# Strategy Risk and Portfolio Allocation Model (copy from nuclear phynance)

Here is a very interesting question that I found at Nuclear Phynance (original author: Strange); I though it is so interesting that it is worthwhile to ask it here:

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:

1. 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.
2. 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?
3. 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?
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it is not "my" question, so I will eventually post answers... – lehalle Aug 31 '12 at 15:33

## 3 Answers

About the 3rd point (i.e. how to include the dynamic nature of each strategy):

The best and rigorous way to do it is to use stochastic control:

• you need a utility function (to balance expectation with risk)
• you have stopping times to enter or exit from your strategies (in fact you have probably laws of the stopping times, at first you can assume they are independent Poisson processes)
• and you know the law of the returns to expect (because of your backtests)

So you can implement a backward scheme to obtain a good mix of your strategies. Ideally (and to maintain your computations easy) you need an end time, take a multiple of all the expectations of your Poisson processes.

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Yeah, I initially thought of modeling each strategy as an asset and simply trying to allocate using some sort of efficient frontier. This is a bit scary, as you end up using strategy performances and "your biggest loss is ahead of you".

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welcome at quant.se – lehalle Sep 1 '12 at 11:59

One way to think about it would be to model each strategy like it were a stock or index. Even if the strategies themselves have during holding periods or assets, they all fundamentally have a PnL every day that you can look at.

So you would model the strategies and any other risk factors that you are worried about your exposure to. The strategies have potentially time-varying exposures to markets that you would need to account for, such as by a DCC copula.

You could then apply portfolio optimization for some generic time horizon with constraints on the total risk and risk factors to ensure market or factor neutrality.

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