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Alex C
Alex C
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Generally the properties market prices must satisfy are of 2 kinds: no arbitrage properties and no-disequilibrium properties.

No arbitrage"No arbitrage" is stronger in that it creates a sure-profit incentive for its elimination. Any economic agent who sees a \$50 USD bill on the floor has an incentive to pick it up. On the other hand, the example you give is a disequilibrium: the stocks have the same risk $\sigma$ but one has a better expected return. There is an economic incentive to eliminate the disequilibrium by investing in 1 rather than 2, but it does not represent a riskless profit opportunity. Only economic agents who had already decided to purchase stock 2 have an incentive to switch to stock 1 when they discover the disequilibrium situation.

In general arbitrage conditions are rare to find (they require that 2 securities are perfect substitutes), and so most loosely related securities (for example stocks of two different companies, say Toyota and Honda) are priced by equilibrium considerations. Only in the field of Financial Derivatives do no-arbitrage conditions solve all our problems. Most questions in Economics (eg. why are oranges more expensive than apples) involve equilibrium considerations, supply (oranges are more difficult to grow) and demand (oranges are more nutritious, can be squeezed to make juice, etc.). "No arbitrage" does not help in relative pricing of oranges and apples (or Toyota and Honda) because they are goods with different properties.

Generally the properties market prices must satisfy are of 2 kinds: no arbitrage properties and no-disequilibrium properties.

No arbitrage is stronger in that it creates a sure-profit incentive for its elimination. Any economic agent who sees a \$50 USD bill on the floor has an incentive to pick it up. On the other hand, the example you give is a disequilibrium: the stocks have the same risk $\sigma$ but one has a better expected return. There is an economic incentive to eliminate the disequilibrium by investing in 1 rather than 2, but it does not represent a riskless profit opportunity. Only economic agents who had already decided to purchase stock 2 have an incentive to switch to stock 1 when they discover the disequilibrium situation.

In general arbitrage conditions are rare to find (they require that 2 securities are perfect substitutes), and most loosely related securities (for example stocks of two different companies, say Toyota and Honda) are priced by equilibrium considerations. Only in the field of Financial Derivatives do no-arbitrage conditions solve all our problems. Most questions in Economics (eg. why are oranges more expensive than apples) involve equilibrium considerations, supply (oranges are more difficult to grow) and demand (oranges are more nutritious, can be squeezed to make juice, etc.).

Generally the properties market prices must satisfy are of 2 kinds: no arbitrage properties and no-disequilibrium properties.

"No arbitrage" is stronger in that it creates a sure-profit incentive for its elimination. Any economic agent who sees a \$50 USD bill on the floor has an incentive to pick it up. On the other hand, the example you give is a disequilibrium: the stocks have the same risk $\sigma$ but one has a better expected return. There is an economic incentive to eliminate the disequilibrium by investing in 1 rather than 2, but it does not represent a riskless profit opportunity. Only economic agents who had already decided to purchase stock 2 have an incentive to switch to stock 1 when they discover the disequilibrium situation.

In general arbitrage conditions are rare to find (they require that 2 securities are perfect substitutes), and so most loosely related securities (for example stocks of two different companies, say Toyota and Honda) are priced by equilibrium considerations. Only in the field of Financial Derivatives do no-arbitrage conditions solve all our problems. Most questions in Economics (eg. why are oranges more expensive than apples) involve equilibrium considerations, supply (oranges are more difficult to grow) and demand (oranges are more nutritious, can be squeezed to make juice, etc.). "No arbitrage" does not help in relative pricing of oranges and apples (or Toyota and Honda) because they are goods with different properties.

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Alex C
Alex C
  • 9.4k
  • 1
  • 22
  • 34

Generally the properties market prices must satisfy are of 2 kinds: no arbitrage properties and no-disequilibrium properties.

No arbitrage is stronger in that it creates a sure-profit incentive for its elimination. Any economic agent who sees a \$50 USD bill on the floor has an incentive to pick it up. On the other hand, the example you give is a disequilibrium: the stocks have the same risk $\sigma$ but one has a better expected return. There is an economic incentive to eliminate the disequilibrium by investing in 1 rather than 2, but it does not represent a riskless profit opportunity. Only economic agents who had already decided to purchase stock 2 have an incentive to switch to stock 1 when they discover the disequilibrium situation.

In general arbitrage conditions are rare to find (they require that 2 securities are perfect substitutes), and most loosely related securities (for example stocks of two different companies, say Toyota and Honda) are priced by equilibrium considerations. Only in the field of Financial Derivatives do no-arbitrage conditions solve all our problems. Most questions in Economics (eg. why are oranges more expensive than apples) involve equilibrium considerations, supply (oranges are more difficult to grow) and demand (oranges are more nutritious, can be squeezed to make juice, etc.).