Module 1 Quiz: The Mechanism

This module built one machine and then took it apart: a price, a book, a fill, a spread, the person who sets it, what your screen does with all of it, and who else is in the room. Six questions, and none of them can be answered by knowing what a word means. The last one takes the two notices you posted in lesson 1 and prices them.

Covers: Lessons 1 to 9, and the two notices at $46 and $48 that the module has been building on since its first page.

Every question below hands you numbers and asks for a number back. Work all 6 with a calculator before you scroll to the answers; each answer shows the arithmetic, so a wrong result tells you which step to go back to rather than only that you were wrong.

The questions

1. A spread you can afford, and one you cannot

An instrument is quoted 1.48 bid and 1.55 ask. You have decided on a stop $0.35 away from your entry.

Ask. What win rate do you need just to break even, before commission?

2. What a 1,200-share market buy actually pays

The ask side of lesson 2’s book, from the top down:

Price	Shares resting
50.05	800
50.04	400
50.03	300

You send a market order to buy 1,200 shares. It fills against the cheapest offers first.

Ask. What is your average fill price, and how far is it above the 50.03 you were quoted?

3. Signing a tape by hand

Five prints from one minute, with the quote standing at each. Apply lesson 7’s rule: at the ask or above is a buy, at the bid or below is a sell, and between the quotes the rule falls back to comparing the print with the last different price.

Time	Print	Size	Quote at the time
10:31:02	50.04	500	50.03 / 50.04
10:31:04	50.03	900	50.03 / 50.04
10:31:05	50.035	700	50.03 / 50.04
10:31:07	50.02	400	50.02 / 50.03
10:31:09	50.03	1,100	50.02 / 50.03

Ask. What is the signed total for the minute, and what does it become if the one print the rule had to guess at was guessed wrong?

4. How wide the delta really is

A bar trades 25,000 contracts and your platform reports a delta of +2,500. Of that volume, 4,000 executed between the quotes, where the sign was decided by the tick test rather than by the quote. The rule called 2,500 of those buys and 1,500 of them sells.

Ask. What buy share does the platform show, and what interval is actually established?

5. Where a day of spread ends up

Eight million shares cross a penny-wide spread in one day, so every one of them pays half a cent against the midpoint. A tenth of that crossing volume is informed, and on those trades price moves three cents the informed trader’s way before the quoter can get out.

Ask. Fill in the three rows of lesson 9’s ledger. What is each party’s net, and do the three sum to zero?

6. The two notices, priced

Back to the first page of lesson 1. You are selling 100 shares at $48. Somebody else is buying 100 at $46. Both notices stand and nothing trades. Suppose you now decide to be the impatient one, and that your stop is $2.50 from your entry.

Ask. What is the spread as a share of your stop, what win rate does that need, and what does the round trip cost on 100 shares?

The answers

Each one is worked in full. Where a figure comes from a lesson rather than from this page, the lesson is named.

1. A spread you can afford, and one you cannot

The round trip costs the full spread: 1.55 − 1.48 = $0.07 a share. Measured against the stop, that is s = 0.07 ÷ 0.35 = 0.20, or 20 per cent.

Lesson 4’s formula is (1 + s) ÷ 2, so the breakeven win rate is (1 + 0.20) ÷ 2 = 0.60, or 60.0 per cent.

Notice what the figure does not depend on. Not the price of the instrument, not the size of your position, and not whether you are any good. Two quoted numbers and one stop distance decide it before you enter.

Answer. 60.0 per cent.

2. What a 1,200-share market buy actually pays

The order takes 300 at 50.03, then 400 at 50.04, then 500 of the 800 at 50.05.

Price	Shares	Cost
50.03	300	$15,009.00
50.04	400	$20,016.00
50.05	500	$25,025.00
Total	1,200	$60,050.00

60,050 ÷ 1,200 = 50.0417 a share, which is 1.17 cents above the quote. The quoted spread was one cent; this order paid more than the whole spread again on top of it, and the quote never mentioned that.

The same order for 300 shares pays 50.03 exactly. The difference between the two traders is size, and it was decided before either was right or wrong about anything.

Answer. 50.0417 a share, 1.17 cents above the quoted 50.03.

