What is the role of a market maker in the crypto world?

Author: incomprehensible sol Source: X, DtDt 666

This sharp drop with a spike has led many brothers to say that there is a problem with Binance's market makers, including the $PAXG pegged to gold, which also spiked.

Why do many retail investors say that every time they buy, the price drops, and every time they sell, the price rises?

So, what do market makers do? How do they operate?

1. Fee Rebate

2. Bidirectional order placement, with both parties transacting after a small spread price difference profit, accumulating thin profits, essentially relying on capturing liquidity through time and information delays.

3. Price discovery helps the market to price efficiently and provides liquidity.

4. Market making, manipulating the market, and selling liquidity to retail investors in conjunction with news.

The English original of “做市商” is Market Maker. In other words, in places where there is no market, the market maker creates a market.

First of all, suppose you are a market maker for a project, and now there is an order book (order book), which looks like this:

Let's make some assumptions first: there are no other investors placing limit orders in this market, you are the only liquidity provider in this market, which means you are the only market maker; the minimum price movement unit is 0.01; all takers ( need to pay a fee of 0.025%, and all makers ) receive a rebate of 0.01%.

You are a market maker, the party that places orders. For all the orders that are executed at the market price with you, you can receive a 0.01% rebate.

The price difference between the best bid and the best offer, referred to as bb/o, is called the spread. The current spread in the order book is 0.01.

Now, a market sell order has come in, which will be executed at your buy price of 100. You paid 100 for this transaction, while the other party actually only received 100 - 0.025*100 = 99.975, of which 0.025 (100*0.025%) is the transaction fee, and you can receive a rebate of 0.01% from this, so you actually only paid 99.99.

Because the buy order has been removed, the structure of the order book has changed, and the current spread has become 0.02. However, the market price is still 100, as this is the last transaction price:

If a buy order comes in at this moment, it will be executed at your sell price of 100.01. You bought the last order at a price of 99.99, and now selling at 100.01, you make a profit of 0.02. Adding the rebate, the total profit from this buy and sell can reach approximately 0.03.

Although your buy 1 (100) and sell 1 (100.01) spread is only 0.01, the actual profit can reach up to 0.03!

If market orders keep coming in and trading with you, you can earn 0.03 with each buy and sell. Accumulating this way, getting rich is just around the corner!

However, it is unfortunate that the market did not develop as smoothly as you expected. After you received the goods at a price of 99.99, the spot market price immediately dropped from 100 to 99.80. You quickly canceled the buy orders at 99.99 and 99.98 to avoid being arbitraged by others.

Because the current price has dropped to 99.80, your sell order is still at 100.01, which is too high, and no one will trade with you at this price. Of course, you can adjust your sell order to 99.81, but it will result in a loss of 0.17.

Don't forget, you are the only market maker in the market, and you can fully leverage this advantage to adjust the order book and minimize losses!

You calculated at what price you need to place a sell order to break even. You received the goods at a price of 99.99 and want to sell at the break-even price to close this order. To sell one, you need to place it at 99.98( because with the rebate, the actual amount received is 99.99, just enough to break even).

So you adjusted the order book, placing orders at 99.80 and 99.79 for the buy one and buy two respectively, and placing an order at 99.98 for the sell one.

Although the price difference is significant now, you are the only market maker in the market, and you can decide not to lower the selling price. If someone is willing to trade at a selling price of 99.98, then everyone is happy. If not, that's okay because your buying price has already been lowered to 99.80, and there will be market orders coming in to trade with you.

At this time, a market buy order comes in and matches with your bid. Now you have 2 contracts, and the holding cost will be averaged to: (99.79 + 99.99) / 2 = 99.89. (In the previous transaction, we matched at a price of 99.99, and this one at a price of 99.79, which is lower than the buy order price because we have a 0.01% fee rebate.)

OK, now the average holding cost has dropped to 99.89. You lower your selling price from 99.98 to 99.89. Suddenly, the huge bid-ask spread has narrowed by half. Next, you can continuously operate like this to gradually reduce costs and narrow the spread.

In the example above, the price only fluctuated by 0.2%. What if the price suddenly fluctuates by 5%, 10%, or even more? Even using the method mentioned above, it may still lead to losses because the price difference is too large!

Therefore, market makers need to study 2 questions:

How much does the price volatility vary under different time windows?

What is the trading volume of the market?

Volatility, simply put, refers to the extent to which the price deviates from its average. The volatility of a price can vary across different time frames. A particular asset may exhibit significant fluctuations on a 1-minute candlestick chart while showing a calm trend on a daily chart. Trading volume informs us about liquidity, which in turn affects the spread of orders and the frequency of transactions.

The diagram above demonstrates 4 types of price fluctuations. For different fluctuation scenarios, market makers need to choose different responses:

If the overall market volatility is low, with both daily volatility and intraday volatility being very low, then a smaller bid-ask spread should be chosen to maximize trading volume.

If the daily volatility is low, but the intraday volatility is high (, it means that although the price fluctuates significantly, there is no substantial change ). You can widen the spread and use a larger order volume. If the price moves in an unfavorable direction, you can use the method mentioned above to lower the average cost to reduce losses.

If the daily volatility is high but the intraday volatility is low (, in other words, the price is moving along the trend at a steady pace ), you should use a smaller, tighter spread.

If both the daily volatility and intraday volatility are high, you should widen the spread and use a smaller order size. This is the most dangerous market condition, often scaring away other market makers. Of course, crises coexist with many opportunities. Most of the time, market makers earn stable profits, but when the market behaves erratically, it can breach one side of your order book, forcing you to exit at a loss.

Market making involves 2 key steps: determining the fair price ( pricing ) and determining the spread ( spread ).

