1. Economics 434: The Theory of Financial Markets
professor Burton
Fall 2016
November 3, 2016

2. Second Mid-Term Coming Up
Thursday, November 30th
Will cover CAPM and APT (as well as everything else in class, powerpoints, readings)
November 3, 2016

3. 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

4. possible states in a two period economy
What can happen?
We can simplify and just think about these three possibilities S1
State 1 – Gets better
Economy
Now S2
State 2 – Gets worse S3
State 3 – Muddles along
September 1, 2015

5. Three possible states and three available assets
Three states can occur – Good, bad, and mediocre (S1, S2, S3)
What are the available assets? X1, X2, X3
How will each asset perform in each state?
September 1, 2015

6. 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
p1,i is the payoff for security i in state one
p2,i is the payoff for security i in state two
p3,i is the payoff for security i in state three
September 1, 2015

7. X1 X2 X3 X4 X5 s1 s2 s3 Definition of Securities p1,1 p1,1 p1,2 p1,3
September 1, 2015

8. What would constitute a riskless asset?
Assume that owning one unit of Xr 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
Xr is the “riskless asset”
Return $1
State 1 – Economy gets better X1 $1
State 2 – Economy gets worse $1
State 3 – Economy muddles along
September 1, 2015

9. What Does a Security Cost Today?
P1 times Ɵ1 is what it costs to buy a quantity Ɵ1 of security one at price P1.
Or simply: P1 Ɵ1
Similarly for 2, 3, etc.
P1. is always a positive number, but what about Ɵ1. That might be negative
You may have sold security one
Long sale if you already owned it, but could be a short sale
September 3, 2015

10. So, What Does a Portfolio of Securities Cost?
A portfolio is three numbers in a world of three securities: Ɵ1, Ɵ2, Ɵ3 where the Ɵ’s are the amounts purchased or sold of securities one, two and three
Ɵ1P1 + Ɵ2P2 + Ɵ3P3
This could be positive or negative
September 3, 2015

11. What does this security pay
What does this security pay? (these can be negative as well as positive)
In state one:
Ɵ1p1,1 + Ɵ2p1,2 + Ɵ3p1,3
In state two:
Ɵ1p2,1 + Ɵ2p2,2 + Ɵ3p2,3
In state three:
Ɵ1p3,1 + Ɵ2p3,2 + Ɵ3p3,3
September 3, 2015

12. The following three conditions:
No Arbitrage Means
P1φ1 + P2 φ2 + P3 φ3 ≤ 0
Implies
The following three conditions:
p1,1φ1 + p1,2 φ2 + p1,3 φ3 ≥ 0
P2,1φ1 + p2,2 φ2 + p2,3 φ3 ≥ 0
P3,1φ1 + p3,2 φ2 + p3,3 φ3 ≥ 0
Where at least one of the last 3 inequalities is strict, otherwise the budget constraint is strict
September 3, 2015

13. Fundamental Theorem of Finance
The Assumption of No Arbitrage is True
If and only if
There exist positive state prices (one for each state) that represent the price of a security that has a return of one dollar in that state and zero for all other states
September 3, 2015

14. November 3, 2016