**By Andrew Royal, Head of APAC Autobahn Analytics and Algorithms, Deutsche Bank**

**Identifying short-term alpha signals in the market ****can improve trading strategy logic.**

**Order book imbalance**

The order book signal at time * t(Q_{t})* can be defined by the difference in bid size

**(**

*q*

^{B}_{t}**)**to ask size

**(**

*q*^{A}

_{t}**)**:

This outcome is on an interval (-1,1), where numbers close to +1 indicate that we are bid side heavy relative to the ask side. Order book imbalance theory (see Cont, Stoikov and Talreja, 2011) suggests that low ask sizes indicate high probabilities of the ask queue becoming zero before the bid queue, and thus the next price we see should be towards the ask side. The reverse holds if the imbalance is negative.

**Trade flow imbalance**

A second signal we can look at is where the trades are occurring. Trade flow can give us good information as to where hidden orders and large meta orders are priced in the market. For example, if there are multiple trades on the ask side, we might conclude a hidden order to be responsible. Hidden orders imply autocorrelation in the trades, and hence multiple trades in a row give us some expectation that the next trade will also be on the same side.

We define the trade imbalance at time * t(T_{t})* by using the volume of trades at either the bid

**(**

**v**^{B}_{t}**)**or the ask

**(**

**v**^{A}_{t}**)**:

This outcome is in the interval (-1,1), with a “+1” value indicating all trades are occurring on the ask side. When * T_{t}* is nearing “+1”, all else being equal, we might expect volume to continue at this price level – there is clearly demand at this price, but there might not be enough supply to satisfy it – that is, the mid-price should tick upwards.

**The model**

Our intention is to determine where the next mid-price at time * t+1(P_{t+1})* is going to move. We let:

The task is to find a function * f* so that we can fit the model:

We find * f* using a feed-forward one-layer neural network. This is quite simple to fit and doesn’t assume any linearity or functional form in the solution.

**A fitted solution**

This model was fitted to stock of HSBC for the six months from 1 January 2018 to 30 June 2018, and data was split into training, testing and validation data. We found the following predictions, which are defined as the function * g(x,y) = f(x,y,…)* and plotted below:

What can we conclude about this surface? Firstly, the signals can be conflicting in nature – a positive trade imbalance (momentum) and a negative orderbook imbalance can reduce the expected price increase.

Secondly, the five-second signal gives the strongest prediction. The strength of the signal declines as the time interval increases. This suggests that some reversion is going on.

Thirdly, the fitted function is non-symmetrical for the five-second prediction – we expect that short selling rules here produce this, making it more difficult to observe an imbalanced book. More research is required to prove this.

**Backtesting**

Here we analyse the predictability of short-term alpha in the stock price for different time intervals, namely: 5, 10, 15, 30, 60, 120 seconds using out-of-sample data for HSBC for the six-month period.

Broadly speaking, the out-of-sample data showed a small decline in the predictability of the stock compared with in-sample data, but it was pleasing to see we were not overfitting the data.

Turning the prediction surface into actions necessarily means a tradeoff between false positives (we let in too many signals) and false negatives (we don’t let in enough). The following ROC graph demonstrates the tradeoff and allows us the appropriate way to quantize our prediction surface into actions. We tend to go for a small type 1 error (small number of false positives). The interesting feature is how quickly the prediction declines with time – five seconds can produce an informative prediction that will help with the strategy as the ROC curve is above the 45-degree line. However, 120 seconds does not create a useful action so we are better off just guessing.

**Usage in the algo suite**

We can use these results in our algo strategy by defining a set of simple rules on top of the best quantization of the prediction surface. Graphically, for a buy order we have the following three possible actions: amend, stay, cross.

For a buy order, the cross action means we should cross the spread immediately if we can, as the price is almost certainly moving away. The stay action means we do nothing as the signals are not strong enough. The amend action means that the price is coming towards us so we should either amend the price down if we are ahead of the volume, or amend the quantity up if we are behind the volume.

**Going forward**

Deutsche Bank Autobahn Equities continues to introduce more alpha signals into our algo strategy logic. Identifying order book and trade flow imbalance is proving to capture short-term alpha and therefore optimize trading performance. We are testing several statistical models that have important applications and expected performance improvements for global markets, leading in APAC.