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  

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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  

liza@flexemarkets.com  

•  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  

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The  Usual  Plot:  

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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  

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