The Leverage Space Portfolio Model in the Real World 387
FIGURE 12.1 RR(.6) for two-to-one coin toss atf=.25
From this data, in methods to be detailed later in the text, we can
determine that the asymptote, that is, the risk of ruin (defined as 60% of our
initial equity left in this instance) is .48406in the long-run sense—that is,
if we continue to play indefinitely.
As shown in Figure 12.1, asqapproaches infinity,RR(b) approaches
a horizontal asymptote. That is,RR(b)canbe determined in the long-run
sense.
Additionally, it is perfectly acceptable to begin the analysis atq=1,
rather thanq=n. Doing so aids in resolving the line and hence its asymp-
tote.
Note that near the end of the previous chapter, a method employed in
one form or another by a good deal of the larger, more successful trend-
following funds, which “can be said to combine mean-variance with value
at risk” was presented. Note that in the method presented—that is, in the
way it is currently employed—it is akin to doing simply one run through
the data, horizontally, withn=qand solely for one value ofk. Note that it
would be if we only looked at the history of two tosses of our coin; there
is no way we can approach or discern the asymptote through such a crude
analysis.
Remember a very important caveat in this analysis: As demonstrated
thus far it is assumed that there is no statistical dependency in the sequence
of scenario outcomes across time. That is, we are looking at the stream of
scenario outcomes across time in a pure sample with replacement manner;
the past scenario outcome(s) do not influence the current one.
And what about more than a single scenario spectrum? This is easily
handled by considering that the HPRs of the different scenario spectrums