Quantitative Finance

Determining the Optimal Equity Portfolio aka Modeling a Basket of Credit Default Swaps

Say you have picked out a couple of companies. Done your detailed research, estimated their potential gains, estimated the time horizons in which the catalysts would occur, and finally decided that they are good buys. So how exactly should your optimal portfolio look like? Do you pick the top 8? the top 10? or maybe just the top 3?

It struck me about 1-2 months ago that modeling this basket of stocks, is very much like modeling a basket of credit default swaps.

Studies have shown that the "jump" or appreciation of a stock's price, typically happens in only a few days in a year; meaning that if you miss out say, the best performing 10 days of your stock, your return will be mediocre. This is very much like a "jump" event, that is currently used to model credit events (default, bankruptcy, downgrade, etc.) for the pricing of credit default swaps.

Hence the techniques used to model CDSes (e.g. poisson processes, copulas, etc.), can be applicable to modeling equity portfolios. The random processes can be simulated, with each jump resulting in an amplitude multiplier representing the potential gain of a stock (i.e. discount to fair value), and the intensity of a process relating to the estimated time horizon in which a catalyst would occur. The simulation would then be able to simulate different portfolio value process, get expected values, stderrs, apply variance reduction techniques and all that good stuff. Different portfolio rules (e.g. after a predicted gain is realised, shift money to highest potential gain stock among those that have not "popped" yet) can be applied in the simulation and their results analysed.

I have not seen such a thing being done before yet. Perhaps it is just rare to find someone with exposures to both fields: value/fundamental investing and mathematical finance.



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