Allocating Capital Across Flash-Crash Buy Orders
Summary
The discussion considers how to divide limited capital among buy orders set at progressively deeper price drops, based on the idea that sharp temporary declines may rebound. It formulates the allocation as an expected-profit optimization: assign probabilities to mutually exclusive drop scenarios, calculate the resulting profit for each allocation, and choose capital weights that maximize the probability-weighted payoff. Under the stated setup, the objective is linear and can be solved with a simple search over the allocation weights.
The example expresses each scenario’s profit as the accumulated gains on orders filled at that depth, then constrains weights to be nonnegative and sum to the available capital. It does not provide event probabilities or empirical results, so it does not identify a best allocation. The calculation depends on assumptions about scenario probabilities and whether the events are mutually exclusive. More realistic path simulations can account for overlapping fills and price movement after entry; risk should also matter, since a deeper decline can leave earlier positions underwater.
Key ideas
- Expected profit depends on both the payoff at each drop depth and the probability of that scenario.
- Capital allocation can be represented as weights across orders, constrained to sum to the available funds.
- With mutually exclusive scenarios and known probabilities, maximizing expected profit is a linear optimization problem.
- A simple grid search can evaluate the small set of allocation choices in the example.
- Path simulations can capture more complex outcomes, including drawdowns on positions filled before a deeper decline.
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# Most profitable? High % but low probability or Low % but high probability # Most profitable? High % but low probability or Low % but high probability I have identified a pattern in different assets where a quick spike/flash crash often occurs, dropping the price between -5% and -15% for a few seconds and then going back to previous average. I am considering setting up buy orders but I do have limited funds. My first instinct was to separate equally my funds in 3 orders: a buy at -5% of price, -10% and -15%. But then I realized that if most spikes are at -5%, I should have more funds over there. Basically the theory is this: -15% spikes should happen less often, but will yield the most profits. -5% should happen more often but will yield less profits. Technically the -5% spikes should happen three times more often than the -15% to have similar profit if I put all my funds in either case. Is there a statistical way of separating my buy orders and funds to maximize profits? ## Answer by Enrico Schumann (score 1) https://quant.stackexchange.com/a/43097 It depends on the assumptions you are willing to make. If you assume that the 5, 10, 15% events are mutually exclusive, and you can come up with probabilities $p_1$, $p_2$, $p_3$ for each, and you wish to only maximise expected profits, then you have a linear optimization model $$\max\ p_1 \pi_1 + p_2 \pi_2 + p_3 \pi_3 $$ with $\pi_i$ the profits under the three scenarios: $$ \pi_1 = 0.05 w_1$$ $$ \pi_2 = 0.05 w_1+0.1 w_2$$ $$ \pi_3 = 0.05 w_1+0.1 w_2 +0.15w_3 $$ The $w$ are the proportions of your capital you invest, so you probably want $w_i \geq 0$ for all $i$ and $\sum w = 1$. There are only three decision variables, so even a simple grid search would do to solve the model. (The solution may not be unique.) For more-complex assumptions, I would suggest to simulate random paths of your assets, and then find an vector $w$ that is optimal for an objective function evaluated for the P/L along those paths. One thing you might particularly be concerned about is risk: after all, when you go to -15% and are invested already, you will also have a drawdown on your P/L.
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