Efficient Frontier And Beyond

noreply@blogger.com (10801) — Wed, 07 Sep 2011 09:32:31 PDT

A sub-project from Math Harbour resulted in a very fast Efficient Frontier -generator. We have been developing a technology by which users can manage indifferent results, not just in list like fashion as in current SE providers. It is not easy task so we are researching ideas from other fields and time-to-time, we publish some of our results to public domain to let users to play with them. For example, we have been using Efficient Frontiers in analyzing certain states which don't seem to have unique solution. Quants can visualize risk-return -relationship with them so we thought let's try -- let's put users on Efficient Frontier! -And guess what?!

We are open-sourcing the code! [look for my repo]

The crux idea in the model is craft distributions with pseudo-numbers to each usage, instead banging head with n-times innermost for-loop. It killed the O(x^n) time-complexity problem. Also, noticeable thing is that you will get odd holes to your sail if you don't use proper epsilon for conditional $abs(sum(proportions)-1)<\epsilon$, floating point oddities at the best. For convenience, I used Python's itertools package for managing iterables, intstead of the copycatted R itertools pkg. Initially, I coded most in Python but I switched to R for statistical- and advanced graphing solutions.

Financial Significance
I may publish a paper on related topic so keep looking. If someone is interested to fund some research idea, please, contact me. The model can be used to analyze number of things from style drift in active funds to arbitrage opportunities.

I have blurred the next example, risk profile of some active funds. I write about it because it think it is of high news -value. Please, take everything with a drain of salt because the time-span is only about 12 years and I haven't done proper analysis between many similar funds. The "safe-haven-marketed" active fund (number 1) has returned poorer risk-adjusted return to AAA cash -fund. For fellow indexers, this is probably nothing new but I suggest other people to think about this case with the frontier, do you buy over-priced counter-funds? Are you sure of your fund provider? The x-axis means years, I don't want to reveal them until proper analysis with other providers, it is technically easy but time-consuming because it requires to find/parse some awkward XLS/CVS files (not in any consistent format).

We have been very positive about R, it is not just statistics, it is much more -- it is a bit like GnuPlot with functional props such as list comprehensions. Think this python one-line `[x*3 for x in range(30)]` is `x<-seq(30); 3*x[x]-3` in R. For some odd reason, indexing starts from 1 in R, hence the -3. Anyway very cool app if you crux python, I like it a lot -- and now I am practicing with some projects dealing in Python, R and some C which I believe can be useful for MH.

You won't hear much of me but you can always read the repo. Let my sail protect you. No more sailing birds.

The MCM competition is over

noreply@blogger.com (10801) — Mon, 04 May 2009 17:50:24 PDT

My friends, Sami Losoi and Esa Vesalainen, and me participated in the Mathematical Contest in Modeling. The problem was about regulating traffic in, around and out of a traffic circle.

Our model is an automaton. Vesalainen wrote the most of the source code in C. I debugged the code, and I synthesized the information in Awk and Excel. My brother Sami edited the information, and he fast found new and relevant information. He mastered Latex and the use of search engines.

The model can be used to improve the safety in traffic circles. Civil engineers may want to know the impact of a broken signal to the amount of cars. Our model shows the amount of extra capacity. It can be used to calculate the critical density to avoid traffic jams.

There are many other applications for the model. A creative person can find the model useful in fields such as Finance and Physics.

Great thanks to Sami and Esa!