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The one period market model is made of 4 securities(A, B, C, D) and has 4 future states. Assume the market model is complete. and the state prices are (-2, 2, 4, 8).

Given that I dont know the payoff of each security in each state; neither do i know the spot price of each security.

How can I find an arbitrage opportunity?

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is this the exercise the way it was written in the book or are you paraphrasing it ? It seems a bit incomplete to me. Perhaps you could just type it down the way it is written in the text-book or on the exercise sheet –  Probilitator Feb 26 at 6:53
    
The question is like this. A one period market model is made of 4 securities and has 4 states at time T>0. Assume that the market model is complete and that the state prices are -2, 2, 4 and 8. show that this market is not arbitrage-free by finding an arbitrage opportunity –  agent251 Feb 26 at 12:44
    
by state prices do you mean a vector $\phi$ with $q=D\phi$ With $q$ being the price vector at $t=0$ , $D$ being the state price matrix (here $4\times 4$) ? –  Probilitator Feb 26 at 17:17

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