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Complete Markets

Complete Markets. Definitions. Event State of the world State Contingent Claim (State Claim) Payoff Vector Market is a payoff vector Exchange dollars today for state-contingent bundle of dollars tomorrow Markets are complete If we can arrange a portfolio with any payoff vector.

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Complete Markets

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  1. Complete Markets

  2. Definitions • Event • State of the world • State Contingent Claim (State Claim) • Payoff Vector • Market is a payoff vector • Exchange dollars today for state-contingent bundle of dollars tomorrow • Markets are complete • If we can arrange a portfolio with any payoff vector

  3. Uncertainty • Market complete? • Interest rate? • Probability of War?

  4. example If I know what pure securities pay TOMORROW ($1 in only one state - e.g. "u" or "d") and I know their prices TODAY (p_u and p_d) then I can figure out the price TODAY of any security generating payoffs (cash flows) TOMORROW. In the example you refer to, we work `backwards'. We know the price TODAY (V_1 = 1) of a security that pays (TOMORROW) 1.5 in the "u" state and 0.5 in the "d" state AND we know the price TODAY of the risk-free bond (b = 1) that pays 1 in BOTH states TOMORROW (that's why it is risk-free - it doesn't matter which state prevails) - note that since b = 1 TODAY, the risk-free rate of interest is 0. Knowing these 2 prices allows us to compute the prices of the pure securities TODAY: p_u = 0.5 and p_d = 0.5. Now we can determine the price TODAY of ANY other security in this world - e.g.: a security that pays (TOMORROW) 0.5 in "u" and 0 in "d," must have a price of 0.25 TODAY ... TODAY, in this example, simply means some time before the state (here "u" or "d") is revealed at some later time (perhaps only an instant later) - here called TOMORROW.

  5. Financial Decision Making • Market prices determine value • Competitive markets • One-sided markets

  6. Time Value of Money • $1 today is worth more than $1 tomorrow • Interest rate is the exchange rate across time • $1 in your pocket is worth more than $1 promised • Which is worth more than $1 expected • Which is worth more than $1 hoped for • Risk-free rates • PV • NPV • NPV + Borrowing or Lending

  7. Time Value of Money • Interest rate is the exchange rate across time

  8. Time Value of Money • PV, NPV

  9. Time Value of Money • NPV + Borrowing and Lending

  10. Arbitrage • Arbitrage • Certain profit by exploiting different pricing for the same asset • Law of one price • An asset has the same price in all exchanges • No-arbitrage and security pricing • Bond • $1000, 1 year, 5% • What if over-priced or under-priced? • Determine interest rates from bond prices • Other securities

  11. Separation Principle • Security transactions in a normal market do not create nor destroy value • This allows us to only focus on the NPV of the project • And not worry about the financing choice • Example: • Cost today: $10M • Benefit in 1 year: $12M • Risk-free rate: 10% • Ability to issue $5.5M security today • Does the issuance matter?

  12. Portfolio Valuation • Value additivity • Price of a portfolio is the sum of the prices of individual securities • A firm is a portfolio of projects • The value of the firm is the sum of the values of all projects • Maximizing NPV for each decision maximizes the value of the firm

  13. Price of Risk • $1 in your pocket is worth more than $1 promised • Which is worth more than $1 expected • Which is worth more than $1 hoped for

  14. Risk Premium • Expected return • Risk premium • No-arbitrage pricing of a risky security

  15. Risk Premiums • Depends on risk • Riskier securities command higher risk premium • Risk is relative to the overall market • Risk premium can be negative

  16. Risk Premiums • Risk premium depends on risk: • rs = rf + (risk premium for investment s)

  17. Arbitrage and Transaction Costs • Two types of costs: • Commissions • Bid-ask spreads • No arbitrage conditions hold “up to transaction costs”

  18. Financial System • Financial market • Security • Bond • Stock • Option • Mutual fund • Exchange-traded fund • Hedge fund • Private equity fund

  19. Asymmetric Information • Adverse selection • Moral hazard • Financial intermediaries • Free markets

  20. Money • Barter system • Money is a medium of exchange • Commodity money • Fiat mondey

  21. Money supply

  22. Money supply

  23. Money Supply

  24. The Euro • What happens if a country imports too much • Currency devaluates • What if currency is fixed (Greece) • Wages must fall or • Output declines

  25. Bitcoin • http://bitcoin.org/en/

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