Winner Strategies in a Simulated Stock Market
Abstract
:1. Introduction
2. Literature Review
3. Model
3.1. Agents
3.2. Assets
3.3. Market
3.4. Simulation
4. Results
4.1. Classification of Results
4.2. Identifying Winners by Scores
4.3. Parameter Distribution of Winners
4.4. Parameter Distribution of Losers
5. Conclusions
Author Contributions
Funding
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Statistical Significance
Appendix B. Kelly in Investment
Notes
1  the oldest source we could find in this regard was Fetter (1904), which was cited in Herbener and Holcombe (1999). 
2  In the simulation, a slightly modified formula is utilized to ensure that the dividends remain positive and do not deviate significantly from the initial value
$${d}_{t+1}=\overline{d}+\rho ({d}_{t}\overline{d})+{\sigma}_{d}{Z}_{t}$$

3  A higher price increases the probability of agents calculating a positive trend, subsequently leading to a positive technical premium. This is why the technical component of the return is computed using the previous periods’ stock prices. 
4  In a pseudorandom number generator such as the one we used, a seed is needed to initiate the generator. Starting with different seeds results in different series of numbers. 
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Number of Gained Positions  

Agent  Score  1st  2nd  3rd  Rank:4th... 6th  Rank:7th... 9th  Other Ranks 
68  474 (397, 547)  26 (18, 33)  12 (8, 17)  9 (5, 14)  13 (8, 19)  5 (2, 9)  35 
194  420 (353, 506)  29 (22, 38)  10 (5, 15)  4 (1, 7)  7 (4, 11)  5 (2, 9)  46 
184  332 (276, 384)  2 (0, 4)  16 (10, 23)  14 (9, 20)  23 (16, 30)  8 (4, 12)  38 
16  287 (239, 340)  0 (0, 2)  6 (2, 10)  17 (11, 24)  29 (20, 37)  9 (5, 15)  38 
118  268 (224, 314)  5 (2, 8)  12 (7, 17)  9 (5, 14)  14 (8, 19)  12 (7, 17)  48 
138  216 (164, 274)  6 (3, 10)  9 (3, 14)  6 (3, 10)  10 (5, 14)  6 (3, 10)  63 
110  154 (118, 187)  0 (0, 0)  0 (0, 1)  0 (0, 2)  32 (23, 39)  18 (13, 24)  49 
172  142 (113, 174)  0 (0, 0)  0 (0, 1)  0 (0, 1)  29 (22, 38)  26 (20, 34)  45 
144  105 (67, 149)  2 (0, 4)  3 (0, 7)  3 (1, 7)  9 (4, 14)  5 (2, 9)  78 
1  83 (37, 140)  4 (1, 8)  3 (1, 6)  2 (0, 4)  3 (0, 6)  1 (0, 3)  88 
Agent  Original Score  Reduced Score  Normalized Score 

68  453  467  667 
194  402  38  475 
184  317  33  275 
16  284  545  568 
118  245  234  509 
138  177  46  128 
110  155  144  288 
172  147  29  161 
1  112  23  23 
144  83  3  9 
Time  

Agent  10  20  50  100  200  500  1000  1500  2000 
1  0  8  154  216  252  243  153  136  112 
8  0  0  92  100  66  13  9  12  5 
16  418  449  201  88  57  90  156  213  284 
22  356  357  148  37  20  31  34  20  39 
32  512  489  200  57  34  16  47  25  28 
35  91  20  38  37  49  51  41  39  32 
68  782  781  370  147  86  151  277  349  453 
69  6  26  58  86  96  100  88  78  50 
74  0  0  240  224  149  74  59  20  32 
89  0  7  107  143  161  160  107  101  67 
97  0  7  72  88  97  100  72  63  49 
110  293  279  113  43  30  57  100  125  155 
112  119  78  27  11  1  6  12  15  18 
118  29  79  73  55  93  157  198  274  245 
119  0  9  138  147  162  141  83  83  70 
125  0  0  87  117  137  133  97  49  38 
129  0  43  115  54  62  33  20  7  6 
138  0  27  229  483  312  322  328  262  177 
144  0  0  0  15  28  20  57  58  83 
172  235  195  78  20  17  31  64  104  147 
173  0  26  130  22  22  10  3  0  0 
179  73  22  22  31  38  38  35  29  21 
181  0  0  42  80  95  83  66  64  55 
184  656  658  294  128  71  109  175  255  317 
194  0  28  72  169  206  286  354  400  402 
$su{m}_{t}$  3535  3408  2104  1874  1667  1802  1945  2219  2375 
$su{m}_{T}$  2413  2504  1584  1364  1152  1466  1862  2176  2375 
Agent  Original Score  Scaled Score 

68  453  469 
194  402  75 
184  317  369 
16  284  280 
118  245  73 
138  177  48 
110  155  217 
172  147  169 
1  112  55 
144  83  0 
cat  
Number of Gained Positions  
cat Range  1st  2nd  3rd  Rank:4th... 6th  Rank:7th... 9th  All (PDF) 
$900\cdots 500$  0  0  1  0  0  <1% 
$500\cdots 300$  0  0  0  0  0  2% 
$300\cdots 200$  3  0  0  0  0  4% 
$200\cdots 100$  5  0  1  0  2  12% 
$100\cdots 50$  2  5  4  4  6  12% 
$50\cdots 20$  3  3  2  13  12  11% 
$20\cdots 10$  2  7  3  11  24  4% 
$10\cdots 5$  4  3  5  26  25  2% 
$5\cdots 1$  9  8  12  21  10  2% 
$1\cdots 5$  26  34  32  70  23  2% 
$5\cdots 10$  4  17  16  72  62  2% 
$10\cdots 20$  3  3  4  29  79  4% 
$20\cdots 50$  13  6  5  11  18  11% 
$50\cdots 100$  6  3  3  6  11  12% 
$100\cdots 200$  12  1  5  11  9  12% 
$200\cdots 300$  1  3  1  14  9  4% 
$300\cdots 500$  6  6  4  9  10  2% 
$500\cdots 900$  1  1  2  3  0  <1% 
dur  
Number of Gained Positions  
dur Range  1st  2nd  3rd  Rank:4th... 6th  Rank:7th... 9th  All (PDF) 
$1\cdots 5$  41  8  11  18  16  5% 
$5\cdots 10$  5  5  2  13  11  5% 
$10\cdots 20$  7  9  9  18  25  9% 
$20\cdots 50$  17  24  23  65  58  21% 
$50\cdots 100$  13  16  26  69  71  24% 
$100\cdots 200$  12  28  15  76  78  23% 
$200\cdots 300$  5  5  9  25  25  9% 
$300\cdots 500$  0  4  5  15  15  4% 
500 ⋯ 700  0  1  0  1  1  1% 
700 ⋯ 1000  0  0  0  0  0  <1% 
tfp  
Number of Gained Positions  
tfp Range  1st  2nd  3rd  Rank:4th... 6th  Rank:7th... 9th  All (PDF) 
$0.0\cdots 0.1$  9  5  6  36  47  10% 
$0.1\cdots 0.2$  10  9  19  35  37  10% 
$0.2\cdots 0.4$  8  16  9  32  33  10% 
$0.4\cdots 0.5$  13  12  10  36  31  10% 
$0.5\cdots 0.6$  8  7  13  33  27  10% 
$0.6\cdots 0.7$  6  15  10  23  24  10% 
$0.7\cdots 0.8$  8  8  15  31  20  10% 
$0.8\cdots 1$  12  14  7  22  33  10% 
$1.0\cdots 1.1$  16  7  4  28  19  10% 
$1.1\cdots 1.2$  9  7  7  23  28  10% 
cat vs. dur  
Number of Gained Positions for Each Time Stamp  
cat Range  5  10  20  50  100  200  300  500  700  1000 
$900\cdots 500$  1  0  0  0  0  0  0  0  0  0 
$500\cdots 300$  0  0  0  0  0  0  0  0  0  0 
$300\cdots 200$  1 ^{①}  0  0  1 ^{①}  1 ^{①}  0  0  0  0  0 
$200\cdots 100$  4 ^{①}  0  1 ^{①}  2 ^{②}  1 ^{①}  0  0  0  0  0 
$100\cdots 50$  3  1  1  4  4  7 ^{②}  2  0  0  0 
$50\cdots 20$  3 ^{①}  2 ^{①}  2  9  9  9 ^{①}  3  1  0  0 
$20\cdots 10$  0  3 ^{①}  2  13 ^{①}  13  16  7  2  0  0 
$10\cdots 5$  0  6 ^{①}  4  18 ^{①}  19 ^{①}  16  4 ^{①}  2  0  0 
$5\cdots 1$  4 ^{①}  2  5 ^{①}  19 ^{③}  12  16 ^{②}  5 ^{②}  0  1  0 
$1\cdots 5$  4 ^{②}  6  19 ^{③}  49 ^{⑤}  42 ^{⑨}  48 ^{⑥}  14 ^{①}  13  0  0 
$5\cdots 10$  5 ^{①}  2  13  37 ^{②}  51  53 ^{①}  15  10  0  0 
$10\cdots 20$  5 ^{②}  7  8  15  45 ^{①}  41  16  13  1  0 
$20\cdots 50$  24 ^{⑪}  5 ^{①}  9 ^{①}  9  5  5  2  2  0  0 
$50\cdots 100$  15 ^{⑥}  1  5  8  3  1  0  0  0  0 
$100\cdots 200$  16 ^{⑧}  3 ^{①}  4 ^{①}  10 ^{②}  4  2  0  1  0  0 
$200\cdots 300$  5 ^{①}  0  1  2  5  12  2  1  0  0 
$300\cdots 500$  7 ^{⑤}  1  0  6  8  5  6 ^{①}  2  1  0 
$500\cdots 900$  1 ^{①}  0  1  1  0  5  0  0  1  0 
dur vs. tfp  
Number of Gained Positions for each tfp  
