Pricing kernels reflect market preferences and are used to adjust the risk neutral density of stock return dynamics. This yields the density of the returns under the physical measure, which captures market expectations. We address the nonparametric estimation of conditional physical density through the maximum likelihood method, by exploring the predictive information in the risk-neutral distribution estimated from option prices. For identification, we propose a theoretical restriction from the long-run risk asset pricing models to decompose the pricing kernel into permanent and transitory components. Using DAX 30 Index return and option data we estimate the pricing kernel and evaluate the forecasting performance of the implied physical densities. The results show that our method provides better forecasts for the realized returns out-of-sample than alternative methods that assume parametric pricing kernel specification.