THE GMEAN (following)
Formulas of the optimal F and the Gmean developed by Kelly, presented to the previous page, offer the advantage to be simple. In counterpart, they don't apply with precision that in cases where there are only only two possibilities.
Ralph Vince in " present Portfolio Management Formulas " a less intuitive version, but more operational of these two elements.
The simultaneous calculation of the optimal F and the Gmean thanks to the solveur of Excel is done directly on a historic.
Téléchargez Solveur f.xls opt that permits to visualize the used formulas.
The unit that serves basis to the system is the strongest decrease on a trade recorded in the set:
This stronger decrease is here on the all last trade, either -29.
Vince calls Holding period HPR return, the result of it% of loss maxi of every trade:
Soit 1 + optimal f * (- result of the trade / maximum loss of the set ) nb: the loss is always a negative number.
Therefore a loss of 24 on the trade n2 will give: 1 + f * (-1*-24/-29) = 0.83448276 with f = 0.2 for the first calculation.
The geometric average of the output will be the product of all HPRS, soit 1,04125694,
This calculation is done with an arbitrary f, we go uses the solveur :
All it will be maybe too detailed for some, but maybe not for everybody.
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LEAF OF DATA PREPARATION |
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F OF DEPARTURE |
0,2 |
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NUM TRADE |
RESULT |
HEAP |
HPRs |
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1 |
18 |
18 |
1,12413793 |
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2 |
-24 |
-6 |
0,83448276 |
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3 |
51 |
45 |
1,35172414 |
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4 |
-12 |
33 |
0,91724138 |
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5 |
-16 |
17 |
0,88965517 |
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6 |
42 |
59 |
1,28965517 |
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7 |
37 |
96 |
1,25517241 |
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8 |
-5 |
91 |
0,96551724 |
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9 |
15 |
106 |
1,10344828 |
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10 |
-21 |
85 |
0,85517241 |
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11 |
39 |
124 |
1,26896552 |
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12 |
27 |
151 |
1,1862069 |
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13 |
14 |
165 |
1,09655172 |
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14 |
-24 |
141 |
0,83448276 |
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15 |
-24 |
117 |
0,83448276 |
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16 |
32 |
149 |
1,22068966 |
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17 |
41 |
190 |
1,28275862 |
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18 |
18 |
208 |
1,12413793 |
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19 |
11 |
219 |
1,07586207 |
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20 |
-15 |
204 |
0,89655172 |
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21 |
17 |
221 |
1,11724138 |
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22 |
-26 |
195 |
0,82068966 |
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23 |
4 |
199 |
1,02758621 |
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24 |
19 |
218 |
1,13103448 |
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25 |
41 |
259 |
1,28275862 |
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26 |
-8 |
251 |
0,94482759 |
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27 |
-18 |
233 |
0,87586207 |
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28 |
20 |
253 |
1,13793103 |
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29 |
14 |
267 |
1,09655172 |
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30 |
-29 |
238 |
0,8 |
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D 38 |
1,04125694 |
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Paramétrage of the solveur:
Cell to define: D38
Selected max
Variable cell: D3
And we get the following picture:
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AFTER OPTIMIZATION |
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OPTIMAL F |
0,4084953 |
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NUM TRADE |
RESULT |
HEAP |
HPRs |
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1 |
71,0 |
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1 |
18 |
18 |
1,25354881 |
1 |
89,0 |
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2 |
-24 |
-6 |
0,66193492 |
1 |
65,0 |
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3 |
51 |
45 |
1,71838829 |
0 |
116,0 |
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4 |
-12 |
33 |
0,83096746 |
1 |
116,0 |
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5 |
-16 |
17 |
0,77462328 |
1 |
100,0 |
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6 |
42 |
59 |
1,59161389 |
1 |
142,0 |
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7 |
37 |
96 |
1,52118366 |
2 |
179,0 |
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8 |
-5 |
91 |
0,92956978 |
2 |
169,0 |
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9 |
15 |
106 |
1,21129067 |
2 |
199,0 |
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10 |
-21 |
85 |
0,70419306 |
2 |
157,0 |
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11 |
39 |
124 |
1,54935575 |
2 |
235,0 |
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12 |
27 |
151 |
1,38032321 |
3 |
289,0 |
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13 |
14 |
165 |
1,19720463 |
4 |
331,0 |
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14 |
-24 |
141 |
0,66193492 |
4 |
235,0 |
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15 |
-24 |
117 |
0,66193492 |
3 |
139,0 |
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16 |
32 |
149 |
1,45075344 |
1 |
235,0 |
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17 |
41 |
190 |
1,57752784 |
3 |
276,0 |
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18 |
18 |
208 |
1,25354881 |
3 |
330,0 |
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19 |
11 |
219 |
1,15494649 |
4 |
363,0 |
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20 |
-15 |
204 |
0,78870933 |
5 |
303,0 |
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21 |
17 |
221 |
1,23946276 |
4 |
388,0 |
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22 |
-26 |
195 |
0,63376283 |
5 |
284,0 |
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23 |
4 |
199 |
1,05634418 |
4 |
304,0 |
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24 |
19 |
218 |
1,26763485 |
4 |
380,0 |
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25 |
41 |
259 |
1,57752784 |
5 |
544,0 |
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26 |
-8 |
251 |
0,88731164 |
7 |
504,0 |
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27 |
-18 |
233 |
0,74645119 |
7 |
378,0 |
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28 |
20 |
253 |
1,2817209 |
5 |
518,0 |
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29 |
14 |
267 |
1,19720463 |
7 |
588,0 |
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30 |
-29 |
238 |
0,5915047 |
8 |
385,0 |
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30 |
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G MEAN |
1,05617286 |
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1,05617286 |
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5,15288088 |
71,0 |
365,8146 |
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MAXI LOSS |
-29 |
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OPT f ($) |
71,0 |
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OPTIMIZED STAKE |
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GAT |
4,0 |
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RETURN WAITED BY TRADE |
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We deduct OPT f of it ($) = loss maxi / optimal f is 29/0.4085 = 71 that represent the sum to detain for trader an unit.
And GAT that is the middle gain by operation.
He/it only remains has exploit these results to determine stakes to achieve, while supposing, very sure that the future trades structure won't defer the one of the past tradeses.
It will make the object of the next page.
While waiting, he/it is possible to deflower the topic while studying the leaf restrained Excel in the following file:
Optimalf.zip file to download: In himself décompactant, the .com file gives a Excel file and his/her/its macro.
If the solveur is not installed:
Installation of the Solveur
1 In menu Tools, click on complementary Macros.
Demonstration
If the Solveur option is not listed in the box of dialogue complementary Macro, click on to Browse and search for the reader, the file and the name of file of the macro complementary Solver.xla, that is usually in the Macrolib\Solveur file, or execute the program of installation if you don't arrive to localize the file.
2 In the box of dialogue complementary Macro, activate the slot to nick Solveur.
Notice The complementary macros that you select in the box of dialogue complementary Macro stay active until you suppressed them.