After a long hiatus, have started writing again., however have moved the blog to GitHub. The new URL is:

After a long hiatus, have started writing again., however have moved the blog to GitHub. The new URL is:

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With market making we can try to be neutral by skewing prices in such a way as to maintain a neutral position. To the extent that the market can become 1-sided (in momentum) or may have large sized requests (if offering at different sizes), one’s portfolio may require explicit hedging.

In a live market-making scenario we can determine how we want to hedge on a case-by-case basis and with a view on where it is cheapest to achieve the hedge. Within a FX portfolio there is opportunity to hedge an excess position in one currency with a position in one or more other currency pairs, potentially taking on some basis-risk.

An interesting inverse problem was posed by a colleague of mine. Supposing one knows the net positions of a portfolio at each time-step historically and want to back out the most conservative view on:

- whether the portfolio is hedged
- what positions it was running (assuming it is not hedged)

This problem cannot be solved definitively as any view on hedging or risk assumes a model of forward price dynamics. However, I thought a reasonable way to approach this would be to:

**determine multivariate model of mean-reversion across assets**- this would allow us to pair more loosely associated assets that tend to mean-revert as opposed to limiting our hedging to assets with a tightly coupled dynamic (i.e. close to 100% correlated)

**determine risk measure on residual portfolio (**after factoring out mean-reverting positions)- i.e. we reduce the portfolio positions by scaled mean-reverting sub-portfolios. If fully hedged, after these reductions, the residual portfolio positions would be close to 0.

**Mean Reversion Model**

There are a variety of choices for mean-reversion model. Some of the simplest are:

- Multivariate Ornstein-Uhlenbeck process:

- Vector Error Correction Model (VECM)

- PCA or ICA based decompositions
- Can use the vectors produced in decomposition to produce mean-reverting sub-portfolios

Regardless of which formulation we start with, can express hedges as a combination of scaled portfolios on subsets of assets in **x**. That is, can determine sparse weighting vectors β_{0}, β_{1}, …, β_{n} such that each linear combination of β_{i}**x** is mean reverting and possibly cointegrating. Note that one can have multiple mean-reverting vectors that include the same asset both because there are different periodicities in mean-reversion and because of the cross-relationships between assets.

For example in a portfolio containing EUR, JPY, CHF, one (cointegrating) weight vector would be: [ 1.0, 0.0, -1.0 ].

**Optimisation Problem**

Assuming we have:

- mean-reverting vectors β
_{0}, β_{1}, …, β_{n} - covariance matrix of returns on
**x**over period ΔT,**Σ**_{ΔT} - net portfolio positions:
**Q**_{t}

The goal is to find the smallest net portfolio after subtracting scaled mean-reverting vectors **ω**_{i}**β**_{i}, over some objective function O(q):

The most appropriate objective function is one that expresses the residual risk of the portfolio. For simplicity, defining the risk objective to be to find the residual portfolio with a minimum covariance matrix volume (i.e. determinant). The intuition is that a covariance matrix with highly aligned (correlated) vectors will have smaller volume. Likewise, lower variance will reduce the magnitude of the vectors (and therefore volume).

Given a covariance matrix on unit positions **Σ**_{ΔT}, can scale the covariance matrix given residual position vector **q** as:

and hence determine the objective function O(q) to be the determinant of the residual covariance:

putting it all together, we want to minimize:

Given a minimizing vector **ω**, we can determine the residual, unhedged position at time step **t** to be:

**Solution**

The optimization problem is similar to the packing problem, where we try to determine how many units of each item, where we have K distinct item types (our beta vectors), optimally fill a bag.

In our case, the items to be packed are the beta vectors and the bag is the position we are trying to reduce. We are trying to determine how many units of each beta vector to use in combination with other beta vectors to achieve the best reduction (packing).

To reduce the combinatorial possibilities to something finite, we can assume that only certain scalings of the beta vectors are used. For a FX portfolio, the market tends to trade in multiples of 100K on one of the currencies (usually the base currency). In equities, the convention would usually be units of 100.

We can then solve this with a combinatorial approach (exponential) or approximately with either a greedy algorithm (polynomial) or meta-heuristic optimization approach.

**Addendum**

I should mention that there are many approaches that can be taken in evaluating portfolio risk. Gary Basin suggested looking at a PCA decomposition of the portfolio. PCA is definitely a useful way in determining the primary determinants of variance in the portfolio. I chose to use a method that allowed me to factor out mean-reverting sub-portfolios. There are so many approaches to this, can’t really comment on what is best.

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Investors are often looking for uncorrelated returns so as to better diversify. If one looks at world indices & equities, there is much less diversity between assets than there was a decade ago, indeed the cross-market correlations are remarkably high.

