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{"sheet":"Working","index":0,"n_rows":43,"n_cols":13,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
[null,"Avg returns on a positive trade are 20%",null,"Example","wealth","money invested","money won","final money"]
[null,"Avg Losses on a negative trade were 10%",null,null,"10000$","100$","20$",{"$f":"10000+20","v":10020},null,100,0.2]
[null,"Wealth","W",null,"x= 0.01",null,null,null,null,"you will end up with $120"]
[null,"Fraction","x%","of my total wealth"]
[]
[null,null,null,null,null,null,null,null,null,"W","10$"]
[null,"Case 1 (I win)",null,null,null,"Case 2 (I lose)",null,null,null,100,"20$","120$"]
[null,"Money invested","xW",null,"Money invested","xW"]
[null,"WIN","0.2xW",null,"Lose","0.1xW"]
[null,"Total Wealth after winning","W+0.2xW",null,"Wealth after losing","W-0.1xW"]
[null,null,"W(1+0.2x)",null,null,"W(1-0.1x)"]
[null,null,null,null,null,null,null,null,null,null,"trade 3 times"]
[null,"Wealth to start","W(1+0.2x)",null,null,"W(1-0.1x)",null,null,null,null,"Win the 1st time"]
[null,"Fraction","x%","of my total wealth",null,null,null,null,null,null,"lose the 2nd time"]
[null,null,null,null,null,null,null,null,null,null,"Win again the 3rd time"]
[null,"Case 1a (I win)",null,null,"Case 2a"]
[null,null,null,null,null,null,null,null,null,"Start","W"]
[null,"Money invested","x*W(1+0.2x)",null,"Money invested","x*W(1-0.1x)",null,null,null,"1st trade","W*(1+0.2x)"]
[null,"WIN","0.2*x*W(1+0.2x)",null,"Lose","0.1*x*W*(1-0.1x)",null,null,null,"2nd trade","W*(1+0.2x)",null,"*(1-0.1x)"]
[null,"Total Wealth after winning","W(1+0.2x) + 0.2x*W(1+0.2x)",null,"wealth after losing","W(1-0.1x)-0.1*x*W*(1-0.1x)",null,null,null,"3rd trade","W*(1+0.2x)*(1-0.1x)",null,"*(1+0.2x)"]
[null,null,"W(1+0.2x)(1+0.2x)",null,null,"W(1-0.1x)(1-0.1x)"]
[]
[null,"Whenever I win---> my money will increase by (1+0.2x)"]
[null,"Whenever I lose---> my money will get multiplied by (1-0.1x)",null,null,null,"If I invest 10 times in this strategy:"]
[null,null,null,null,null,"win 5 times"]
[null,null,null,null,null,"lose 5 times"]
[null,null,null,null,null,"Wealth ---> W(1+0.2x)^5*(1-0.1x)^5"]
[]
[]
[]
["Example with numbers",null,null,null,null,null,null,null,null,"Starting Wealth is W"]
["W",10000,null,null,null,null,null,null,null,"Win 'n' times"]
["x",0.1,null,null,null,null,null,null,null,"Lose 'm' times"]
["Win%",0.2]
[null,null,null,null,null,null,null,null,"Total W =","W*(1+0.2x)^n  * (1-0.1x)^m"]
["Money invested",{"$f":"B32*B33","v":1000}]
["Win",{"$f":"B36*B34","v":200}]
["Total wealth",{"$f":"B37+B32","v":10200},"W*(1+0.2x)"]
[]
["Case 1a"]
["Money invested",{"$f":"B38*B33","v":1020}]
["Win",{"$f":"B41*B34","v":204}]
["Total wealth",{"$f":"B42+B38","v":10404},"W(1+0.2x)(1+0.2x)"]

{"sheet":"Kelly","index":1,"n_rows":106,"n_cols":6,"rows_kept":106,"cut":false,"hidden":false,"merged":[]}
["Winning Returns",0.2,null,{"$f":"B1","v":0.2},null,"Avg. Returns of +ve trade"]
["Losing returns",0.1,null,{"$f":"B2","v":0.1},null,"Avg. Returns of -ve trade"]
["Number of time invested the strategy",100]
["Prob of winning",0.35]
["Prob of Losing",{"$f":"1-B4","v":0.65}]
[100,null,"Fraction of money invested","Wins","Losses","Final Wealth"]
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{"sheet":"Kelly_SMA","index":2,"n_rows":106,"n_cols":6,"rows_kept":106,"cut":false,"hidden":false,"merged":[]}
["Winning Returns",0.1038,null,{"$f":"B1","v":0.1038},null,"Avg. Returns of +ve trade"]
["Losing returns",2.9000000000000001E-2,null,{"$f":"B2","v":2.9000000000000001E-2},null,"Avg. Returns of -ve trade"]
["Number of time invested the strategy",100]
["Prob of winning",0.38]
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[10,null,"Fraction of money invested","Wins","Losses","Final Wealth"]
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