The Leverage Space Portfolio Model in the Real World 403
There are additional real-world implementation issues in terms of
adding floating point numbers millions of times considering the floating
point roundoff errors, and so on. Ultimately, we are trying to get a “reason-
able and real-world workable” resolution of the curves forRRandRDso
that we can determine their asymptotes.
This particular shortcut is invoked only if the number of permutations
at a givenqexceedsnq. If not, just run all the permutations. For example,
whereq=1, where we start, there are 10^1 =10 permutations. Thus, we
just run all 10. Atq=2, we have 10^2 =100 permutations, and again run
all permutations. However, at 10^7 =10,000,000, which is greater than the
6,250,000 sample size required, we would begin using the sample size when
q=7 in this case.
Let’s look at a real-world implementation of what has been discussed
thus far. Consider a single scenario spectrum with the following scenarios:
Outcome Probability− 1889 0.015625
−1430.42 0.046875
− 1295 0.015625
− 750 0.0625
− 450 0.125
0 0.203125
390 0.078125
800 0.328125
1150 0.0625
1830 0.046875This is a case of a single scenario spectrum of 10 scenarios. Therefore,
on ourn=qpass through the data (i.e.,q=10), we are going to have
n∧q,or10∧ 10 =10,000,000,000 (ten billion) permutations, as alluded to
earlier.
Now, we will attempt to calculate the risk of ruin, with ruin defined as
having 60% of our initial equity left.
Running these 10 billion calculations outright gives:
RR(.6, 10)=. 1906955154at anfvalue of .45.Using (12.10) withs=5,x=.001,p=.5, we iterate throughqobtaining
quite nicely, and in a tiny fraction of the time it took to actually calculate the