The Leverage Space Portfolio Model in the Real World 411
FIGURE 12.2 RR(.6) observed and calculated for two-to-one coin tossf=.25
by taking 6,250,000 samples for eachq(beyondq=6) , and using these 10
data points (q=1... 19) as input to find those values of the parameters in
(12.11) that minimize the sum of the squares of the differences between the
answers given by those parameters in (12.11) and the actual values we got
[by estimating the actual values using (12.10)], gives us the corresponding
best fit parameters for (12.11) as follows:
asymptote= 0.397758
exponent= 0.057114
coefficient= 0.371217The data points and corresponding function (12.11) then appear graph-
ically as Figure 12.3.
And, if we extend this out to see the asymptote in the function, we can
compress the graphic as shown in Figure 12.4.
Using these two shortcuts allow us to accurately estimate what the
function forRX( ) is, and discern where the asymptote is, as well as how
manyq—which can be thought of as a surrogate for time—out it is.
Now, if you are trying to fit (12.10) to a risk of ruin,RR(b), you will fit
to find the three parameters that give the best line, as we have done here.
However, if you are trying to fit to risk of drawdown,RD(b), you will
only fit for variableAand variableB. You willnotfit for the asymptote.
Instead, you will assign a value of 1.0 to the asymptote, and fit the other two
parameters from there.