Matrix methods in portfolio analysis

How much money will you make in the future when you make an investment?

YR = assets* returns matrix

Y = asset = single row of the value of assets

R = returns = column x row = state x assets

YR = return of assets in state 1, state 2, ... state n

Arbitrage Portfolio State Price Vectors Finding SPV
 * If the portfolio cost nothing eg: the sum of all assets in Y = 0
 * If none of returns >= 0, no loss
 * If there is at least one asset > 0, at least some profit
 * if SPV == true,
 * then Arbitrage == false
 * if SPV == false,
 * then Arbitrage == true
 * calculate YR = column of 1
 * but asset is p1, p2, .... pn
 * solve for p1, p2, ... pn
 * If answer exists, SPV exists and Arbitrage does not
 * If answer doesn't exist, SPV doesn't exist and Arbitrage exists