Back to course

Hit Ratio vs. Spread: The Core Tradeoff

Every quoting decision comes back to one tension. Tighter quotes trade more often and earn less each time; wider quotes earn more per trade and trade less.

Expected P&L=Fill rate×Profit per fill\text{Expected P\&L} = \text{Fill rate} \times \text{Profit per fill}

Both terms depend on the spread, in opposite directions, so there is an interior optimum rather than a corner solution.

Working the numbers

Worked example: where the product peaks

Suppose fair value is 100.00 and, over some interval, fill rate falls as you widen:

Half-spread Fills per hour Profit per fill Expected P&L
1 cent 100 $0.01 $1.00
2 cents 60 $0.02 $1.20
3 cents 35 $0.03 $1.05
4 cents 20 $0.04 $0.80

The optimum here is two cents. Note it is neither the tightest nor the widest, and note how flat the peak is: one cent and three cents both give within 20% of the best. That flatness is genuinely useful, because it means approximately right is good enough, and the cost of being slightly wrong is small.

Hit ratio against spread

1c2c3c4c5c

The dots are the lesson's measured rows; the line is the model through them. Anywhere in the shaded band earns within 10% of the best, which is 1.6 cents wide. Being a cent off the optimum costs almost nothing, and that is why fair value deserves the attention instead.

0.0c
0.54

E[P&L] = fills(s) x (s − adverse), optimum at s = adverse + 1/decay

Best half-spread
1.85c
At that spread
$1.17
Within 10% of best
1.2-2.8c

The dots are the lesson's table. The shaded band is how flat the peak really is.

Then add adverse selection and watch the optimum walk outwards. That is the correction below: if part of every fill is lost to better-informed flow, the spread that pays has to be wider than the naive table says.

Key takeaway

The expected-P&L curve has a broad peak. Being a cent off the optimum costs little; being on the wrong side of the market by ten cents costs a lot. Prioritise getting fair value right over optimising spread width.

What the simple model misses

The table above assumes profit per fill equals the half-spread. It does not, because of adverse selection.

Fill rate and information content rise together. Tightening your quote attracts more volume, but the extra volume is disproportionately from traders who most wanted to trade, and those are the ones most likely to know something. So the true relationship is closer to

Profit per fill=half-spread−expected adverse selection cost\text{Profit per fill} = \text{half-spread} - \text{expected adverse selection cost}

where the second term also grows as you tighten. This pushes the optimum wider than the naive calculation suggests, and it explains why market makers do not simply undercut each other to the tick.

What moves the optimum

Volatility. Higher volatility raises inventory risk per fill, moving the optimum wider.

Competition. More market makers means your fill rate at any given spread drops, since you are sharing the flow. Optimum tightens, because you must compete to trade at all.

Flow composition. Venues with predominantly retail (uninformed) flow support tighter quotes profitably. Venues with institutional flow require wider.

Inventory. When you need to reduce a position, the calculation changes entirely: you may quote at a loss on one side because the value of getting flat exceeds the spread given up.

The two ways to be wrong

Too tight: high fill rate, thin margins, and heavy adverse selection. The P&L looks busy and goes nowhere or slowly down. This is the more common failure among new traders, who mistake volume for progress.

Too wide: barely trading. Safe, and pointless, since you cannot make money on trades you do not do, and you lose queue position and market share to competitors.

Tip

In a market making game, if you are filling on almost every quote you are too tight; if you are barely filling you are too wide. A moderate fill rate with balanced buys and sells is what a healthy quote looks like.

Practise the balance in the market games, where the P&L breakdown makes the tradeoff visible in a way that description cannot.

Test your knowledge

A market maker compares two quoting strategies. Strategy A is a narrow spread with an 80% hit ratio and $0.05 profit per fill. Strategy B is a wider spread with a 30% hit ratio and $0.20 profit per fill. Which gives the higher expected P&L per quote, and what is it?
The simple model assumes profit per fill equals the half-spread. Adding adverse selection changes the answer. In which direction, and why?
NextMaking Markets in Options