3. Signing a tape by hand

Four of the five are decided by the quote. The 700 at 50.035 sits between the quotes, so the rule compares it with the last different price, 50.03, finds it higher, and calls it a buy.

Print	Size	Signed
50.04 at the ask	500	+500
50.03 at the bid	900	−900
50.035 between, tick test	700	+700
50.02 at the bid	400	−400
50.03 at the ask	1,100	+1,100
Total	3,600	+1,000

So +1,000 on 3,600 shares. Now flip the one guess. Reclassifying a print moves the total by twice its size, because it comes off one side and goes on the other: 1,000 − 1,400 = −400.

One print, 19 per cent of the minute’s volume, on the single row the rule is least sure about, and the summary changes sign.

Answer. +1,000 as the rule signs it, and −400 if the one uncertain print was guessed wrong.

4. How wide the delta really is

The reported figure first. Lesson 8’s table gives the buy share as (1 + D ÷ V) ÷ 2, so (1 + 2,500 ÷ 25,000) ÷ 2 = (1 + 0.10) ÷ 2 = 55.0 per cent.

Now the interval. Reclassifying a print moves delta by twice its size. If all 2,500 of the tick-test buys were really sells, delta is 2,500 − 5,000 = −2,500. If all 1,500 of the tick-test sells were really buys, delta is 2,500 + 3,000 = +5,500.

Case	Delta	Buy share
Every uncertain print a sell	−2,500	45.0%
As the platform signed them	+2,500	55.0%
Every uncertain print a buy	+5,500	61.0%

So the established range is 45.0 to 61.0 per cent, and it contains 50. The screen says the bar was bought; the arithmetic cannot rule out that it was sold. The bar is not lying, it is just narrower on the screen than it is in reality.

Answer. The platform shows a buy share of 55.0 per cent. What is established is 45.0 to 61.0 per cent, an interval that contains 50.

5. Where a day of spread ends up

Four numbers and nothing else: 8,000,000 shares, half a cent each, 800,000 of them informed, three cents of move on those.

Who	Paid	Received	Net
Uninformed (7,200,000 shares)	$36,000 in spread	—	−$36,000
Informed (800,000 shares)	$4,000 in spread	$24,000 from the move	+$20,000
Market makers	$24,000 to the informed	$40,000 in spread	+$16,000

They sum to zero, which they have to. The reading that matters is vertical: the $36,000 the uninformed paid is exactly the $16,000 the quoters kept plus the $20,000 the informed took. Not approximately, because there is nowhere else it could have come from.

The quoters collected forty thousand and handed twenty-four back. The transfer that actually happened ran from the seven point two million uninformed shares to the eight hundred thousand informed ones.

Answer. −$36,000, +$20,000 and +$16,000. They sum to zero.

6. The two notices, priced

The spread is 48 − 46 = $2.00, on a midpoint of $47. Against a $2.50 stop that is s = 2.00 ÷ 2.50 = 0.80, or 80 per cent.

Lesson 4’s formula gives (1 + 0.80) ÷ 2 = 90.0 per cent. Nothing wins nine times in ten. And the round trip on 100 shares is 100 × $2.00 = $200, paid before the position can make a penny.

That is the whole module in one line. Two notices with a two-dollar gap between them are not a market you can trade; they are a market with nobody in the middle. Everything the module added afterwards — the book, the depth, the quoter, the four reasons anybody is there — is the machinery that closes that gap to a penny and takes a cut for doing it. In lesson 1 the gap was $2 and you needed to be right nine times in ten. In lesson 9’s instrument it is one cent, and on the same $2.50 stop you need 50.2 per cent.

Answer. 80 per cent of the stop, a 90.0 per cent breakeven win rate, and $200 on 100 shares.

What this quiz was testing

Not whether you can define a spread. Whether, handed a quote and a stop, you produce a breakeven win rate; handed a book and an order size, you produce a fill price; handed a tape, you produce a signed total and know how far to trust it. Those are the three things this module was for, and a reader who can do them has it.

Module 2 asks what the whole thing costs, and starts from a fact this module has made unavoidable: every position you will ever open starts at a loss. On one ordinary trade the four charges come to $9.29, which moves the win rate you need just to break even from 50.8 to 53.9 per cent.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.