'No arbitrage' vs 'Efficient market' I am trying to wrap my head around the 'no arbitrage' (NA) and 'efficient market' (EM) assumptions, in particular their difference. 

Please correct me if I am wrong, but NA just claims that there is no trading strategy that generates profit but has zero risk, while by contrast EM states that the (historical) price data of an asset already contains all that there is to know about its future development. 

Does one of them imply the other?
NA, in my opinion, is the lack of a trading strategy to generate excess returns, that means returns greater than those of assets in the same risk category. Note that it doesn't mean no risk.

A market is efficient, again in my own understanding, when all the contents of an information set are reflected in the market's assets prices. There are 3 forms of market efficiency weak, semi-strong and strong.


Weak form efficiency is given when the information set contains historical data about the assets, for example past prices, returns, past news about the companies, etc. An example of weak form efficiency would be when past growth data of a company is incorporated into its equity prices.
Semi-strong form efficiency occurs when the market is weak form efficient and the information set also includes all currently available public data about the assets in the market. For example press releases, macroeconomic indicators, etc. An example of semi-strong efficiency would be when due to an increase in the interest rate, the cost of capital of a company increases and the equity prices fall.
Strong form efficiency takes place when a market is semi-strong form efficient and the information set also includes all available private information about assets in the market. For example, plans yet not publicly available about a new product release or private events in the lives of the members of the management team. An example of strong form efficiency would be if, due to the CEO of the company going through a divorce, the company's shares prices fall.