dur Range  0.12  0.24  0.36  0.48  0.60  0.72  0.84  0.96  1.08  1.20 
$1\cdots 5$  5 ^{④}  9 ^{①}  10 ^{④}  16 ^{⑤}  8 ^{④}  11 ^{②}  9 ^{④}  11 ^{⑤}  11 ^{⑦}  7 ^{④} 
$5\cdots 10$  10  7 ^{②}  2  5 ^{①}  4  5  2  3 ^{①}  0  1 ^{①} 
$10\cdots 20$  10  13  6 ^{①}  8 ^{①}  6  6 ^{①}  6 ^{①}  9 ^{①}  3 ^{①}  7 ^{①} 
$20\cdots 50$  20 ^{①}  26 ^{②}  17 ^{②}  32 ^{④}  25 ^{②}  10  23 ^{③}  15 ^{①}  18 ^{②}  17 
$50\cdots 100$  33 ^{③}  28 ^{①}  17  19  22 ^{②}  15 ^{①}  16  28  23 ^{④}  18 ^{②} 
$100\cdots 200$  28  22 ^{②}  39 ^{①}  28 ^{②}  18  19 ^{①}  23  24 ^{④}  16 ^{②}  19 
$200\cdots 300$  7 ^{①}  10 ^{②}  9  7  7  12 ^{①}  8  5  5  6 ^{①} 
$300\cdots 500$  4  3  7  2  6  6  6  5  3  5 
500 $\cdots 700$  0  0  1  0  0  0  0  0  3  0 
700 $\cdots 1000$  0  0  0  0  0  0  0  0  0  0 
cat  
Number of Gained Positions  
cat Range  worst 1%  worst 5%  worst 10%  worst 25%  worst 50%  all 
$900\cdots 500$  0  0  0  0  0  <1% 
$500\cdots 300$  8  10  9  6  4  2% 
$300\cdots 200$  9  10  9  8  6  4% 
$200\cdots 100$  13  14  16  15  16  12% 
$100\cdots 50$  5  7  8  10  15  12% 
$50\cdots 20$  2  5  5  11  14  11% 
$20\cdots 10$  1  2  3  7  6  4% 
$10\cdots 5$  1  2  4  4  3  2% 
$5\cdots 1$  2  3  5  4  3  2% 
$1\cdots 5$  2  2  2  2  1  2% 
$5\cdots 10$  0  2  3  2  1  2% 
$10\cdots 20$  0  3  5  4  3  4% 
$20\cdots 50$  10  6  7  10  7  11% 
$50\cdots 100$  12  11  9  8  8  12% 
$100\cdots 200$  22  15  10  6  9  12% 
$200\cdots 300$  8  4  3  2  3  4% 
$300\cdots 500$  4  3  2  1  1  2% 
$500\cdots 900$  0  0  0  0  0  <1% 
dur  
Number of Gained Positions  
dur Range  worst 1%  worst 5%  worst 10%  worst 25%  worst 50%  all 
$1\cdots 5$  10  7  5  4  3  5% 
$5\cdots 10$  33  23  15  9  6  5% 
$10\cdots 20$  31  26  22  15  11  9% 
$20\cdots 50$  18  25  29  28  25  21% 
$50\cdots 100$  4  10  15  21  23  24% 
$100\cdots 200$  2  6  10  15  21  23% 
$200\cdots 300$  0  2  4  5  7  9% 
$300\cdots 500$  0  0  1  2  4  4% 
500 ⋯ 700  0  0  0  0  0  1% 
700 ⋯ 1000  0  0  0  0  0  <1% 
tfp  
Number of Gained Positions  
tfp Range  worst 1%  worst 5%  worst 10%  worst 25%  worst 50%  all (PDF) 
$0.0\cdots 0.1$  1  2  3  5  8  10% 
$0.1\cdots 0.2$  2  5  5  7  9  10% 
$0.2\cdots 0.4$  8  5  6  8  9  10% 
$0.4\cdots 0.5$  8  7  8  9  10  10% 
$0.5\cdots 0.6$  11  11  10  11  10  10% 
$0.6\cdots 0.7$  11  11  11  11  10  10% 
$0.7\cdots 0.8$  13  12  13  11  11  10% 
$0.8\cdots 1$  15  13  13  11  11  10% 
$1.0\cdots 1.1$  14  17  15  13  11  10% 
$1.1\cdots 1.2$  18  17  16  13  11  10% 
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Taherizadeh, A.; Zamani, S. Winner Strategies in a Simulated Stock Market. Int. J. Financial Stud. 2023, 11, 73. https://doi.org/10.3390/ijfs11020073
Taherizadeh A, Zamani S. Winner Strategies in a Simulated Stock Market. International Journal of Financial Studies. 2023; 11(2):73. https://doi.org/10.3390/ijfs11020073
Chicago/Turabian StyleTaherizadeh, Ali, and Shiva Zamani. 2023. "Winner Strategies in a Simulated Stock Market" International Journal of Financial Studies 11, no. 2: 73. https://doi.org/10.3390/ijfs11020073