The first step is to determine the fair price, which is to identify the price at which to place the order. Pricing is the first step and also a very important one. If your understanding of the fair price deviates too much, then your “inventory” is likely to be unable to sell, and you will ultimately have to liquidate your position at a loss.

The first method of pricing is to reference the price of the asset in other markets. For example, if you are trading USD/JPY in the London market, you can refer to its pricing in the New York market. However, if there are abnormal fluctuations in prices in other markets, this method of pricing can become very unreliable.

The second pricing method is to use the mid price for pricing, mid price ( = (Buy 1 price + Sell 1 price) / 2. Pricing using the mid price is a seemingly simple yet very effective method because the mid price is the result of market competition. Quote around mid, the market is probably right. Pricing with the mid price, the market is likely correct.

In addition to the two pricing methods mentioned above, there are many other pricing methods, such as algorithm-based models and market depth pricing methods, which will not be elaborated on here.

The second issue that market makers need to consider is the spread. To determine an appropriate spread, you need to consider a series of questions: What is the average trading volume in the market? How much does this trading volume vary ) in terms of variance (? What are the average size and variance ) of the active buy orders (? What is the order volume near the fair price? And so on. In addition, you also need to consider price fluctuations and variance in very small time windows, the fees that market makers have to pay/collect, and other minor factors such as interface speed, the speed of placing and canceling orders, etc.

In a very short period, the profit expectation for market makers is actually negative because each proactive buy order )taker order( wants to trade with you when they have a price advantage, unless it is a forced stop-loss order. Every other participant in the market wants to profit at your expense.

Imagine you are a market maker, where would you place your orders?

Under the premise that the orders can be executed, to take advantage of the maximum price difference, you need to place your order at the very front of the order book, which is at the buy one/sell one price level. As soon as the price changes, your order at the buy one level will be executed quickly. However, frequent price fluctuations are a bad thing— for example, if you just received the goods and the price changes, your original sell one order can no longer be executed at the order price.

In a market with insufficient liquidity and small price movements, placing orders at the best bid/ask can be safer, but this raises another issue—other market makers will notice you and place their orders ahead of you with smaller spreads. Everyone will compete to continuously tighten the spread until there is no profit left.

Now let's explore from a mathematical perspective how to determine the price difference. We start with volatility. We need to know the magnitude of the volatility of this asset's price/volume around its mean over very short time periods. The subsequent mathematical calculations will assume that price activity follows a normal distribution, which will of course deviate from actual conditions.

Assuming we take 1 s as the sampling period and the past 60 s as a sample, suppose the mean of the current midpoint is the same as the mean 60 s ago ) remember that the mean here is unchanged (, and this mean has a standard deviation of 0.04 from the current price. Since we previously assumed that price movements follow a normal distribution, we can further conclude that, 68% of the time, the price will fluctuate within 1 standard deviation from the mean ) $-0.04-$+0.04 (; and 99.7% of the time, the price will fluctuate within 3 standard deviations from the mean ) $-0.12-$+0.12 (.

Ok, we are quoting with a price difference of 0.04 on both sides of the midpoint, meaning the spread equals 0.08. The price will fluctuate around the mean within 1 standard deviation )$-0.04-+$0.04( for 68% of the time. Therefore, for the orders on both sides to be executed at this time, the price fluctuation must break through the prices on both sides, which means exceeding 1 standard deviation. There is a 32% chance )1-68%=32%( that the price fluctuation will exceed this range. Therefore, we can roughly estimate the profit per unit time: 32% * $0.04 = $0.0128.

We can continue to extrapolate: If we place orders with a price difference of 0.06 (located 0.03 away from the midpoint), it corresponds to 0.75 standard deviations (0.03/0.04=0.75), and the probability of price fluctuations exceeding 0.75 standard deviations is 45%, estimating the profit per unit time to be 45% * 0.03 = $0.0135. If we place orders with a price difference of 0.04 (located 0.02 away from the midpoint), it corresponds to 0.5 standard deviations (0.02/0.04=0.5), and the probability of price fluctuations exceeding 0.5 standard deviations is 61%, estimating the profit per unit time to be 61% * 0.02 = $0.0122.

We found that placing an order with a price difference of 0.06, which is at the position of 0.75 standard deviations, can yield the maximum profit, which is $0.0135! In this example, we compared the situations of 1/0.75/0.5 standard deviations, and it turns out that 0.75 standard deviations can achieve the highest profit. To further validate this intuition, I used Excel to derive the expected returns under different standard deviations and found that the expected return is a convex function, which just reaches its maximum value near 0.75 standard deviations!

The above assumption is that price fluctuations follow a normal distribution with a mean of 0, meaning that the market's average return rate is 0, while in reality, the mean of the prices will change. A shift in the mean makes it more difficult for orders on one side to be executed. When we have inventory, not only do we incur losses, but the expected profit margin also decreases.

In summary, the expectations of a market maker consist of two parts: first, the probability that the order will be executed; for example, if an order is placed at 1 standard deviation, it will be executed 32% of the time; second, the probability that the order will not be executed; for example, if an order is placed at 1 standard deviation, the price will move within the spread 68% of the time, resulting in the order not being executed.

In the case where the limit order cannot be executed, the average price is likely to change, so market makers need to manage the “inventory cost.” This “inventory cost” can be seen as a loan that incurs interest, and the passage of time will lead to an increase in volatility, which in turn raises the borrowing interest. Market makers can formulate a mean reversion strategy based on the average volatility over various periods to limit holding costs.

Finally, brothers, why do many retail investors say that as soon as they buy, the price drops, and as soon as they sell, it rises? This is not baseless; this article provides the answer!