There are many examples of prices moving in the same way. It is normal because assets are related and there are events that affect many of them simultaneously. But what about efficiency of this relation? What if response of one asset to price change in another is convex? For example, price model of asset A contains multiplication of asset B price and some parameter that move in the same way as asset A. If this is the case then it is possible to create profitable portfolios (even arbitrage portfolios).
In an ideal world it has to be impossible. But we do not live in an ideal world. Actually, the more I look the more I find examples of such type of relationship. They exist because so are economical relationships. Moreover, it looks like processes in real economy (technological, natural, political, etc) that create such behavior know nothing about arbitrage, free lunch, efficiency and related conceptions. It seems it is pretty fundamental.
Theoretical question. What would be the world without these opportunities? If they are not efficient because of arbitrage then someday they will disappear.
Practical question. How to make use of them?
Relativity of prices
Here I present a hypothesis that price efficiency is a relative conception. Efficiency depends on what you want to maximize. On efficient market prices are optimized to the goal. For example, price should not allow “free lunch”, i.e. making more than risk-free profit without taking a risk. If price is higher then demand rises and price goes down. If price is lower then demand falls and price goes up. But what if different people have different goals? If you want to make more euro then you have increased expectations of return from investments into USA companies comparing to EU companies. Moreover, is amount of currency what do you want the most? Maybe you want to consume more goods and services instead of currency? If so then in theory there are strategies that allow you to earn what you want.