The Geometry of Leverage Space Portfolios 349
(5.06) to determine the FGHPR) Next we plug these values into Equations
(10.14), (10.15), and (10.16). Whichever of these three equations results in
the greatest value is the technique we go with.
To illustrate by way of an example, we now return to our familiar two-to-
one coin toss. Let’s assume that this is our only scenario set, comprising the
two scenarios heads and tails. Further, suppose we are going to trade it at a
.2 fraction (i.e., one-fifth optimalf). Thus, FRAC is .2, the geometric mean is
1.06066, and the AHPR is 1.125. To figure the FGHPR, from Equation (5.06)
we already have FRAC and AHPR; we need only SD, the standard deviation
in HPRs, which is .375. Thus, the FGHPR is:
1. 022252415 =
(√
((1. 125 −1)∗. 2 +1)^2 −(. 375 ∗.2)^2
)
Plugging these values into the three gradient functions, Equations
(10.14) through (10.16), gives us the following table:
Eq. (10.14) Eq. (10.15) Eq. (10.16)T Constant Contract Staticf Dynamicf1 0.024390244 0.022498184 0.012492741
2 0.023809524 0.022998823 0.013250551
3 0.023255814 0.023510602 0.014054329
4 0.022727273 0.02403377 0.014906865
5 0.022222222 0.024568579 0.015811115
6 0.02173913 0.025115289 0.016770217
7 0.021276596 0.025674165 0.017787499
8 0.020833333 0.026245477 0.018866489
9 0.020408163 0.026829503 0.02001093
10 0.02 0.027426524 0.021224793
11 0.019607843 0.02803683 0.022512289
12 0.019230769 0.028660717 0.023877884
13 0.018867925 0.029298488 0.025326317
14 0.018518519 0.02995045 0.026862611
15 0.018181818 0.030616919 0.028492097
16 0.017857143 0.03129822 0.030220427
17 0.01754386 0.031994681 0.032053599
18 0.017241379 0.03270664 0.03399797
19 0.016949153 0.033434441 0.036060287
20 0.016666667 0.034178439 0.038247704We find that we are at the greatest gradient for the first two holding
periods by trading on a constant contract basis, and that on the third period,
we should switch to staticf. On the seventeenth period, we should switch