Probit vs Logit

On 19 December 2018, S&P500 dropped 1.54%, the next day (20 December 2018), KLCI dropped 0.31%.  The linear and logit regression model published on 14 December 2018 (Read more here) predicted the KLCI would fall 0.37% and the chances of the drop are as high as 75%.  This shows that the quantitative approach is indeed decent. 

Besides logit model, one could also use a probit model to run similar analysis.  In the logit model the log odds of the outcome is modelled as a linear combination of the predictor variables.  Meanwhile, in the probit model, the inverse standard normal distribution of the probability is modelled as a linear combination of the predictors.

Chart 1 shows the probability plot for both logit and probit models.  Both models should give similar results.  The slight difference is logit model has fatter tail.

Chart 1

Table 1 is the summary of the probit regression with the estimated coefficients.  The p-values show that the slope is significant but the intercept is not significant.  However, the impact of the intercept to the estimated probability is about 0.5%, which is relatively small, and also the condition where X = 0 is not modelled in this setup.

Table 1