Capital Allocation On Simultaneously Arriving Signals in the Same Direction but....

Nonius · Post by **Nonius** » Fri May 04, 2012 1:25 am

different stop loss levels and stop gain levels.

let's assume the entry is a market order.

each signal/trader/model/bot has its own assessment of the probabilities of success and failure.

eg, model A says buy at time t with a stop loss of x and stop gain of y (and maybe sell by t time) and model B says ditto at ditto with a stop loss of z and stop gain of w. you have a bunch these things and the arrival of the signal is precisely one moment in time.

what are your approaches?

Tradenator · Post by **Tradenator** » Fri May 04, 2012 1:44 am

If we assume all trading is the exact same critter (if derivatives then all params are identical), then I would trade the sum of both positions at any time. Here, I am assuming you have one account in which you trade multiple models together under one mandate. In this way, the sum on N positions won't violate exposure boundaries and simultaneous buys/sells get netted off before going to market. In what you describe, you would then carry a suite of stops at various levels, kind of like what Fibonacci folks do. Your inventory is simple, and if you use DMA in realtime then you don't need to broadcast your stop levels because you can just execute those at market when your levels get tripped.

For perf attribution to each model where there are offsetting positions, you can scale your model results to the actual P&L and that should be good enough. The error here includes bid/ask on the offsetting trades and transaction costs, which you have avoided by netting.

TonyC · Post by **TonyC** » Wed May 09, 2012 5:42 pm

a couple of papers on combining portfolio rules attached below

[url=/User%20Files/45/Combining%20Portfolio%20Rules.zip]Attached File: Combining Portfolio Rules.zip[/url]

Nonius · Post by **Nonius** » Fri May 11, 2012 11:22 pm

thanks Tony for the papers.

thanks Tradenator; I was sort of heuristically thinking along those lines.

Nonius · Post by **Nonius** » Fri May 11, 2012 11:53 pm

by the way, If I'm not too lazy, I'll work out what Thorp would say you should do.

Nonius · Post by **Nonius** » Sat May 12, 2012 11:50 pm

fuck.

maybe I'm making this too complicated.

for a stop loss level L, a stop gain G and a time horizon T.

there are obviously only three things that can occur in time T. I get stop lossed out. I get stop gained out. I ride it to T.

consider three stopping times. a is stopping time to L. b is stopping time to G. c is T.

there are six combos of what arrives in what order.

but that maps to the three things that can happen.

ie, asuppose I have two such time localized contemporaneous (let's call it wavelet signals, but it's not based on wavelets) signals/strategies.

if I want to do Kelly, I first need to compute the joint probabilities. it's a table with 9 probs. four of the entries are obvious.

anyway, there's a bunch of papers on simultaneous bets, but this is a special case and I don't want to appeal to stylized assumptions about distributions, and, in fact, structurally it's a discrete model.

the problem is, I've empirically found that for some liquid stocks I'm getting on average around 20 or so signals at the same time, but with different stop loss and stop gain prescriptions. combinatorially, that looks intractable in discrete space at least from a computational complexity perspective. I've also tried simple shit like doing what Tradenator suggests, but the long term difference between doing that and doing something else, such as simply taking the best kelly bet, is huge.

NeroTulip · Post by **NeroTulip** » Sun May 13, 2012 12:26 am

You could rebalance your portfolio each time you get a new signal or a stop loss/gain is hit. Count the number of remaining buy and sell signals, and that gives you a net direction and an overall signal strength. Bet a percentage of your capital that is proportional to signal strength. Then you can experiment with different functions to map number of signals to signal strength.

Nonius · Post by **Nonius** » Sun May 13, 2012 12:50 am

isn't signal strength kelly?

rdg · Post by **rdg** » Sun May 13, 2012 9:14 am

I think a big question is whether you want to assume the signals are independent or not. I personally think it's ballsy to assume dependence and try to trade off the joint probabilities unless your sample set is crazy huge.

An idea you might try is to assume the signals are independent and work out the Kelly bet for each signal individually. Then allocate from largest to smallest bet size until the sum of the (absolute value) of the exposures hits your limit.

Ie, if you have a long signal that's a sure thing and a bunch of lower quality short signals, you bet 100% on the sure thing. If you have 2 signals that call for 50% long and 50% short along with other lower quality signals, you are flat. Then you rebalance whenever a new signal arrives or when you exit an existing trade.

I admit this isn't what I do since I have a different set of problems to solve, so take it for what it is: just another idea to test.

NeroTulip · Post by **NeroTulip** » Sun May 13, 2012 10:22 am

Kelly says bet edge/odds. Signal strength is the edge part.