1. Economics 434 Professor Burton Fall 2015 September 1, 2015

2. Public Stock Main subject of this course Anonymous purchase and sale using a broker-dealer registered with SEC Return has two main components August 28, 2014 Capital Gain Increase in stock value P t+1 - P t Dividend Cash payments Usually every 3 months D t Where P is price, t is time, D is dividend at time t

3. Calculating the Rate of Return for a stock September 1, 2015 Where D is total dividends received during the period from t-1 to t

4. September 1, 2015 Over the past 100 years, the average stock has returned approximately 10 percent per year Considerable volatility(variance) involved with this return 10 percent is an extraordinarily high number; larger than one would expect But, it is what it is!

5. Calculating returns for today is fine and all, but what we really want to know is the stock’s return in the next period (t+1) But we can only guess since all we know today is P t September 1, 2015

6. Asset choice in a two period economy Suppose that the world only has two periods; there is only one more period after today Suppose we want to buy assets now (in this period) that will do well by the end of this upcoming single period What should we own? September 1, 2015

7. Possible states in a two period economy What can happen? We can simplify and just think about these three possibilities September 1, 2015 Now S2S2 S1S1 S3S3 State 1 – Gets better State 2 – Gets worse State 3 – Muddles along Economy

8. Three possible states and three available assets Three states can occur – Good, bad, and mediocre (S 1, S 2, S 3 ) What are the available assets? X 1, X 2, X 3 How will each asset perform in each state? September 1, 2015

9. The Definition of a “Real-World” Security Given the states of the world: s1, s2, s3 A security is defined by its payoff in dollars in each state of the world – p i, 1 is the payoff for security i in state one – p i, 2 is the payoff for security i in state two – p i, 3 is the payoff for security i in state three September 1, 2015

10. s1s1 s3s3 s2s2 Definition of Securities X1X1 X2X2 X3X3 X4X4 X5X5 P 1,1 P 1,2 P 1,1 P 1,3 P 2,1 P 2,2 P 2,3 P 3,1 P 3,2 P 3,3 P 4,1 P 5,1 P 4,2 P 5,2 P 4,3 P 5,3 September 1, 2015

11. What would constitute a riskless asset? A riskless asset returns the exact same amount in each state – Might be negative (a riskless asset can have a negative return), but this loss is known in advance – Return has to be same in each state to have no risk – If there is more than one riskless asset, “the” riskless asset used will be the one with the highest return September 1, 2015

12. What would constitute a riskless asset? Assume that owning one unit of X 1 will return exactly 1 dollar regardless of state – Return doesn’t have to be 1; could be anything. Easier to simply assume 1 unit of return in each state X 1 is the “riskless asset” September 1, 2015 X1X1 $1 State 1 – Economy gets better State 2 – Economy gets worse State 3 – Economy muddles along Return

13. September 1, 2015