Product Portfolio Evaluation and Differentiated Pricing: A Risk Management Perspective

Posted: 21 Nov 2011 Last revised: 4 Nov 2012

Date Written: November 20, 2011


We consider a retailer that sells a product line to a market with multiple segments. The risk neutral or averse retailer can tailor product assortment and differentiate product prices to each submarket, in which heterogenous customer demand takes a logit form. We derive the optimal pricing operator, which is increasing and concave in a product line power index and determines the optimal product prices in each submarket. From a risk management perspective, we evaluate the product line performance as a financial portfolio problem, in which the optimal pricing operator can be viewed as a utility function, each product variant as a stock with random payoff and each submarket as a state of nature. First, we calculate and characterize the risk aversion coefficient of the optimal pricing operator. Second, we obtain managerial insights for product portfolio evaluation via mean-variance analysis and using stochastic orders. The principles of forming an efficient product line are to select products with high average popularity, low heterogeneity risk across submarkets and low/negative correlation among each other. Selecting products that are popular in separate submarkets generates low/negative correlation among the products.

Keywords: Bayesian Logit, differentiated pricing, mean-variance analysis, product assortment and positioning, risk aversion, Sharpe ratio, stochastic orders, weak majorization

Suggested Citation

Xu, Xiaowei, Product Portfolio Evaluation and Differentiated Pricing: A Risk Management Perspective (November 20, 2011). Available at SSRN: or

Xiaowei Xu (Contact Author)

Rutgers Business School ( email )

The State University of New Jersey
1 Washington Park
Newark, NJ 07102-3122
United States
9733535186 (Phone)

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