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Ok, let's say I'm trading a spread of two stocks, X & Y, The spread is calculated as a ratio (Spread = X / Y). I use rolling stats to calculate the mean, standard deviation and hence the z-score of the spread, as such, I take the usual entry/exit signals of entering trades when the z-score exceeds 2 the then closing them on return to zero. There are, of course, the usual ways of sizing the legs. (dollar neutral for example). What I want to do is size the legs according to a z-score stop loss. Let's say that I'm going to define a z-score that exceeds 4 as my disaster stop. Given the amount of my account (in dollars) I want to lose if the stop is hit, how do I size the legs on entry of the trade? (Let's assume the mean and standard deviation remain constant).

Update: In the meantime I've been pondering this, this only thing I can think of is to hold one leg constant and work backward. This can be done for each leg in turn. But I'd still be interested in other ideas.

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Might be simpler to use some measure of dollar risk (fractional empirical kelly criterion), then see what the ex ante leg commitments are that result in a 4-sigma loss of the desired dollar risk. The trouble is that this may over-size your legs since the ex ante volatility is likely lower than the in the ex post stop scenario, meaning the 4-sigma stop will be much further away than expected. –  experquisite Jan 30 at 22:40
    
Yep, I'm seeing that in my testing, basically, the volatility is volatile. Hmmm...what to to... –  Craig Jan 31 at 0:27

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Interesting idea. I would like to have the reference you are using for this scheme? You are treating X/Y as a stock and then using Bollinger Band kind of signalling mechanism. I would think you would define the entry/exits more strictly to make it profitable.

If you are making a lot of trades using this system, then from backtesting, you can figure out your winning and losing trades and probabilities and use Money Management using Kelly Fraction for sizing trade investment.

In Bollinger band(+/- 2 sigma from mean), generally 14 or 21 day rolling window, when stock is above mean (z-score 0), it tends to stay up. It is a trend following indicator. With z-score>0, you can stay with positive trend. Of course, you need to build in some loss rule like 5-8% loss from mean to avoid whipsaws. A trend up is higher high and higher lows, trend down the opposite. You initiate a trade only if the trend is established. If the stock moves downward then play that once the trend develops. If the sigma becomes small then it tends to explode either to the up or down side. You could hedge this by buying a strangle one sigma away cheap and then once you make money ride with this system. I have outlaid this as if you are using S=Y/X as a stock. In pair trading, if you buy a spread and it widens it is the same thing.

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