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BEM 113
Class 2
2013
1
Today
1. Practical – Tonight’s Trading Session
2. Walrasian Equilibrium
3. Next Week’s Trading Session
2
1. Tonight’s Trading Session
• 9pm
• Go to http://class.filagora.caltech.edu/class/
• Log in with your ID and password
• Go to marketplaces
3
Marketplaces
• Four marketplaces:
1. Widgets-‐Private-‐1
2. Widgets-‐Public-‐1
3. Widgets-‐Public-‐2
4. Widgets-‐Private-‐2
4
Instructions
• When you are a Buyer then
– You start with ZERO widgets
– You will get a reward for each of the first 3
Widgets you buy (see email)
– Buying > 3 Widgets: gain = sales price – purchase
price
5
Instructions
• When you are a Seller then
– You start with THREE widgets
– You will be charged for each of the first 3 Widgets
you sell (see email)
– Buying extra Widgets: gain = sales price –
purchase price
6
Consequently
• A buyer should try to end with 3 widgets
• A seller should end with zero widgets
• Both buyers and seller make money by buying
low and selling high extra widgets
– Buyer: buying more than 3 widgets
– Seller: buying one or more widgets (after selling 3)
7
Further Practicalities
• Each instance lasts 5 minutes (trading)
• Follow announcements in MESSAGE window
• Send email to Elizaveta Bradulina
• Performance will be computed after all
marketplaces close (presumably next day).
8
2. Walrasian Equilibrium
A. Theory…
B. Financial Markets Case
C. Equilibrium In Complete Financial Markets
9
A. The Theory
• Nobody on the demand and supply side can affect prices
• Announced prices are such that:
DEMAND = SUPPLY
• This is the competitive equilibrium
• A.k.a. the Walrasian equilibrium, after Léon Walras, from
Lausanne (1800s)
• Sharp predictions about (net) quantity that will be traded,
who trades, and at what prices
10
The Usual Plot:
11
Important Remark
• The theory is SILENT about
– How to implement competitive markets
– Specifically, how to get to equilibrium
12
So:
• When economists claim that “markets always work best”,
they are really talking about the beautiful abstract
constructions of the theory
• Whether a given market institution can be associated with
the markets in the theory is not a foregone conclusion
• Unfortunately, many economists believe that any
“free” (unregulated) market will do…
13
Are The Following Competitive Markets?
• Ebay: probably not, because it is one-‐sided
• Treasury auctions: same problem
• OTC derivatives markets: not everyone trades at
the same price
• Real estate market: like the OTC markets?
• The NYSE: looks more like a competitive market
14
For Competitive Markets, We Need, At A Minimum:
Price taking on both
demand and supply side
15
Important Remark
COMPETITIVE
≠
STRATEGIC
(In fact, in a competitive situation, strategy is
not supposed to work…)
16
B. Financial Markets Case
• It would seem that this “first welfare
theorem” (Pareto efficiency of competitive
equilibrium) applies to financial markets as well
• However, there is a hidden assumption:
Utility is defined only with respect to TRADED goods
17
What if…
• Two securities, with payoffs:
• … but agent wants a security that insures her against
disaster in state Y ONLY?
• (Like: agent wants kiwis, but only apples and
strawberries are available)
18
One Needs
• … complete (set of) markets to ensure Pareto
efficiency
• This means: number of securities with linearly
independent payoffs = number of states
• (Intuitively: insurance for all possible casualties needs to exist, otherwise competitive
equilibrium may not be optimal)
19
C. Equilibrium In Complete Financial Markets
• Let there be a complete set of state securities
– These pay $1 in one state, zero elsewhere
• Prices of state securities are state prices
• State price probabilities are ratio of state prices and state probabilities
• (BEM 105: state price “density”)
20
Necessary Condition For Equilibrium
21
@)llfr L Ê '+sr l t N. t eq",L r I (? , ,1 - t
l , f . o t \ . . ^ - . t s - s o f a \ s - l , ,
c f " " { , . , - ) y e t ( r , < ' i
f ; = l a r ; . . - f G t . t < l , ' ( ' - r d * 7 ) _ - , v c a f t r { ,
R r ' t p - r . ( l c s a \ r < l L ( ' ' l 5 b - 5 r . s u l ' ) - - t v e - r [ ) t l e
e f . t C v . t > ( - J L ^ - ( F i c f 6 a \ > r [ !
