I've taken two very simple approaches to assessing the relationships between these factors and the S&P 500.  They should be viewed as "approximations" at best.

The first approach is to calculate the correlation between the S&P 500 and these factors since September, both with and without a one-day lag.  

Without a lag, the correlation between the log-return of the S&P 500 and the dollar, gold, and political environment are -0.54, 0.37, and 0.17 respectively.  These coefficients can be interpreted as indicating that, within a given day, the S&P tends to move the opposite direction as the dollar and the same direction as gold and the probability of a Republican-controlled House.  Of these, the magnitude of the coefficient is largest on the dollar index, indicating that this relationship is likely strongest.

When we consider a lagged correlation between the S&P 500 and these factors, we obtain a different picture.  In this case, the correlation between the S&P 500's return tomorrow and today's return in the dollar, gold, and the probability of Republican House control are 0.55, -0.29, and -0.39 respectively.  These coefficients suggest the opposite of the within-day coefficients above, though the magnitude of the dollar correlation remains strongest.  This reverse relationship is likely due to the significant negative autocorrelation in the S&P 500 over the sample.

The second approach to assessing this relationship is to fit a GLM to the data to predict tomorrow's S&P 500 return from today's return in the factors.  In this case, I fit a simple normal model and obtain values of \beta of 0.79, 0.11, and -0.068 for the dollar index, gold, and probability of Republican-controlled House.  However, the t-statistic is only greater than 2 for the dollar index coefficient.

There are some measurement issues to address.  First, we're comparing the spot equity market to futures markets for gold and the dollar index.  Second, InTrade's probability of a Republican-controlled House is a very imperfect proxy for political environment. Not only does this probability ignore both the Senate and the Executive branch, but it also assumes that the House and Republican policy is capable of improving business climate.

However, taking this naive analysis at face value, it appears that the dollar does appear to be driving the S&P 500 more than gold or expectations of political environment.

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This first plot shows the cumulative log-return of the S&P 500 (SPY).  The blue line tracks the return of the S&P 500 itself, confirming 3% increase over this period that most media sources have focused on.  The green line, however, shows the return of the S&P 500 net of the return on gold.  This green line has fallen 5% over the same time period.

Many “gold bugs”  believe that gold is the appropriate numeraire for pricing since its value is not as subject to the monetary policy of governments.  While gold is certainly not a perfect proxy for purchasing power, it is likely more indicative of the purchasing-power-return than a simple dollar-return.  If we do take this logic at face value, then the real purchasing power of an S&P 500 portfolio has decreased, not increased.

One might therefore ask whether the correlation between the S&P 500 and gold is decidedly positive or negative on short time-scales.  The figure below shows the trailing 60-minute correlation between SPY and GLD.

This figure indicates that the correlation seem to oscillate between mild positive and negative correlations.  On average, this correlation is mildly positive at 0.12  with a standard deviation of 0.22.

In conclusion, though the return of an S&P 500 portfolio denominated in gold has been negative over the past month, the short-term correlation between the S&P 500 and gold is neither strongly positive nor negative.

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