# Bulls and Bears

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;; Bulls & Bears ;; A Minimalist Artificial Stock Market globals [ ;; From sliders: ;; investors ;; total number of investors/agents ;; fraction-contrarians ;; percentage of investors that are contrarians ;; memory ;; number of periods m that price is remembered ;; wealth-factor ;; coefficient k1 ;; maximum-herd-effect-followers ;; coefficient k2 ;; maximum-herd-effect-contrarians ;; coefficient k3 ;; maximum-risk-appetite ;; coefficient k4 ;; price-sensitivity-to-demand ;; coefficient k5 ;; Others: num-contrarians ;; total number of contrarians num-followers ;; total number of followers risk-appetite-big ;; used for ma >=0 risk-appetite-small ;; used for ma < 0 tot-demand-followers ;; total demand of followers tot-demand-contrarians ;; total demand of contrarians tot-demand ;; total value of shares demanded ;; tot-share-demand ;; total number of shares demanded price ;; current calculated price last-price ;; price at time t-1 return ;; percentage price change from t-1 to t value-traded ;; equal to smaller of demands, to clear market volume-traded ;; value traded divided by share price followers-wealth ;; total wealth of followers contrarians-wealth ;; total wealth of contrarians total-wealth ;; total wealth of all investors max-wealth ;; highest wealth of all investors min-wealth ;; lowest wealth of all investors max-demand-c ;; maximum demand of contrarians max-demand-f ;; maximum demand of followers max-demand ;; highest demand of all investors min-demand ;; lowest demand of all investors all-return-list ;; collects all returns return-list ;; collects last m returns moving-average ;; average return over last m periods all-volatility-list ;; collects all volatilities volatility-price-list ;; collects last 36 prices volatility ;; standard deviation of returns over last 36 periods value-traded-list ;; collects values traded volume-traded-list ;; collects volumes traded graph-max ;; maximum of previous two lists graph-min ;; minimum of previous two lists ] turtles-own [ follower contrarian cash shares-value shares wealth wealth-effect ;; part of investors' demand function herd-effect-follower ;; part of followers' demand function herd-effect-contrarian ;; part of contrarians' demand function risk-appetite ;; part of investors' demand function demand-follower demand-contrarian shares-value-transacted ] to setup ca random-seed 1051100757 ;; if required ask patches [ set pcolor white ] ;; create a blank background create-turtles investors [ setxy random-xcor random-ycor set size 3 ] ;; Create empty lists for return histogram, moving average of last m returns, 36-period price volatility, trade set all-return-list [ 0 ] ;; for histogram scaling set return-list [] ;; for moving average while [ length return-list < memory ] [ set return-list lput 0 return-list ] set all-volatility-list [ 0 0.2] ;; for volatility graph scaling set volatility-price-list [] while [ length volatility-price-list < 36 ] [ set volatility-price-list lput 100 volatility-price-list ] set value-traded-list [] ;; for trade graph scaling set volume-traded-list [] ;; for trade graph scaling set num-contrarians round ( ( fraction-contrarians ) / ( 100 ) * ( investors ) ) set num-followers ( investors - num-contrarians ) ;; Initialise some variables set price ( 100 ) set moving-average ( 0 ) set graph-min ( 0 ) set graph-max ( 1 ) ;; Divide into two investor types ask turtles [ set cash 50 set shares-value 50 set wealth cash + shares-value ifelse who < num-contrarians [ set contrarian 1 set follower 0 set shape "wolf 3" set color red ] [ set contrarian 0 set follower 1 set shape "cow skull" set color blue ] ] reset-ticks end to go ;; For each investor calculate *magnitudes* of demands, i.e. "desired size of bet" set risk-appetite-big maximum-risk-appetite / 1 * moving-average set risk-appetite-small maximum-risk-appetite / 2.5 * moving-average ;; investors hate losses ~2.5 times as much as they love gains ask turtles [ ;; Wealth: range of wealth parameter (i.e. on slider) and other parameters need to be determined empirically set wealth-effect ( ( wealth-factor ) * ( wealth ) ) ;; this is per investor ifelse contrarian = 1 [ ;; Herding: the susceptibility of investors to herding by their own type ranges randomly from zero to the maximum set herd-effect-contrarian random-float abs ( ( maximum-herd-effect-contrarians ) * ( tot-demand-contrarians ) / ( num-contrarians ) ) ;; normalize per investor ;; Risk appetite: ifelse moving-average >= 0 [ set risk-appetite random-float risk-appetite-small ] [ set risk-appetite random-float ( - ( risk-appetite-big ) ) ] ;; this is per investor set demand-contrarian max list 0 ( wealth-effect + herd-effect-contrarian + risk-appetite ) ;; Full demand function: is "desired size of bet" so cannot be less than zero; the sign is then determined purely by type of investor set demand-contrarian min list demand-contrarian wealth ;; Can't bet more than one's wealth ;; Scaling for main graph if ticks > 2 [set color scale-color blue risk-appetite ( max [ risk-appetite ] of turtles + 1 ) ( min [ risk-appetite ] of turtles) ] ;; + 1 is error trap for when m.a. = 0 set size min list ( 0.5 * herd-effect-contrarian + 1.3 ) 7 ] [ set herd-effect-follower random-float abs ( ( maximum-herd-effect-followers ) * ( tot-demand-followers ) / ( num-followers) ) ifelse moving-average >= 0 [ set risk-appetite random-float ( - ( risk-appetite-big ) ) ] [ set risk-appetite random-float