Presentation on theme: "1 Complete Markets. 2 Definitions Event State of the world State Contingent Claim (State Claim) Payoff Vector Market is a payoff vector Exchange dollars."— Presentation transcript:
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
4 Uncertainty Market complete? Interest rate? Probability of War?
5 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.
6 Financial Decision Making Market prices determine value Competitive markets One-sided markets
7 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
8 Time Value of Money Interest rate is the exchange rate across time
10 Time Value of Money NPV + Borrowing and Lending
11 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
12 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?
13 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
14 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
15 Risk Premium Expected return Risk premium No-arbitrage pricing of a risky security
16 Risk Premiums Depends on risk Riskier securities command higher risk premium Risk is relative to the overall market Risk premium can be negative
17 Risk Premiums Risk premium depends on risk: r s = r f + (risk premium for investment s)
18 Arbitrage and Transaction Costs Two types of costs: Commissions Bid-ask spreads No arbitrage conditions hold “up to transaction costs”
19 Financial System Financial market Security Bond Stock Option Mutual fund Exchange-traded fund Hedge fund Private equity fund
20 Asymmetric Information Adverse selection Moral hazard Financial intermediaries Free markets