u o , . . l , J " F J f , r - . f : ' r -
)
f A , c e r ' R r r c J A t C , r r l i {t '
C c r . l = e 1 1 1 r J L A ' N A C ' r - f , 7 j
z . €, , ( ( "1 , , ï È , " , , tr;t c LI
, fÇ L
) 6 f . " r -
A Y
v . . I
j ' t
n{
J . d c r r ^ . , ' r t a d o r , * c - o i 1
-l
(L x t ) i
- l
t , *
t ) /L r (
3 . ( ) a l r e \ . c , * e r , , f ; I r : e *
P t J . , .L 4 . ' - - r { \ 5 - à)
- - ,
9 , a L l r ' '
t/
L 1 . [ * - , - r f r r c r l - " " 1 ( ; * . t -
Ê . ^ ( ' l / ' , , " ' ç *
IL
( ) q " , ( o n l L L : , r : d - . 4 . . î r ( i S ( f i l ^ . , l . r l ; : P s ( - ; - - )
@)llfr L Ê '+sr l t N. t eq",L r I (? , ,1 - t
l , f . o t \ . . ^ - . t s - s o f a \ s - l , ,
c f " " { , . , - ) y e t ( r , < ' i
f ; = l a r ; . . - f G t . t < l , ' ( ' - r d * 7 ) _ - , v c a f t r { ,
R r ' t p - r . ( l c s a \ r < l L ( ' ' l 5 b - 5 r . s u l ' ) - - t v e - r [ ) t l e
e f . t C v . t > ( - J L ^ - ( F i c f 6 a \ > r [ !
u o , . . l , J " F J f , r - . f : ' r -
)
f A , c e r ' R r r c J A t C , r r l i {t '
C c r . l = e 1 1 1 r J L A ' N A C ' r - f , 7 j
z . €, , ( ( "1 , , ï È , " , , tr;t c LI
, fÇ L
) 6 f . " r -
A Y
v . . I
j ' t
n{
J . d c r r ^ . , ' r t a d o r , * c - o i 1
-l
(L x t ) i
- l
t , *
t ) /L r (
3 . ( ) a l r e \ . c , * e r , , f ; I r : e *
P t J . , .L 4 . ' - - r { \ 5 - à)
- - ,
9 , a L l r ' '
t/
L 1 . [ * - , - r f r r c r l - " " 1 ( ; * . t -
Ê . ^ ( ' l / ' , , " ' ç *
IL
( ) q " , ( o n l L L : , r : d - . 4 . . î r ( i S ( f i l ^ . , l . r l ; : P s ( - ; - - )
Apply to state securities: With decreasing marginal utility, and since everyone faces SAME prices, all wealth across states should be inversely ranked to state price probabilities Or: state price probabilities are ranked inversely to aggregate wealth
(Another Consequence)
• Everyone satisfies his/her first-‐order-‐conditions for optimization (FOC), so everyone is always marginal
• (As prices change, everyone changes portfolio)
• This means that the concept of “marginal investor”
often referred to in MBA finance is wrong-‐headed
– Who is marginal? Is the marginal investor smart, then
pricing will be ?smart” otherwise it won’t be
22
3. Next Week’s Trading Session
• … will have a “complete” set of markets!
• But NOT state securities…
• Go to instructions web site
23
Remember
• … how to compute expected payoffs, payoff
variances
• (Mean-‐variance return frontier?)
• (Sharpe ratio?)
24
Your performance numbers may look analogous
25