Online product returns risk assessment and management

Abstract

Commonly viewed as a cost center from an operations perspective, product returns have the potential to strongly influence operating margins and business profitability, thus constituting a risk for online retailers. This work addresses the problem of how to assess and manage product returns costs using a risk analysis methodology. Online product returns are seen as a random phenomenon that fluctuates in severity over time, threatening the profitability of the online store. Therefore, the starting point is that this risk can be modeled as a future random stream of payments. Given one or many future time periods, we aim to assess and manage this risk by answering two important questions: (1) Pricing—or what dollar amount factored on top of the current price of goods sold online would cover the cost of product returns, and (2) Reserving—or how much capital does an online retailer need to reserve at the beginning of each period to cover the cost of online product returns. We develop our analysis for one period (a month) by a closed formula model, and for multi-period (a year) by a dynamic simulation model. Risk measurements are executed in both cases to answer the two main questions above. We exemplify this methodology using an anonymized archival database of actual purchase and return history provided by a large size US women’s apparel online retailer.

Appendices

Appendix A: One-year numerical results, case of $l=0.025,c=0.1,C_0 ^{\prime }={\$} 335,796$,$C_t ^{\prime }=0(t>1)$.

See Tables 4, 5, 6, and 7.

Table 4 Loss ratio statistics in the case of $l=0.025,C_0 ^{\prime }=\$ 335,796$, and $C_t ^{\prime }=0(t>1)$. $\hbox {VaR}_{0.995}$ are far greater than 1, contrary to the established decision rule of being lower than 1

Table 5 Monthly survival probabilities in the case of $l=0.025,C_0 ^{\prime }=\$ 335,796$, and $C_t ^{\prime }=0\,(t>1)$

Table 6 VaR and TVaR of ruin capital samples $K_t^d (t=1,\ldots ,12)$ for the case $l=0.025,C_0 ^{\prime }=\$ 335{,}796$, and $C_t ^{\prime }=0\,(t>1)$

Table 7 Survival probabilities for the case $l=0.025, C_0 ^{\prime }=\$ 335,796$, and $C_t ^{\prime }=\mathrm{VaR}_{0.99} \left( {K_t^d } \right) (t>1)$ found in Table 6

Appendix B: One-year numerical results, case of $l=0.025,c=0.1,C_0 ^{\prime }=\$ 335,796, and C_t ^{\prime }=-\mathrm{VaR}_{0.005} (\pi _{t+1} -\chi _{t+1} )\left( {t=1,\ldots ,11} \right)$

See Tables 8, 9, 10 and 11.

Table 8 Monthly reserved capital calculated by means of $C_t ^{\prime }=-\mathrm{VaR}_{0.005} (\pi _{t+1} -\chi _{t+1} )\left( {t=1,\ldots ,11} \right)$

Table 9 Monthly survival probabilities case of $l=0.025,c=0.1,C_0 ^{\prime }=\$ 335{,}796$, $C_t ^{\prime }=-\mathrm{VaR}_{0.005} (\pi _{t+1} -\chi _{t+1} )\left( {t=1,\ldots ,11} \right)$

Table 10 VaR and TVaR of ruin capital samples $K_t^d (t=1,\ldots ,12)$ for the case $l=0.025,c=0.1,C_0 ^{\prime }=\$ 335{,}796$, and $C_t ^{\prime }=-\mathrm{VaR}_{0.005} (\pi _{t+1} -\chi _{t+1} )\left( {t=1,\ldots ,11} \right)$

Table 11 VaR and TVaR of monthly invested capital samples $C_t (t=1,\ldots ,11)$ in the case $l=0.025,c=0.1,C_0 ^{\prime }=\$ 335,796$, and $C_t ^{\prime }=-\mathrm{VaR}_{0.005} (\pi _{t+1} -\chi _{t+1} )\left( {t=1,\ldots ,11} \right)$