Can anyone tell me why condition 1 is wrong?
Maalouf explains, “Valuation using a binomial interest rate tree is based on the principle of no arbitrage. In order for there to be no arbitrage in a financial market, three conditions must be met:
- Condition 1: If the risk of any security is higher than that of another, its expected return must also be higher.
- Condition 2: The price of any two risk-free securities with the same timing and amount of payoffs must be the same.
- Condition 3: The price of any portfolio of securities must equal the sum of the prices of the individual securities in the portfolio.”
What I think that is Condition 1 is more of a general statement that high risk securities should have high return, it is not a condition to prevent arbitrage from happening.
Condition 2 refers to Dominance Arbitrage while Condition 3 refers to Value Additivity Arbitrage. If any one of them does not hold good then arbitrage will take place.