carrot dicing l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Carrot Dicing PowerPoint Presentation
Download Presentation
Carrot Dicing

Loading in 2 Seconds...

play fullscreen
1 / 23

Carrot Dicing - PowerPoint PPT Presentation


  • 279 Views
  • Uploaded on

Carrot Dicing A Model for the Tote Price Distribution for Horseracing Charles Magri ( cmagri@mbox.com.au ) 2 December, 2002 Roadmap for Presentation The Model Full Description The Evidence Empirical Distribution Fit Exploitation – A profitable strategy

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Carrot Dicing' - niveditha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
carrot dicing

Carrot Dicing

A Model for the Tote Price Distribution

for Horseracing

Charles Magri

( cmagri@mbox.com.au )

2 December, 2002

roadmap for presentation
Roadmap for Presentation
  • The Model
    • Full Description
  • The Evidence
    • Empirical Distribution Fit
    • Exploitation – A profitable strategy
  • Generalisation of Application
    • Share markets, Portfolio Selection
    • Parimutuel Financial markets
      • Deutsche & Goldman options on economic statistics
  • Further Work
the recipe
The Recipe
  • Ingredients
    • 8 different sized pots
    • A case of whiskey, rum, brandy or vodka
    • A meat axe
    • About 10,000 carrots
  • Method
    • Consume about half a bottle of the liquid and stand for about 15 to 20 minutes
    • Select a carrot. Make 7 random chops into carrot with axe
    • Place the biggest piece in the biggest pot, the second biggest in the second biggest pot, etc.
    • Repeat last two steps taking two swigs of the liquid between carrots making sure not to spill any of the liquid onto the food
some statistics a
Some Statistics (a)

U1, U2, ..., Un i.i.d U(0,1) Cutting locations

sort ascending

U(1), U(2), ... U(n)Ordered Statistics

successive differences

S1, S2, ..., Sn, Sn+1Sample Spacings

where Sj = U(j) - U(j-1), U(0) = 0, U(n+1) = 1

sort (descending)

S(1), S(2), ..., S(n), S(n+1)Ordered Spacings

CARROT DICING MODEL

some statistics b
Some Statistics (b)

Order Statistics

  • The density function for U(k) is given by :-

n k-1 n-k

gk (x) = (k-1, 1, n-k) . x (1 -x)

some statistics c
Some Statistics (c)

Order Spacings

The density function for S(k)is given by :-

n + 1

hk (x) = (k-1, 1, n-k+1) . n! .

 ... xj x: j=1, ... k-1dx1 dx2...dxn

xjx , j=k, ..., n, n xj = 1 - x

some statistics d
Some Statistics (d)

  • Favourite in a 3-horse race (n=2, k=1)
  • hk(x) = 6. du dv = 6. min(x, 1-x) du

u,v  x max(0, 1 - 2x)

u+v = 1-x

0 if x < 1/3

= 6 ( 3x -1 ) 1/3  x < 1/2

6 ( 1 - x ) if 1/2  x < 1

  • E(Fav price) = E. 1 . = 6 ln(4/3) x ( 1 +  ) ( 1 +  )

 1.73 / ( 1 +  )

{

(

)

evidence i a
Evidence I(a)
  • Distribution of Favourites ( 11 horse race )
the data
The Data
  • Saturday races
    • for the major metropolitan centres, SR, MR, BR, AR
    • from 9 March 02 to 2 November 02 ( 8 months )
    • Tote prices are Final Dividends from NSWTAB
    • 1110 races in all
    • 11-horse race - most frequent (161 races )
evidence i b
Evidence I(b)
  • Distribution of Favourite ( 11 horse race )
evidence i c
Evidence I(c)
  • Distribution of 2nd Favourite ( 11 horse race )
evidence i d
Evidence I(d)
  • Distribution of 3rd Favourite ( 11 horse race )
evidence i e
Evidence I(e)
  • Distribution of 4th - 7th Favourites ( 11 horse race )
evidence i f
Evidence I(f)
  • Distribution of 8th - 11th Favourites ( 11 horse race )
a strategy
A Strategy
  • Define n sig =  i = 1( carrot i - fav i)2
  • Target :
    • proportionate to sig
    • inv proportionate to n

Tgt = 100 x sig x 8 / n

  • Bet only if favourites are long
  • Bet on horses that are long but have short place prices investing in win bets so as to make the target Tgt
  • Abandon race if just betting on very long-odds horses
evidence ii b
Evidence II(b)
  • Long Favourite - minimum 20% outlay
evidence ii d
Evidence II(d)
  • Long Favourite - minimum 20% outlay
evidence ii e
Evidence II(e)
  • Long Favourite - minimum 30% outlay
evidence ii f
Evidence II(f)
  • Long Favourite - minimum 10% outlay
other financial market applications
Other Financial Market Applications
  • Portfolio Selection
    • allocation of funds amongst n competing assets
  • Parimutuel Markets
    • Deutshe & Goldman Sachs options on economic data using Longitude’s PDCA (Parimutuel Digital Call Auction) technology
further work
Further Work
  • Investigate “Local Exchanges (Totes)” for BR and AR
  • Look at mid-week races also
  • Find more exploitation strategies
  • Research further the “short favourite” instances and relate to “crowd behaviour” models or ising models in physics
  • Investigate Tote distributions for overseas horse races
  • Tidy up analytic work on order spacings
  • Investigate other applications in finance
  • Investigate price slippage in last minute impact on results