returns. For example, a question that investors may want to ask is, ‘What is the probability that
a portfolio of stocks will lose money in any given year?’ Without a crystal ball, no one can answer that
question precisely, but a close inspection of Figure 6.5 shows that returns were negative in 29 out of the
last 111 years, or about 26% of the time. At least as a starting point, we can estimate a 26% probability
that equities will lose money in a particular year.
If we could list every possible outcome that might occur in the share market and attach an exact
probability to each outcome, then we would have a probability distribution. Some probability distributions are
easy to describe. For example, the probability distribution that governs outcomes of a coin toss is given below:
Unfortunately, the probability distribution for future stock
returns is unknown. We rely on Figure 6.5 to give us clues
about the characteristics of this distribution. From the shape
of the figure, we may surmise that the unknown distribution of
stock returns is a normal curve with a mean return (or average
return) of 11.4%. A normal distribution is symmetric, so there is an equal chance of experiencing an
above-average and a below-average outcome. Since 1900, the split between above-average and below-
average years in the stock market is 60 to 51, very close to even. This suggests that our assumption of an
underlying normal distribution may be a good approximation of reality.^88 Extensive research on the distribution of equity return teaches us that the normal distribution is only a rough approximation of the actual
returns distribution. For example, equity returns do not appear to be distributed symmetrically around the mean. This makes sense in light of
the limited liability feature of the US legal system. A fortunate stockholder might earn a return in excess of 100% in any given year, but no
investors can experience a loss greater than 100% (unless they are buying stocks using borrowed money). When we examine historical stock
returns, we do observe outcomes that are far above the mean more frequently than we see outcomes well below the mean.LO6.3Outcome Probability
Heads 50%
Tails 50%