In an earlier post entitled “Kerry Up, Markets Down? A Regression Analysis“, I reported the results of the following regression equation:

(1) r_{S&P500,t} = *a* + *b**r*_{Kerry,t} + *e*_{t},

where *r*_{S&P500,t }= daily return on the S&P 500, *r*_{Kerry,t }= daily return on the Kerry Futures contract, *a* = intercept, *b *= slope; and *e*_{t}= error term. I was motivated to estimate this regression equation after reading a *Wall Street Journal *article entitled “Kerry Up, Markets Down” which claimed that “…when Kerry’s political fortunes rise, the stock market tanks.” The evidence presented in this article for this conjecture did not seem all that robust; specifically, it was based upon graphically comparing 5 day moving averages of Kerry Futures Contract prices (available from the Iowa Electronic Markets website) with 5 day moving averages of the S&P 500 index. A more convincing analysis is possible by running this very simple regression equation given in (1) above. I found that while there is statistically significant inverse relationship, the economic significance of the effect is rather negligible; specifically, a 1 percent change in the value of the Kerry Futures contract is associated with a -0.0389% change in the value of the S&P500 index.

It struck me that if Kerry was “bad” for the stock market, it would be interesting to find out whether Bush was “good” for the stock market, so I decided to reestimate regression equation (1) and also run a similar regression (given by equation (2) below) on the Bush Futures contract.

(2) r_{S&P500,t} = *a* + *b**r*_{Bush,t} + *e*_{t},

where *r*_{Bush,t} represents the return on the Bush Futures contract. For both contracts, I used realized daily returns from the period June 2, 2004 through September 9, 2004, resulting in 69 daily observations for the futures contract and stock market returns.

The “new” Kerry results are given in the following table:

*Kerry Regression Statistics*

*R*^{2 }= 0.0508

Observations: 69

*a *= 0.00001 (*P-value *= 0.9921)

*b*= -0.03789 (*P-value* = 0.0626)

Compared with the original regression results from August based upon 47 daily observations from the period June 2, 2004 through August 10, 2004, there has hardly been any change in the parameter values. The correlation between daily returns on the Kerry Futures contract and daily returns on the S&P 500 index is -0.225, and although this inverse relationship is statistically significant (as indicated by the low “P-value” in the table above), it is not economically significant, since it implies that a 1 percent change in the value of the Kerry Futures contract is associated on average with a -0.03789% change in the value of the S&P500 index.

Next, let’s turn our attention to the parameter estimates for regression equation (2), which relates stock market returns to Bush Futures contract returns. There, we find the following:

*Bush Regression Statistics*

R^{2 }= 0.1007

Observations: 69

*a *= -0.00005 (*P-value *= 0.9525)

*b*= 0.06997 (*P-value* = 0.0079)

The correlation between daily returns on the Bush Futures contract and daily returns on the S&P 500 index is .317, and although this positive relationship is statistically significant (as indicated by the negligible “P-value” in the table above), it also (like the Kerry contract) is not economically significant, since it implies that a 1 percent change in the value of the Bush Futures contract is associated on average with a 0.06997% change in the value of the S&P500 index.

While this represents an interesting statistical exercise, the low goodness of fit (*R*^{2}) and the *b *values reported in these tables indicate that there are other (probably much more) important determinants of stock market returns other than the odds of who our next president will be. On the other hand, it is interesting to note that if you take the net difference in the two beta values for Kerry and Bush (0.10786) and assume an expected annual return of 7-10% on the S&P 500, Kerry “costs” investors roughly 75 to 100 basis points per year, the order of magnitude of which is comparable in many cases with the management fees that are typically charged by actively managed mutual funds.