1.
Risk and Return in World Markets
October 16, 2001
By
Students in QTM7010/MBA Statistics
Professor Sharpe
Babson College
Fall, 2001
2.
Objectives
Deciding how to invest money is an important decision for many people but raw data can be misleading. By
applying a variety of statistical tools to a sample of stock market data from 1995 the value of statistical analysis in
making investment decisions becomes clear. The challenge then becomes one of interpreting the sample data to
determine the degree of risk and return on investment for investors with differing objectives.
Methods
The sample data set is comprised of monthly and annual stock market returns for Australia, Europe, Japan and the
US from 1975 to 1996. The data is presented in a box plot format for easier analysis1 because box plots provide a
visualization of outliers, mean, standard deviation, and normal distribution. Since all of the sample data appears
normal a comparison of the stock markets from different countries is possible. Descriptive statistics assign values
to the mean, median, standard deviation, maximum values, minimum values and confidence intervals (CI). These
statistics are useful for calculating more meaningful information such as the coefficient of variance (CV). The CV
provides insight into the degree of risk taken by investing in the stock markets of various countries.
Results1
The mean alone provides very little information but examination of both the mean and the median for the monthly
returns indicates that the distribution for the US and European stock markets approximate normal curves.
Conversely, Australia and Japan have greater variability most likely attributable to several large returns, causing the
mean to be larger than the median and the data to be skewed to the right.
By creating box plots for annual and monthly returns (Figure 1 and 2), the distributions are more easily compared.
Australia clearly has the largest inter-quartile range indicating that the Australian stock market has the greatest
variability in annual returns (excluding outliers). Not surprisingly, this is not as obvious in the monthly return box
plot because annual returns often magnify what appear to be small variations in monthly returns.
Neither the monthly nor annual box plots explain the volatility in the stock markets of Japan and Australia.
Analyzing the standard deviation, CI and CV offers a more comprehensive explanation. The resulting data (Table 2
and 3) demonstrate that Japan has a larger standard deviation, CI and CV than Australia on the basis of annual
return. In 1986 the Japanese stock market rewarded investors with a 72% return yet four years later investors
suffered a 35% loss on their investment.
A comparison of the CV calculations reveals that the US stock market appears to be less volatile, while providing
the same average return as other, more volatile markets. Australia’s CV calculation varies more on a monthly basis
while Japan tends to experience more variation on an annual basis.
Since the CI for all countries overlaps, there is no statistically significant difference in the average returns between
any countries in the sample from the case study. Nonetheless, it appears the US offers a more stable investment
environment than Japan or Australia.
Conclusion1
The concept of investing is based on the principle of risk and reward; the cliché “no free lunch” defines this
principle. “No free lunch” represents investor’s appetite for risk, and the willingness to pay a premium in their
search for maximizing total return. Historically investors have expected to be rewarded for taking risk. Some have
invested in highly volatile markets, foregoing the safety of stable performance (premium payment) in exchange for
the chance to make huge returns. However, Table 1 below (and Figures 3 and 4 of the appendix) illustrate that
seeking additional risk does not necessarily correlate to higher returns on average (average investment return over
time). Based on a sample time period (1/1/79 – 12/31/96), it is clear (based on annualized figures) that the United
States and Europe offer investors higher returns with significantly less risk.
Table 1: 1/1/79 - 12/31/96
Country Annualized Return, % Annualized StdDev, %
United States 16.14 14.39
Europe 14.24 16.14
Japan 11.17 24.09 2
Australia 12.85 24.77
3.
Despite posting some of the higher monthly returns, the volatility of the Australian and Japanese markets does not
offer investors an appealing risk/reward scenario. According to the data provided in this case, the average return
for the four stock markets in the sample are very similar. In the Risk/Return Diagram (Figure 3), areas toward the
right (more standard deviation of returns) are only attractive with increases in total annualized return. The upper
left corner is the point of optimization (high returns, low deviation). Therefore, the European and United States
stock markets offered investors a more appealing risk/reward investment strategy. Japanese and Australian
investors were not rewarded for investing in such volatile markets.
Further analysis, using a 36-Month moving window, helps support our hypothesis. Based on a five year (12/31/91
– 12/31/96), rolling 36-month annualized window, Figure 4 provides a graphical illustration of the extreme
volatility in the Japanese and Australian markets. “Spikes” in the Australian Market do go beyond any returns in
the European or United States markets, but also dip below the low end of European returns. The Japanese market is
shown to be very volatile in this graph, having extreme lows without the highs to reciprocate. This is an excellent
example of how volatility may provide an opportunity for increased returns (Australia) over stable markets, but
might also provide only poor to poorer results (Japan).
In contrast to our suggested reasoning for investing in the United States and Europe, an additional attraction for
risk-takers is the possibility to buy low and sell high over short periods of time. Again, the volatility presented in
the Japanese and Australian markets gives high-risk takers the hunger for large returns. However, investors often
“pay for their lunch” only to have it eaten by the market.
1
See Appendix
3
4.
Appendix
Monthly Returns Annual Returns
Japan
US-Annual
US
Japan-Annual
Australia
Europe
Australia-Annual
-50 -40 -30 -20 -10 0 10 20 30
Europe -40 -20 0 20 40 60 80
Australia-Annual
Figures 1 and 2: Monthly and Annual Box Plots
Table 2: Monthly Returns
Variable Mean Median StDev 95.0 % CI 99.9 % CI CV*
Europe 1.29 1.34 4.78 (0.71, 1.87) ( 0.31, 2.27) 3.71
Australia 1.32 1.15 7.03 (0.47, 2.17) (-0.12, 2.76) 5.33
US 1.30 1.35 4.19 (0.80, 1.81) ( 0.45, 2.16) 3.22
Japan 1.31 0.88 6.65 (0.50, 2.12) (-0.05, 2.67) 5.08
Table 3: Annual Returns
Variable Mean Median StDev 95.0 % CI 99.9 % CI CV*
Australia 15.84 18.30 23.17 (5.57, 26.12) (-3.03, 34.71) 1.46
Japan 15.71 19.81 23.77 (5.17, 26.25) (-3.65, 35.06) 1.51
US 15.65 17.98 12.07 (10.29, 21.00) ( 5.82, 25.48) .77
*Coefficient of Variation
4
5.
Figure 3: Risk/Return Diagram
RISK/RETURN 1/1/79 - 12/31/96
24
Eur ope
22 Austr alia
United States
20 J apan
Cash
18
Total Annualized Retur n, %
16
14
12
10
8
6
4 Created with MPI Stylus™
2
0
0 5 10 15 20 25 30 35
Total Annualized StdDev, %
Figure 4: Rolling 36 Month Annualized Risk/Return Diagram
36-MONTH MOVING WINDOW* 12/31/91 -
12/31/96
25
Japan
Australia
20 Europe
United States
Total Annualized Return, %
Cash
15
10
5
0
0 5 10 15 20 25 30 35
Total Annualized StdDev, %
Created with MPI Stylus™
5 Year (12/31/91 - 12/31/96)
Countr y Annualized Retur n, % Annualized StdDev, %
United States 15.06 8.65
Europe 13.16 11.00
Australia 12.36 16.96
Japan 0.26 23.60
5
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