risk-appetite-small ] set demand-follower max list 0 ( wealth-effect + herd-effect-follower + risk-appetite ) set demand-follower min list demand-follower wealth if ticks > 2 [ set color scale-color red risk-appetite ( max [ risk-appetite ] of turtles + 1 ) ( min [ risk-appetite ] of turtles ) ] set size min list ( 0.5 * herd-effect-follower + 1.3 ) 7 ] ] ;; In the risk appetite calculation above it is assumed that if e.g. moving-average >= 0 followers would have largely been long, so their ;; risk appetite will be big, with the converse for contrarians. Ideally, each investor should have their own personal moving-average. ;; For each investor type, aggregate demand set tot-demand-followers sum [ demand-follower ] of turtles if tot-demand-followers = 0 [ set tot-demand-followers (10) ] ;; error trap for division by zero set tot-demand-contrarians sum [ demand-contrarian ] of turtles if tot-demand-contrarians = 0 [ set tot-demand-contrarians (10) ] ;; error trap for division by zero ;; For each investor type now calculate *sign* of aggregate demand, i.e. direction of aggregate bet ifelse return > 0 [ set tot-demand-contrarians (- tot-demand-contrarians) ] [ set tot-demand-followers (- tot-demand-followers) ] set tot-demand ( tot-demand-followers ) + ( tot-demand-contrarians ) ;; i.e. is *net* demand ;; Calculate new price set last-price price set price ( ( last-price ) + ( price-sensitivity-to-demand ) * ( tot-demand ) ) if price <= 0 [set price (1)] ;; error trap - price floor ;; Calculate return over period set return ( ( price ) / ( last-price ) - ( 1 ) ) * ( 100 ) ;; Add return to the all-return list, then the moving-average return list and take average of this list set all-return-list lput return all-return-list set return-list lput return return-list set return-list remove-item 0 return-list set moving-average ( mean return-list ) ;; Add price to the volatility price list, take standard deviation of list, cumulate volatilities set volatility-price-list lput price volatility-price-list set volatility-price-list remove-item 0 volatility-price-list set volatility ( standard-deviation volatility-price-list ) if ticks > 36 [ set all-volatility-list lput volatility all-volatility-list ] ;; start to cumulate volatilities when past initialized dummy data ;; Calculate value traded (equal to smaller of demands, to clear market) and volume set value-traded min list abs tot-demand-followers abs tot-demand-contrarians set volume-traded ( value-traded ) / ( price ) * ( 100 ) ;; For trade graph scaling set value-traded-list lput value-traded value-traded-list set volume-traded-list lput volume-traded volume-traded-list set graph-max max list ( max value-traded-list ) ( max volume-traded-list ) set graph-min min list ( min value-traded-list ) ( min volume-traded-list ) ;; Recalculate investors' wealth ask turtles [ ifelse contrarian = 1 [ set shares-value-transacted ( demand-contrarian ) / ( tot-demand-contrarians ) * ( value-traded ) ;; get share value allocated pro-rata to relative demand ;; change investors' cash and share balances ifelse return >= 0 [ set shares-value shares-value - shares-value-transacted set shares ( shares-value ) / ( last-price ) set cash cash + shares-value-transacted ] [ set shares-value shares-value + shares-value-transacted set shares ( shares-value ) / ( last-price ) set cash cash - shares-value-transacted ] ] [ set shares-value-transacted ( demand-follower ) / ( tot-demand-followers ) * ( value-traded ) ifelse return >= 0 [ set shares-value shares-value + shares-value-transacted set shares ( shares-value ) / ( last-price ) set cash cash - shares-value-transacted ] [ set shares-value shares-value - shares-value-transacted set shares ( shares-value ) / ( last-price ) set cash cash + shares-value-transacted ] ] set wealth ( shares ) * ( price ) + ( cash ) ;; update investors' wealth ] ;; Scaling of main graph set followers-wealth sum [ wealth ] of turtles with [ follower = 1 ] set contrarians-wealth sum [ wealth ] of turtles with [ contrarian = 1 ] set total-wealth sum [ wealth ] of turtles set max-wealth max [ wealth] of turtles set min-wealth min [ wealth] of turtles if max-wealth = min-wealth [ set max-wealth ( max-wealth + random ( 10 ) ) set min-wealth ( min-wealth - random ( 10 ) ) ] ;; error trap to stop division by zero in plot set max-demand-c max [ demand-contrarian ] of turtles set max-demand-f max [ demand-follower ] of turtles set max-demand max list max-demand-c max-demand-f ;; must be a cleverer way to do this set min-demand min list min [ demand-contrarian ] of turtles min [ demand-follower ] of turtles ask turtles ;; [ if wealth >= 0 [ ifelse contrarian = 1 [ setxy ((( wealth - min-wealth ) / ( max-wealth - min-wealth ) * ( max-pxcor - min-pxcor)) + min-pxcor ) ((( demand-contrarian - min-demand ) / ( max-demand - min-demand ) * ( max-pycor - min-pycor)) + min-pycor ) ] [ setxy ((( wealth - min-wealth ) * ( max-pxcor - min-pxcor) / ( max-wealth - min-wealth )) + min-pxcor ) ((( demand-follower - min-demand ) / ( max-demand - min-demand ) * ( max-pycor - min-pycor)) + min-pycor ) ] ;; ] ] tick end

There is only one version of this model, created 10 months ago by Franco Busetti.

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File | Type | Description | Last updated | |
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Bulls and Bears.png | preview | Preview for 'Bulls and Bears' | 10 months ago, by Franco Busetti | Download |

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