We investigate the persistence in monthly KSE100 excess stock returns over the Treasury bills rates using non-Gaussian state space or unobservable component model with stable distributions and volatility persistence. Results from our non-Gaussian state space model, which is an improvement over Conard and Kaul (1988), show that the conditional distribution has a stable of 1.748 and normality is rejected even after accounting for GARCH. There exists a statistically significant predictable component in the KSE 100 excess stock returns. The optimal predictor in the unconditional expectation of the series is estimated to be 0.18 percent per annum. An evidence of highly nonconstant scales in different periods of time exhibits a tendency towards stock market crashes which invites remedial policy action.