Market making group exercise

Glad you asked this (even though I am late to answer). I was once in a similar position and felt very awkward at those career events and had no idea what was going on. It was embarrassing but I don't blame myself given, as others have mentioned, a lack of resources available on how to play this game. I will try to be a resource for people on this thread. Looking back, it becomes intuitive and you become better at the game by practicing casually with your friends. Let me explain.

Making a market essentially means facilitating a trade, i.e. quoting two prices - standing ready to buy at a certain price and being ready to sell at a certain price. You see, banks aren't in the business of doing what hedge funds do: speculating and calling the bottoms and tops and taking outright, one-directional views. Rather, they'll act as a buyer to any seller and a seller to any buyer. And in doing so, they charge a commission (or spread). 

To understand the game, you need to understand commonly used terms:

1) Market maker: described above. Sell side firm like banks act as market makers in many different asset classes in both exchange traded and OTC products. Citadel, IMC, and other prop trading firms are examples of market makers in equity options, ETFs, and so on. 

2) Market taker: the investor (person or institution) who takes the speculative position as we mentioned earlier. They are the ones who buy or sell directly from the bank hoping to make a profit from a speculative position.

3) Bid/Ask/Spread: putting these together to reduce confusion in these terms. When you buy a stock from your broker you'll see two prices next to one another, the bid and the ask. Say the stock price is listed as 102.48. You don't actually pay 102.48 to long (buy) or short (sell) that stock. You'll see two prices instead, such as 102.46 - 102.53. The number on the left (102.46) represents the bid price while 102.53 represents the ask price. A market taker always buys at the ask price (higher price) and sells at the bid price (lower price). This means if I think stock will go up I have to buy from the market maker at 102.53, not 102.48, even if stock is technically at 102.48. This is because the market maker will charge a spread on top of the listed price to compensate them for selling you the product. You'll notice now however, on the flip side of that same trade, market makers are the ones who buy at the bid (lower price) and sell at the ask price (higher price). These favorable trading terms are because the market maker must be paid in some way to provide liquidity. The difference between the bid and the ask price, i.e. ask price - bid price, is known as the bid-ask-spread ("BAS"). Stocks that aren't as liquid (e.g. pharmaceuticals) will have a higher BAS relative to the ones you most likely know (big tech). Typically, higher dollar stock names also have higher BAS and this is one reason companies issue stock splits. The order book will have many bids and ask prices but the "best bid" is the highest bid and the "best ask" is the lowest asking price. 

4) Calculating P&L: if you buy at $25 and the actual price turns out to be $32 your P&L is 7 (if actual price is $19 you are at -$6). If you are short at $1062 and the price falls to $1000 your P&L is $62 (if price moves higher to $1075 your P&L is -$13). 

Given you understand these terms, we can now play the game. Typically the firm you are interviewing with will put one of their employees to announce a market - it doesn't have to be a stock. For instance, they might ask, "make a market on how many benches are there in Central Park?". There is a theoretical answer but most people in the audience won't know so they have to make their best judgement. Each person in the audience can act as both a market maker and a market taker while the employee will keep track of all the ongoing trades and P&L of each person in the audience. The first person in the crowd to speak will make the market. If you are this person, you'll wan't to quote a wide BAS to limit your losses. You'll also only wan't to quote a market if you have some information or have done some logical reasoning in your head (no calculators) to figure out a reasonable answer. 

For simplicity, say we have the firm's employee Jack (acts as a moderator), and three people in the audience: Sam, Jenny, and Charles. Sam (in his head) thinks his theoretical price ("theo") is 8800. We use the term "price" here but we are actually talking about park benches. He's sure its over 7000 but also thinks it could be a lot higher and that he is underestimating. So Sam says: "bid 6000 ask 14000". Note his market is 8k wide which is conservative enough to limit losses - he quoted 1k below his lower bound of 7k just to be sure. Also note it is not an unreasonably conservative market like 100-100k - no one would trade and it defeats the purpose of making some educated guess with an additional pricing in of an edge. Once a market maker has announced their bid and ask, a market taker can do one of two things: 1) trade and hit the bid (i.e. sell to the market maker, i.e. go short) or lift the ask (i.e. buy from them, i.e. go long); 2) improve the market by either (a) raising the bid (b) lowering the ask. The reason is simple. If Jenny is definitely confident about it being above 8k and lower than 12k, then there's no incentive for her to trade as buying at 14k after announcing actual price is lower he would have negative P&L and vice versa for shorting too low. Jenny steps in and says: "bid 8200 sell 13000". Jack keeps track of the new, updated market. Charles thinks both Sam and Jenny are way underestimating the amount of park benches, and thinks its closer to the vicinity of 15k. He lifts Jenny's ask of 12k. If he is right, then he will have realized a P&L of 15k-12k=3k. The first trade is recorded by Jack. Charles is now long at 12k and Jenny is short at 12k. No one else budges. Tempted to cover her short, Jenny decides to raise the current and best bid of 8200 slightly to 8900. Sam thinks Jenny has raised her bid too high because his theo was 8600. He hits Jenny's bid of 8900 hoping to make $300. Sam is now short at 8900 while Jenny is long at 8900. No one else decides to trade and the game is now over. The moderator announces the true answer: 10k park benches in Central Park. The winner is the person with the highest P&L (in this case I am equating park benches to dollar terms but you can size it however you want or use different units). Tallying up:

Sam - short at 8900. Theo is 10,000 --> P&L = -$1100. 

Charles - long at 12,000. Theo is 10,000 --> P&L = -$2,000.

Jenny - long at 8900 short at 12,000 --> P&L = 12,000 - 8,900 = $3,100. Note here Jenny doesn't have to benchmark her P&L to theo because she didn't take any one sided risk. She bought at 8900 and sold at 12000 effectively locking in a risk-free $3,100. Jenny is the winner and this example demonstrates how market makers make money.

Typically the moderator will give the audience more information if they are way off in quoting their market or no one is trading to incentivize people to trade as they'll have a better idea of where to guess theo is at. 

There is also a variation of the game, Trade or Tighten, which essentially is the same concept but instead of quoting actual levels of the market bid and ask prices, you just quote a BAS you are willing to take. Someone can improve the market by lowering the BAS you quoted. Note the lower BAS you quote the more confidence you have. When it's low enough and no one else is willing to quote lower, the other person will say "Trade!" and the person who quoted is the market maker and quotes a bid and an ask which differ by an amount the BAS was quoted. The market taker can now choose to take whichever side they want. If the theo falls within the BAS the market maker wins, else the market taker wins.

These market making games are really fun: I spend time with my industry friends making markets at dinner checks (losers have to split the check while the winner eats free). Also for random debates when we rather debate something quantitatively. Also a good way to kill time. Hope you found this helpful and elucidates how these games work. Hopefully everyone here now crushes the interview when this game is played. Let me know if you have any questions. 

Happy market making!