Summary: It is standard in quantitative risk management to model a random vector \(\mathbf{X}:=\{X_{t_k}\}_{k=1,\ldots,d}\) of consecutive log-returns to ultimately analyze the probability law of the accumulated return \(X_{t_1}+\cdots +X_{t_d}\). By the Markov regression representation (see [L. Rüschendorf and V. de Valk, Stochastic Processes Appl. 46, No. 2, 183–198 (1993; Zbl 0779.60058)]), any stochastic model for \(\mathbf{X}\) can be represented as \(X_{t_k}=f_k(X_{t_1},\ldots,X_{t_{k-1}},U_k)\), \(k=1,\ldots,d\), yielding a decomposition into a vector \(\mathbf{U}:=\{U_{k}\}_{k=1,\ldots,d}\) of i.i.d. random variables accounting for the randomness in the model, and a function \(f:=\{f_k\}_{k=1,\ldots,d}\) representing the economic reasoning behind. For most models, \(f\) is known explicitly and \(U_{k}\) may be interpreted as an exogenous risk factor affecting the return \(X_{t_{k}}\) in time step \(k\). While the existing literature addresses model uncertainty by manipulating the function \(f\), we introduce a new philosophy by distorting the source of randomness \(\mathbf{U}\) and interpret this as an analysis of the model’s robustness. We impose consistency conditions for a reasonable distortion and present a suitable probability law and a stochastic representation for \(\mathbf{U}\) based on a Dirichlet prior. The resulting framework has one parameter \(c\in [0,\infty]\) tuning the severity of the imposed distortion. The universal nature of the methodology is illustrated by means of a case study comparing the effect of the distortion to different models for \(\mathbf{X}\). As a mathematical byproduct, the consistency conditions of the suggested distortion function reveal interesting insights into the dependence structure between samples from a Dirichlet prior.