[GSoC-PortA] mapping function

[Ross Bennett]

On Tue, Jul 9, 2013 at 6:14 PM, Ross Bennett <rossbennett34 at gmail.com>wrote:

>
> On Mon, Jul 8, 2013 at 6:59 AM, Brian G. Peterson <brian at braverock.com>wrote:
>
>> Also elsewhere in this thread was a discussion of transforming the entire
>> vector to meet the leverage constraint.  While this 'works', it has two
>> drawbacks.  The first is that you may then violate the box constraints.
>>  The second is that you will be further from the edges of the feasible
>> space.  It may make sense to write a simple test script  on 50,100,200,500
>> assets that either transforms one asset at a time, or *first* transforms
>> the entire vector, and then transforms individual assets
>>
>
> I will write the simple test script per your comments to compare the two
> methods. I agree with you that the major downside is that the box
> constraints will likely be violated. it is also likely that group
> constraint will be violated and the weights vector will just have to be
> transformed again to satisfy the constraints.
>

I added a script to the sandbox folder called
leverage_transformation_testing.R. I tested a handful of scenarios for
different box constraints and starting values for the sum of weights. What
I found is that the success rate is pretty sensitive to the box constraints
and starting value of the sum of portfolio weights. Success rate defined as
the percentage of portfolios that still meet box constraints after
transforming the whole vector to meet leverage constraints.

 - 95%+ success rate when the min vector of lower bounds for box
constraints is all 0s

 - For the case of 250 assets, if I set just 10 elements of the min vector
equal to 0.01    the success rate drops from 96% to 37%... very sensitive
to positive elements in the min vector.

I could do some more exhaustive testing, but I'm not sure how much we'll
gain. Even if we transform the entire vector first, some of the time we'll
have to transform again to satisfy box constraints. How often "some of the
time" is could vary from 4% to 63% of the time based on the testing I did.
I think the two drawbacks you listed above outweigh the time we'll save by
not having to transform individual elements some of the time to satisfy
leverage constraints.

Ross
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