The Leverage Space Portfolio Model in the Real World 413
This is not as damning a statement as it appears on first reading. Con-
sider the real-world example just alluded to whereinRR(.6)=0.397758.
Since the probability of hitting a drawdown of any given magnitude (let’s
say, a 99% drawdown, for argument sake) approaches 1 asqapproaches
infinity, yet there is only a roughly 40% chance of dropping back to roughly
60% of starting equity, we can only conclude that so manyqhave transpired
so as to cause the account to have grown by such an amount that a 99%
drawdown still leaves 60% of initial capital.
What we can know, and use, is that (12.05b) can give us a probability
of drawdown for a givenq. We can use it to know, for instance, what the
probability of drawdown is over, say, the next quarter.
Further, since, we have a geometric mean HPR for each value of
(12.05b), we can determine whatTwe are looking at to reach a specified
growth.
T=logGtarget (5.07b)where: target=The target TWR.
G=The geometric mean HPR corresponding to the
allocation set used in (12.05b).Thus, for example, if my target is a 50% return (i.e., target TWR=1.5)
and my geometric mean HPR from the allocation set I will use in (12.05b)
is 1.1, then I will expect it to takeTperiods, on average, to reach my target
TWR:
T=log 1. 11. 5 = 4. 254164
So I would want to consider theRD(b, 4.254164) in this case to be below
my threshold probability of such a drawdown.
Notice that we are now considering a risk of drawdown (or ruin) versus
that of hitting an upper barrier [i.e., target TWR, orufrom (12.01)]. Deriving
Tfrom (5.07b) to use as input to (12.05) is akin to using Feller’s classical
ruin given in (12.01) only for the more complex case of:
1.A lower barrier, which is not simply just zero.
2.For multiple scenarios, not just the simple binomial gambling sense (of
two scenarios).
3.These multiple scenarios are from multiple scenario spectrums, with
outcomes occurring simultaneously, with potentially complicated joint
probabilities.
4.More importantly, we are dealing here with geometric growth, not the
simple case in Feller where a gambler wins or loses a constant unit with
either outcome.