My first assignment for my Quantitative Finance Masters is to design a portfolio that theoretically makes money under any market movement. I am also asked to state all necessary assumptions.
What I'm investigating: I wrote a C++ application that generates a payoff diagrams at maturity with any combination of financial derivatives. I have been researching various well known option strategies (such as straddle, bear-spread, strangle etc).
The problem I am facing: All of these strategies only work under certain predictions about the market. None of them work for all market movement.
Question: Under suitable assumptions, is it possible to design a portfolio that theoretically makes money under any market movement?
I suppose what I am really asking: Does there exist theoretical arbitrage opportunities under certain market assumptions? I am not looking for anything overly complex here. I have very little finance knowledge. If this topic is deemed too broad to answer, I would appreciate some direction toward particular readings.
Edit: I am still looking for more readings on possible models.