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Total Posts: 1578
Joined: Jun 2004
Posted: 2012-08-31 07:43
I could not find anything on the web (not surprising, really, not really a clear academic problem), so as usual, this is more of an invitation for discussion.

I have N strategies, across a variety of assets and time frames (from intra-day to month holding times). Each strategy is sort-of-kind-of market-neutral and mostly carrying idiosyncratic risk. Since we all know it's not really true, I do evaluate the market-factor risk for each strategy position (delta, vega, correga, whatever applicable) to get an understanding of my gap/systemic risk. On the other hand, strategies do go boom because of idiosyncratic reasons - some stock goes bust like Enron in one of my single name strategies or maybe Obama decides to sell tons of S&P skew to improve the morale. This is non-controllable risk that I simply need to diversify away.

So, this brings multiple questions:
(a) assuming that I got the market-risk modeling under control, how do I assign an idiosyncratic risk value to a strategy? I was thinking of some sort of Poisson process, but can't even think of how to properly combine multiple distributions in that case.
(b) is there a clean way to construct a portfolio allocation model that on one hand will neutralize market risk but on the other hand would keep idiosyncratic risk diverse enough for me to sleep at night?
(c) how do i include the dynamic nature of each strategy in the allocation process? For example, some strategies are expiration-date specific, some fire fairly infrequently etc. Do I allocate hard dollars? Do I look at the new signals and allocate given the current risk in the portfolio?

I am sure people have bumped into this problem while looking after their stat-arb and HFT books, so maybe we can have some insight from there?

“My dear, here we must run as fast as we can, just to stay in place. And if you wish to go anywhere you must run twice as fast as that.”


Total Posts: 15
Joined: May 2009
Posted: 2012-08-31 09:08
you question is so interesting that I posted it at quant.stackexchange ( )


Total Posts: 225
Joined: Apr 2009
Posted: 2012-09-02 10:04
I guess you have a somehow different setup than me. Anyway I'll try to explain what I do:

I simply glue the backtests of each individual strategy together (dollar weighted) and run a style analysis on this portfolio. The style analysis is basically a regression on my strategies versus drivers I find important. Each strategy might have different important drivers like S&P, VIX, return on VIX, currencies, ... . Important drivers are usually found by looking at the drawdowns.

The regression is run both on daily backtest data and on monthly data because I have found that this type of analysis tends to be noisy. E.g. if your strategy lags the VIX level depending on some regime 3-5 days behind, you won't have an easy time to identify that on daily data.

The style analysis basically tells me important risk factors. I then put my strategies together with the important factors into Markowitz to find whether I can lift the Sharpe Ratio by mixing with (tradable) risk factors. This never happened, so I stopped to think here.

To adapt this setup to your questions:
(a) The regression weight of an index representing most closely your tradeable universe should be your systematic factor. There could be several of them. If you build a portfolio with short positions of these risk factors you should see your idiosyncratic risk in the draw down graph?
(b) This sounds like you want to use allocation with constraints. See the fPortfolio package of R.
(c) I think if you have daily backtests these kind of effects are represented in the daily pnl fluctuation. I would always allocate on how you actually trade them. If you have limited capital and a bunch of strategies that may trade more than you have capital, you need to adjust your backtests to reflect whether you have capital for a trade or not. Of course if this implies that your strategies trade systematic and allocation is not done by your gut feeling.

If you have further ideas, I am happy to listen to you.


Total Posts: 1578
Joined: Jun 2004
Posted: 2012-09-02 19:03
Yeah, that was pretty much my original thought process - I would glue all of the strategies together with changes of some reasonably independent market factors. Once that's done I'd create a daily correlation matrix and use PCA to find the most neutral weighting (fairly easy). But then I decided that I want to risk manage to a daily gap risk - it's a low probability but a high impact event.

Out of curiosity, do you hold many positions overnight or is your portfolio mainly intra-day?

“My dear, here we must run as fast as we can, just to stay in place. And if you wish to go anywhere you must run twice as fast as that.”


Total Posts: 1262
Joined: Feb 2005
Posted: 2012-09-03 08:48
Maybe something like this or am I not understanding what you mean by controlling daily gap risk?

Dilbert: Why does it seem as though I am the only honest guy on earth? Dogbert: Your type tends not to reproduce.


Total Posts: 225
Joined: Apr 2009
Posted: 2012-09-03 09:35
I hold stuff for a few days, my execution is just too lousy to compete intraday.

Of course PCA is another way to go to find explaining drivers. Another tool I like to explore strategies is VaR, but not for risk attribution. As correlation/volatility does not distinguish between upside and downside you can get a feel for your strategies by looking at parametric VaR vs actual outcome. If your strategy has an edge, is broadly diversified and your holding time is not too long, then you should almost never see any VaR breaks. On the other hand if you calculated 95%-VaR and get VaR breaks 5% of the time your strategies behave like that portfolio, thrown together without any clue (edge) about it's dynamics.

This opinion might be a little bit strong, but captial allocation with VaR seems to be good for several desks, not so much for a individual trader.


Total Posts: 890
Joined: Jun 2004
Posted: 2012-10-02 22:36
How about Ralph Vince (multi-dimensional Kelly) -LSPM stuff?
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