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.


2 Answers 2


If I understand the question correctly, you're asked to invent a strategy that if under some unrealistic assumptions, your strategy will always earn at a rate higher than the risk-free rate without any risk. This is important because simply buying a risk-free zero-coupon-bond will make money for you, but this is not arbitrage.

One of the simplest assumptions is the Put-call parity. If you can assume your call option is always cheaper than it's theoretical value, you can take a long position on the cheaper call option and a short position on the put option. You can cover up your investment by short selling your stock. If you draw a payoff diagram, your portfolio will always generate positive profits.

There is a PDF document that may be helpful.

  • $\begingroup$ Thank you very much for your response. The professor was very broad as per the exact requirements. The project is purposefully open-ended so that we can think about many different portfolio options. He said to combine as many assets and derivatives as we can. $\endgroup$ Commented Aug 31, 2015 at 6:57
  • $\begingroup$ Well. In this case, every model in QF can be on your assignment. All QF models are built on assumptions and no-arbitrage. $\endgroup$
    – SmallChess
    Commented Aug 31, 2015 at 7:01
  • $\begingroup$ Any other papers you would suggest reading on one of such models, preferably a simple one? $\endgroup$ Commented Aug 31, 2015 at 15:55
  • $\begingroup$ By the way, the article you provided was very helpful. $\endgroup$ Commented Aug 31, 2015 at 16:49
  • $\begingroup$ I will soon. Still waiting on more possible input from others. $\endgroup$ Commented Sep 1, 2015 at 3:29

Reading your comment on Student T's answer, it could be possible that your professor is expecting you to come up with the simple fact that, under assumptions of no arbitrage, there is now way to generate a return superior to the risk-free rate without taking any risk.

Note that making money is probably not the right terminology, making on average more money than the risk-free bond is probably what he meant, and in all market conditions would mean without risk.

This is a typical question you ask to beginners in finance in general, to generate the concept that there is no free lunch.

  • $\begingroup$ So even under unjustly assumptions there are no free lunches? I have been using StudentT's suggestion to exploit the put-call parity. Is that not an example of a free lunch? $\endgroup$ Commented Aug 31, 2015 at 23:06
  • $\begingroup$ If there are no free lunches, then calls are not cheaper than their theoretical price (that would be the free lunch). $\endgroup$
    – SRKX
    Commented Sep 1, 2015 at 3:59

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