On the other hand, from a trading perspective, generally want to be able to reduce the risk by hedging or spreading against related assets. For example in FX, when market making the G10 currencies, one typically offsets inventory risk with a position in another highly correlated currency or portfolio of currencies.

With that in mind let’s look at bitcoin (BTC) vs a variety of ETFs representing FX, IR, world indices, and commodities.

Below have computed 1day, 5day, and 15day return correlations across BTC + variety of FX, IR, Commodities, and world indices. To reduce the impact of outliers (return spikes), made use of my Minimum Covariance Determinant covariance implementation.

**IR & FX**

**Commodities**

**World Indices**

**All Together** (1day, 5days, 15days)

The VECM model can be used to express the co-movement of related assets across time, formulated as the change in asset prices as:

Δx[t] = δ0 + δ1 t + δ2 t^{2} + … + Π x[t-1] + Φ1 Δx[t-1] + Φ1 Δx[t-2] + … + ε

or alternatively can be formulated as the VAR model:

x[t] = δ0 + δ1 t + δ2 t^{2} + … + Γ1 x[t-1] + Γ2 x[t-2] + Γ3 x[t-3] + … + ε

The two variations of cointegration will look at are:

- constant drift, no time trend, lag 1:
- x[t] = δ0 + Γ1 x[t-1] + ε

- constant drift + time trend, lag 1:
- x[t] = δ0 + δ1 t + Γ1 x[t-1] + ε

Finding cointegrated assets that do not drift away from each other, even “deterministically”, over time is far preferable to time-based drift. I was not able to find any trivially cointegrated assets in my sample set, however, there were a number of assets with strong “type 2” cointegration. Here is one of a number that showed 95% confidence:

BTCcoint1 = Johansen (Pbtc14[['BTC','IEF']], p=1, k=1) BTCcoint1.critical_trace

BTCcoint1.eigenvectors

0 | 1 | |
---|---|---|

BTC | 0.037677 | -0.019919 |

IEF | 0.999290 | 0.999802 |

The key linkages between Bitcoin and other assets will be driven by investor trading patterns as opposed to fundamentals at this point. Should Bitcoin become more of a transactional “currency” may start to see more fundamental linkages.

I am dusting off some code from a few yrs ago to create a rolling view on spread asset ratios. Need to rework this and apply as pairs / basket strategy. Will post some results at a later point in/out-of-sample.

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I have 4 Bitcoin L3 exchange feeds running smoothly out of a data center in California (which is slightly closer to Asian exchanges and Coinbase than the east coast). It took a bit of error handling and exponential back-off, to handle the unreliability of connectivity with these exchanges, where connections can intermittently be overwhelmed (returning 502 / 503 errors due to the poor choice of a REST-based API).

I am thinking to add Bitstamp and Kraken to the mix, even though they are smaller. Bitstamp seems to have recovered somewhat since its security breach and Kraken is unique due to its EUR denominated trading.

**HFT Opportunity**

Bitcoin trading & order volume is quite far from the hyper-fast moving equities, FX, or treasuries markets. That said, it has significant potential for market makers and short-term prop-trading given the greater transparency of microstructure in this market. The caveat to this is that the transaction costs on many exchanges are enormous (10+bp or 20+bp round-trip), though for BTCChina is surprisingly free (fees are on withdrawal).

I am really at the beginning of collecting HFT-style data for the main exchanges, so while I have tested a couple of signals on very small samples, want to collect a larger data set for backtest and fine-tuning. The 2 signals have tested are around short-term momentum detection, so can either use to follow momentum or use as a risk-avoidance in a market making engine. In the later case would remove my offer from one side of the market if detect 1-sided direction, avoiding adverse selection.

**Restrictions**

Some marketplaces look to put in measures to keep their marketplace sane for lower-freq / non-HFT specialized traders. In looking at the Kraken API today, noticed the following:

We have safeguards in place to protect against abuse/DoS attacks as well as

order book manipulationcaused by the rapid placing and canceling of orders …The user’s counter is reduced every couple of seconds, but if the counter exceeds 10 the user’s API access is suspended for 15 minutes. The rate at which a users counter is reduced depends on various factors, but the most strict limit reduces the count by 1 every 5 seconds.

So effectively Kraken will allow for a small burst of order adjustments or placements, but only allows an average of 1 adjustment / 5 sec. For a market maker 1 every 5 seconds (or 2 sides every 10) is too limiting. This can become a problem for both market makers and trend / momentum followers if the market is moving. Perhaps this limit should scale with respect to price movement or be combined with a higher limit + minimum TTL (time to live).

