Coach and Ralph Lauren are still growing because they understand what middle-class shoppers can afford. Markets have an uncomfortable message for Europe's top luxury tycoon, Bernard Arnault. Shareholders now value his company LVMH at a slight discount to Ralph Lauren, which sells less expensive luxury goods.

The takeaway is that European luxury brands have to make difficult decisions to cut prices if they want to win back shoppers. LVMH's stock is 3% cheaper than the American brand as a multiple of expected earnings. The owner of Louis Vuitton and Christian Dior has been losing its edge for a while.

Its shares used to trade at a big premium to the American label, but the valuation gap has evaporated. The last time this happened was more than a decade ago, when Louis Vuitton's sales were sluggish because consumers had grown tired of logoed designs. LVMH gave the brand a refresh and returned it to strong growth.