lm(to.quarterly(SP5["2010-04-01::2016-03-01"])[,6] ~ GDPC96["2010-04-01::2016-01-01"] )

A strong correlation exists on those periods, however, the degree of correlation is lower in different terms. It seems that the relationship between GDP and  stock price is more likely to become solid in an upward trend.

> summary(lm(to.quarterly(SP5["2010-04-01::2016-03-01"])[,4] ~ GDPC96["2010-04-01::2016-01-01"] ) )

Call:
lm(formula = to.quarterly(SP5["2010-04-01::2016-03-01"])[, 4] ~  GDPC96["2010-04-01::2016-01-01"])

Residuals:
    Min      1Q  Median      3Q     Max 
-196.63  -85.43   12.53   71.48  171.59 

Coefficients:
                                                      Estimate       Std. Error     t value Pr(>|t|)    
(Intercept)                                       -7.791e+03  6.168e+02  -12.63 1.47e-11 ***
GDPC96["2010-04-01::2016-01-01"]  6.036e-01  3.954e-02   15.27 3.45e-13 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 105.7 on 22 degrees of freedom
Multiple R-squared:  0.9137, Adjusted R-squared:  0.9098 
F-statistic:   233 on 1 and 22 DF,  p-value: 3.453e-13

This model indicates that S&P 500 will up 248 points when GDP annual growth rate is 2.5%.

> last(as.numeric(GDPC96)) * 0.025 * 0.603

[1] 248.6282