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.

 

LEAF OF DATA PREPARATION

F OF DEPARTURE

0,2

NUM TRADE

RESULT

HEAP

HPRs

1

18

18

1,12413793

2

-24

-6

0,83448276

3

51

45

1,35172414

4

-12

33

0,91724138

5

-16

17

0,88965517

6

42

59

1,28965517

7

37

96

1,25517241

8

-5

91

0,96551724

9

15

106

1,10344828

10

-21

85

0,85517241

11

39

124

1,26896552

12

27

151

1,1862069

13

14

165

1,09655172

14

-24

141

0,83448276

15

-24

117

0,83448276

16

32

149

1,22068966

17

41

190

1,28275862

18

18

208

1,12413793

19

11

219

1,07586207

20

-15

204

0,89655172

21

17

221

1,11724138

22

-26

195

0,82068966

23

4

199

1,02758621

24

19

218

1,13103448

25

41

259

1,28275862

26

-8

251

0,94482759

27

-18

233

0,87586207

28

20

253

1,13793103

29

14

267

1,09655172

30

-29

238

0,8

D 38

1,04125694

Paramétrage of the solveur:

Cell to define: D38 

Selected max

Variable cell: D3

And we get the following picture:

 

AFTER OPTIMIZATION

OPTIMAL F

0,4084953

NUM TRADE

RESULT

HEAP

HPRs

1

71,0

1

18

18

1,25354881

1

89,0

2

-24

-6

0,66193492

1

65,0

3

51

45

1,71838829

0

116,0

4

-12

33

0,83096746

1

116,0

5

-16

17

0,77462328

1

100,0

6

42

59

1,59161389

1

142,0

7

37

96

1,52118366

2

179,0

8

-5

91

0,92956978

2

169,0

9

15

106

1,21129067

2

199,0

10

-21

85

0,70419306

2

157,0

11

39

124

1,54935575

2

235,0

12

27

151

1,38032321

3

289,0

13

14

165

1,19720463

4

331,0

14

-24

141

0,66193492

4

235,0

15

-24

117

0,66193492

3

139,0

16

32

149

1,45075344

1

235,0

17

41

190

1,57752784

3

276,0

18

18

208

1,25354881

3

330,0

19

11

219

1,15494649

4

363,0

20

-15

204

0,78870933

5

303,0

21

17

221

1,23946276

4

388,0

22

-26

195

0,63376283

5

284,0

23

4

199

1,05634418

4

304,0

24

19

218

1,26763485

4

380,0

25

41

259

1,57752784

5

544,0

26

-8

251

0,88731164

7

504,0

27

-18

233

0,74645119

7

378,0

28

20

253

1,2817209

5

518,0

29

14

267

1,19720463

7

588,0

30

-29

238

0,5915047

8

385,0

30

G MEAN

1,05617286

1,05617286

5,15288088

71,0

365,8146

MAXI LOSS

-29

OPT f ($)

71,0

OPTIMIZED STAKE

GAT

4,0

RETURN WAITED BY TRADE

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.