Ralph Vince - Portfolio Mathematics

The Leverage Space Model 311

k HPRk Probk

1 0.956395 0.125

2 1 0.125

3 1 0.125

4 1.033339 0.125

5 1 0.125

6 1.033339 0.125

7 1.033339 0.125

8 1.060511 0.125

Summing up all the Probk, given by Equation (9.03), per Equation (9.04),
we get 1. Now, taking the product of all of the HPRs, per Equations (9.01)
and (9.04), we obtain 1.119131. Performing Equation (9.01), then, we get a
value ofGof 1.119131 which corresponds to thefvalues .1, .1, .1 forf 1 ,f 2 ,
andf 3 , respectively.

G(.1,.1,.1)=

(

∏m

k= 1

HPRk

)

(

1

/∑m

k= 1

Probk

)

G(.1,.1,.1)=(. (^956395) (^1) . (^1) 1. (^033339) (^1) 1. 033339
^1.^033339 *^1 .0605011)
(1/(. 125 +. 125 +. 125 +. 125 +. 125 +. 125 +. 125 +.125))
G(.1,.1,.1)=(1.119131)(1/1)
G(.1,.1,.1)= 1. 119131
Now, depending upon what mathematical optimization method we were
using, we would alter ourfvalues. Eventually, we would find our optimalf
values at .21, .21, .21 forf 1 ,f 2 , andf 3 , respectively. This would give us:
kHPRk Probk
1 0.883131 0.125
2 1 0.125
3 1 0.125
4 1.062976 0.125
5 1 0.125
6 1.062976 0.125
7 1.062976 0.125
8 1.107296 0.125