Are national interest rates good predictors of a country’s stock market performance? Why or why not?
1) Part A: The means give the average values for the given sample. The standard deviations are a measure of the variation about the mean. With the small sample sizes it is difficult to draw accurate conclusions based on these numbers alone. It is also not recommended to assume a normal distribution. For that reason a hypothesis test to see if the means are significantly different from zero will be conducted using a t test.
Part B:
First for the market indices.
The null hypothesis is that the mean is equal to zero.
The alternate hypothesis is that the mean is not equal to zero.
The test statistic is
t = (30.48 – 0) / [ 14.56 / 101/2 ]
t = 6.62
This particular test has 18 – 1 = 17 degrees of freedom. From the associated tables this corresponds to a p-value of 4.337*10-6.
Since the p-value is less than 0.05, the null hypothesis is rejected and it is concluded that the mean is significantly different from zero.
Now repeat the process for the interest rates.
The null hypothesis is that the mean is equal to zero.
The alternate hypothesis is that the mean is not equal to zero.
The test statistic is
t = (97.19 – 0) / [ 251.75 / 101/2 ]
t = 3.162
This test, in the same fashion as the previous test, also have 18 – 1 = 17 degrees of freedom. The corresponding p-value is 0.00569.
Since the p-value is less than 0.05, the null hypothesis is rejected and it is concluded that the mean is significantly different from zero.
Selected Economic Statistics for 2005 and 2006 by Country*
Country 2005 Market Index** 2006 Market Index 2005 Interest Rates*** 2006 Interest Rates 2006 Per Capita GNI 1000’s $ 2006 Inflation Rate 2006 Unemploy-ment Rate % Change in Market Indices % Change in Interest Rates
Australia 312.5 400.6 5.46 5.81 35.86 3.5 4.8 28.19 6.41
Belgium 321.2 427.5 2.02 2.73 38.46 1.8 8.2 33.09 35.15
Canada 369.4 425.7 2.73 4.03 36.65 2.0 6.3 15.24 47.62
France 273.3 365.7 2.03 3.05 36.56 1.6 9.2 33.81 50.25
Germany 224.3 302.8 2.03 3.08 36.81 1.7 9.8 35.00 51.72
Indonesia 79.0 128.0 6.78 9.18 1.42 13.1 NA 62.03 35.40
Italy 213.8 280.6 2.17 3.18 31.99 2.1 6.8 31.24 46.54
Japan 113.5 115.8 0.01 0.12 38.63 0.2 4.1 2.03 1100.00
Malaysia 119.5 158.9 2.48 3.23 5.62 3.6 NA 32.97 30.24
Mexico 360.1 501.0 9.20 7.19 7.83 3.6 NA 39.13 -21.85
Netherlands 309.6 401.8 2.02 3.07 43.05 1.1 3.9 29.78 51.98
Singapore 176.3 249.4 2.04 2.95 28.73 1.4 NA 41.46 44.61
Spain 288.6 422.1 2.19 3.26 27.34 3.5 8.5 46.26 48.86
Sweden 378.3 542.6 1.72 1.75 43.53 1.4 7.0 43.43 1.74
Switzerland 452.5 577.6 0.71 1.36 58.05 1.1 4.0 27.65 91.55
Thailand 76.7 81.3 2.62 4.64 3.05 4.6 NA 6.00 77.10
United Kingdom 217.6 278.3 4.55 4.65 40.56 3.2 5.3 27.90 2.20
United States 302.4 343.2 3.15 4.72 44.71 3.2 4.6 13.49 49.84
* Source: U.S. Census Bureau and United Nations Mean 30.48 97.19
** Dow-Jones World Stock Index Std Dev 14.56 251.75
*** Treasury Bill Rates, if NA Money Market Rates Used