Various forms of psychotic disorders, including schizophrenia, can influence how we speak. Therefore, clinicians assess speech and language behaviors of their patients. While it is difficult for humans to quantify speech behaviors precisely, acoustic descriptors, such as tenseness of voice and speech rate, can be quantified automatically. In this work, we identify previously unstudied acoustic descriptors related to the severity of psychotic symptoms within a clinical population (N=29). Our dataset consists of semi-structured interviews between patients and clinicians. Psychotic disorders are often characterized by two groups of symptoms: negative and positive. While negative symptoms are also prevalent in disorders such as depression, positive symptoms in psychotic disorders have rarely been studied from an acoustic and computational perspective. Our experiments show relationships between psychotic symptoms and acoustic descriptors related to voice quality consistency, variation of speech rate and volume, vowel space, and a parameter of glottal flow. Further, we show that certain acoustic descriptors can track a patient's state from admission to discharge. Finally, we demonstrate that measures from the Brief Psychiatric Rating Scale (BPRS) can be estimated with acoustic descriptors.