Sub-sample analysis

A sub-sample analysis was carried out to determine the relationship between commodities‟ price cointegration and the stock and bond markets during different periods in the economy. There is no clear distinction between the recession and recovery periods to enable selection of an exact date to separate samples. Therefore, a year end was selected as a separator between

the recession and recovery periods. This is supported by the S&P 500 daily closing prices, shown in Figure 6.6. The samples in the figure are separated between the end of 2008 and the beginning of 2009. The first sample is from 6 September 2007 to 31 December 2008, where two events took place: the easing of the global energy crisis, and the easing of the stock market recession. The second sample is from 1 January 2009 to 20 January 2012;

during this period the stock market experienced recovery and commodities‟

cointegration grew stronger. Regression results for the first sample are shown in Table 6.3.

Figure 6.6: S&P 500 Closing Daily Prices

Table 6.3: Gold-silver, Gold-oil, and Silver-oil λ-trace Statistic Returns on the S&P 500 and the Barclays Global Aggregate Bond Index

Regression

Results shown are for the period 6 September 2007 to 31 December 2008

From Table 6.3 we can see that during the first sample period the Barclays Global Aggregate Bond Index returns appear to have strong explanatory power over the strength of gold and silver cointegration; statistical probability is 0.0412 and the relationship is positive: 14.9581. Note that these numbers are stronger than for the whole sample period outlined in Table 6.2.

During this period returns on the debt market decreased, bonds became less expensive and valuable, and the economy was destabilising. Market turbulence and speculation increased, gold and silver prices deviated from their normal long-run relationship, and cointegration became weaker.

Variable Coefficient Prob. Coefficient Prob. Coefficient Prob.

S&P500 Returns 0.8092 0.7965 -8.1384 0.0344 -6.2367 0.0470

S&P500 Volatility 3.3662 0.4125 0.7041 0.8884 1.6580 0.6857

Barclays Global Aggregate

Bond Index Returns 14.9581 0.0412 21.1769 0.0182 8.4802 0.2451

Barclays Global Aggregate

Bond Index Volatility -0.1896 0.9611 -1.0056 0.8322 -2.0221 0.6018

R-squared

Dependent Variable

Gold-Silver Gold-Oil Silver-Oil

0.0138 0.0080 0.0163

The Barclays Global Aggregate Bond Index appears to have high impact on gold and silver, with a coefficient of 14.9581. This supports gold‟s safe haven attributes and the similar properties of debt instruments, especially during crises.

For gold and oil, the S&P 500 and the Barclays Global Aggregate Bond Index returns appear to have strong explanatory power: probabilities are 0.0344 and 0.0182 respectively. The relationship is negative for S&P 500 returns: -8.1384; but positive for the Barclays Global Aggregate Bond Index returns: 21.1769. Again, note that these numbers are stronger than for the whole sample period outlined in Table 6.2.

The explanation of a positive relationship between gold and oil cointegration and returns on the Barclays Global Aggregate Bond Index is similar to the previous explanation. During this period, returns on the debt market went down, bonds became cheaper, and the economy was slowing down. Market turbulence and speculation increased, gold and oil prices deviated from their normal long-run relationship, and cointegration became weaker. The negative relationship between gold and oil cointegration and returns on the S&P 500 is supported by returns on the stock market decreasing, and stocks becoming less expensive and valuable – signaling that the economy was shrinking. During the crisis, when returns on the stock market dropped, market players invested more in gold, balancing

investments to gold and oil – which lead to the gold and oil relationship returning to its long-run equilibrium. Interestingly, it appears that the Barclays Global Aggregate Bond Index has greater absolute impact than the S&P 500, 8.1384 vs. 21.1769, and greater significance, 0.0344 vs. 0.0182.

This could mean that gold‟s safe haven attributes have more economical weight than oil‟s speculative features.

For silver and oil it appears that S&P 500 returns have strong explanatory power over the strength of silver and oil cointegration: statistical probability is 0.0470, and the relationship is negative: -6.2367. This supports the assumption that in a bad economic climate, when stock market volatility increases, returns decrease – and the price relationship between silver and oil becomes stronger, as oil becomes a less speculative asset.

Table 6.4 shows results of the second sample. Interestingly, it appears that during this period neither the S&P 500 nor the Barclays Global Aggregate Bond Index have strong explanatory power over the cointegration strength of gold and silver, gold and oil, and silver and oil. It appears that the S&P 500 returns have some explanatory power over the strength of gold and silver cointegration: statistical probability is 0.1136, but the number is not significant. Also, there are a number of cases where probabilities are approaching 0.2000 – 0.3000 levels, but do not appear to be significant.

This could mean that gold and silver, gold and oil, and silver and oil price relationships are unaffected by both the stock and bond markets during this

period, and are probably explained by other factors. It is possible that although the economy seemed to be growing, it was a period of uncertainty with no real trends – in which case there is no meaningful output of the regression. Further research is required to understand this relationship better.

In summary, we can conclude that hypothesis 4 is correct: over the sample period, cointegration strength between gold and silver, gold and oil, and silver and oil falls during periods of crises, recessions and market turbulence in the stock and bond markets.

Table 6.4: Gold-silver, Gold-oil, and Silver-oil λ-trace Statistic Returns on the S&P 500 and the Barclays Global Aggregate Bond Index

Regression Results

Results shown are for the period from 1 January 2009 to 20 January 2012

Variable Coefficient Prob. Coefficient Prob. Coefficient Prob.

S&P500 Returns 6.7670 0.1136 -0.8105 0.8305 -4.4565 0.3058

S&P500 Volatility -4.3632 0.4603 4.6051 0.3793 0.0344 0.9954

Barclays Global Aggregate

Bond Index Returns 3.1165 0.8606 4.2499 0.7870 -1.1341 0.9500

Barclays Global Aggregate

Bond Index Volatility -4.5615 0.7444 -9.9221 0.4237 -16.7703 0.2393

R-squared

Dependent Variable

Gold-Silver Gold-Oil Silver-Oil

0.0049 0.0017 0.0036