Ralph Vince - Portfolio Mathematics

214 THE HANDBOOK OF PORTFOLIO MATHEMATICS

Converting these to outcomes yields:

Toss#

123

2

2

− 1

2

2

− 1

− 1

2

2

− 1

− 1

2

− 1

− 1

If we go back with a computer and iterate to that value forfwhich
maximizes expected average compound growth when quitting after three
tosses, we find it to be .37868. Therefore, converting the outcomes to HPRs
based upon a .37868 value forfat each toss yields:

Toss#

123

1.757369

1.757369

.621316

1.757369

1.757369

.621316

.621316

1.757369

1.757369

.621316

.621316

1.757369

.621316

.621316

Now we can express all tosses subsequent to the first toss as TWRs by
multiplying by the subsequent tosses on the tree. The numbers following
the last toss on the tree (the numbers in parentheses) are the last TWRs