I am actually **for** certain restrictions in the market. The equities market, in particular, needs to be cleaned up, not with new taxes or ill-conceived regulation (reg-NMS for example), but with:

- time-based priority / price-level (believe it or not, there are order types that allow HFT to jump the queue)
- minimum TTL (time-to-live)
- some reasonable maximum # of orders / unit time on a security

#2 and #3 would remove many of the games on the exchange that do not serve the market.

Filed under strategies

I’ve been a bit distracted recently brainstorming some blockchain-related ideas with colleagues, and working on a research & trading UI.

**OxyPlot**

First I wanted to give a plug for OxyPlot. If you use F#/C# or the .NET ecosystem, OxyPlot is a well designed interactive scientific plotting library. The library renders to iOS, Android, Mono.Mac, GTK#, Silverlight, and WPF. If one is dealing with a manageable amount of data, highly recommend Bokeh & python. However if you need significant interactive functionality or need to interact with large data sets, OxyPlot is a great solution:

I wanted to build a UI to allow me to observe and develop better intuitions around order book characteristics. OxyPlot did not have good financial charts, so contributed high-performance interactive candlestick & volume charts that can handle millions of bars (points) and some pane alignment controls to the project. Here is an example of the sort of UI one can put together with OxyPlot:

**Feed Status**

I was awaiting a reply from BTCChina regarding their broken FIX implementation. As the API issue has not been resolved, implemented the BTC China REST API and deployed the feeds for the 4 exchanges of primary interest:

Though 2 of the exchanges require 4-sec sampling (due to the lack of streaming APIs), all intervening trades are captured between queries. For L2 sources, order book transactions are implied by looking at the minimum sequence of transactions that would produce the difference between 2 successive snapshots of the order book. All of the feeds yield a common transaction format:

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Ok, what I am going to say here is probably Bitcoin heresy, in that I am going to advocate more centralized clearing and management of assets wrt exchange trading.

I want to be able to scale trading in bitcoin and execute across multiple exchanges. However have the following problems

- lack of trust in (most) of the bitcoin exchanges
- security of the exchange against attackers
- degree of trust in the ownership re: my assets on deposit

- inability to trade across a variety of exchanges on a net / credit basis
- require depositing cash (fiat) and/or bitcoin on each exchange

**Solution**

I want to keep my “working” fiat & bitcoin assets for trading with a trusted agent (a “Prime Broker” in the traditional trading space) who will grant me credit across a fairly wide range of exchanges. To completely isolate both the trader and the prime broker from exchange risk:

- exchanges should not hold trader’s bitcoin or fiat
- exchanges send/receive net fiat funds + cryptocurrency to/from Prime Broker based on net P&L + fees
- reconciliation between exchange and PB done as a secure transaction between the two. Could probably devise a protocol based on asymmetrical trust, which is near-transactional. The element which is least transactional is the wiring of funds (amusingly).
- much of the reconciliation can be done intra-PB or between PBs

Case in point, exchanges such as BTC-e trade BTC/USD at a 100-150bp discount to bitfinex. Why? I think this due to the perceived credit risk of depositing funds with BTC-e and possibly issues in moving assets to net.

Perhaps there is an even more interesting angle, PrimeBrokerage V2, using the bitcoin ledger, ascertaining trust, etc. But for the moment, taking exchange risk out of the equation would open up the market further.

**Advantages**

Above and beyond solving the trust issue, more centralization or a way to coordinate amongst exchanges could help with:

- “locate”: the process of finding cryptocurrency that can be borrowed for shorting
- potentially offer a meta-exchange, where participants can interact with a cross-exchange orderbook, data, etc.

Filed under strategies

I have implemented 4 bitcoin exchange interfaces now that produce a live L3 stream of orderbook updates + trades of the form:

Given the above, can reconstitute the orderbook as it moves through time, and can likewise be used to create BBO quotes and bars of different granularities. The status of the exchange implementations is:

I am looking to run this on a remote machine (preferably linux) and write to an efficient hierarchical file-based tick DB format that I use for equities, FX, and other instruments. Have not yet decided on a hosting service yet (welcome suggestions).

I am happy to share the collected data, though if becomes too burdensome, may need to find a way to host and serve it properly.

Once I get this running on a host, collecting data, want to get back to analysis of signals. Will revisit new exchange implementations later.

**Notes**

[1] Bitfinex does not yet have a streaming API, so am polling the orderbook on a 4sec sample and determining the net transactions between snapshots. Though the orderbook is sampled, no trades are missed, as queries relative to the last trade seen. Expect that will see a new exchange implementation from AlphaPoint sometime later this year.

[2] BTCChina is implemented, however their FIX responses are not providing the documented data, so awaiting a solution from them.

Filed under strategies