## Market Making

### February 6, 2010

Supposed you are trading gold in Asia market, daily vol is 25%. During the day, your largest source of liquidity, TOCOM trade 2 mio oz gold in 8 hours time span from 9:00 to 16:00. now a client call you asking for gold price, market is trading 1000/0.5 3X3 koz with more order on EBS 999.75/1000.75 10X10 koz. what should be you quote and how should you execute to lay off the risk? let’s say you made 999.5/1000.5 and the client lift your offer for 10k oz gold. Now what’s next? On one hand you are worried about if you execute the order immediately on exchange, the market impact will eat off your spread, and you will lose 30 cents on the trade, on the other hand if you trade two slowly, market may move around and you’re facing increasing risk linear to square root of T. The optimal strategy is to strike a balance between this two conflicting factors.

A few factors need to be taken into consideration: market volatility going fwd during the trading period, market volume during the trading period and instantaneous market impact. With respect to these parameters an optimal point, which maximize the instantaneous sharp ratio can be calculated.

In this case, given 0.5 spread(from mid) and 0.8 instantaneous impact(I). The optimal strategy is to layoff the risk in 10 minutes buy trading 1k oz per minute. Given TOCOM’s 2mio oz trading volume in 8 hours, this give you a participation ratio (trade volume/market volume) roughly around 25%, this reduce the theoretical impact k=I* (0.95*participation ratio +0.05 ) to around 27 cents. The instantaneous sharp ratio is 0.4, with profit distribution ~N(2588,5022) in dollar term. The simplified average slicing scheme aim to achieve VWAP during the execution period and with expected value of P_0. If you keep trading in this way, time will help to take care of the volatility(remember mean is linear to number of trade (N), while risk is linear wrt to sqrt(N)). If you do this kind of 10k trade one time a day for a year, your year end sharp ratio should be improved by 14 time, a nice 5.4.

a few interesting property can be observed here:

- your optimal point is always close to 50~25% participation ratio
- your spread can be pretty tight, half of instant impact you are still very profitable with acceptable PnL risk
- assuming random with drift (fwd rate) and trying to achieve VWAP is what a purist market marker will do
- never willingly cross the spread (motto of oliver weldon) will help to improve it further
- negative selection could be a problem( large distributed order, interbank), if there is no reciprocity there should be no love for this.
- MM is really fill the bathtub with teaspoon, but should be and could be automated with this framework
- Trading strategy could fine tuned using more elaborated scheme, uneven distribution in volume and time, tracing liquidty.
- better way to predict instantaneous impact, vol and volume, incorporate some correlation structure between them?

Here is the nice ‘theoretical’ result: