Daily rhythms occur in numerous physiological and behavioral processes across an immense diversity of taxa, but there remain few cases in which mechanistic links between rhythms of trait expression and organismal fitness have been established. We construct a dynamic optimization model to determine whether risk allocation provides an adaptive explanation for the daily foraging rhythm observed in many species using the orb-weaving spider Cyclosa turbinata as a case study. Our model predicts that female C. turbinata should generally start foraging at lower levels of energy reserves (i.e., should be less bold) during midday when predators are most abundant. We also find that individuals' foraging efficacy determines whether daily rates of encounters with predators or with prey more strongly influences boldness under high risk. The qualitative model predictions are robust to variation in our parameter estimates and likely apply to a wide range of taxa. The predictions are also consistent with observed patterns of foraging behavior under both laboratory and field conditions. We discuss the implications of our study for understanding the evolution of daily rhythms and the importance of model predictions for interpreting empirical studies and generating additional hypotheses regarding behavioral evolution.