Module 2 Quiz: The Cost of Trading

This module priced a seat. Four charges, the one of them that grows with your size, the ratio that ranks an instrument before you trade it, the four legal objects, the collateral that is not a loss, and the five rules under which somebody else acts in your account. Six questions, every one of them arithmetic. The last takes the trade lesson 10 priced at minus $9.29 and holds it for a month instead of three nights.

Covers: Lessons 10 to 16, and the 200 shares of a $50 stock stopped $0.60 away that lesson 10 costed and this quiz costs again.

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. Four charges, one bill

Buy 400 shares of a $25 stock, a $10,000 position, with a stop $0.40 away. The stock is quoted two cents wide. Your broker charges half a cent a share each way, with a $1.00 minimum. The entry filled a cent past the quote and the exit filled at the quote. You bought on 2:1 margin, so $5,000 of it is borrowed at 9 per cent a year, and you held it five nights.

Ask. What is the whole bill, what is s, and what win rate does the trade need just to break even?

2. What the walk costs in a thin name

A $20 small cap is quoted 19.95 bid, 20.00 ask. The offer side of its book:

Price	Shares resting
20.00	400
20.05	400
20.10	500

You send a market order to buy 1,200 shares, and you would stop out 1 per cent of price away.

Ask. What is the average fill, what does the entry cost against the midpoint, how much of that is the walk rather than the spread, and what share of the risk has the entry alone spent?

3. Which of the two is cheaper to be in

Two candidates, measured over sixty sessions.

Instrument	Price	Spread	Average daily range
X	$80.00	2 cents	1.6 per cent of close
Y	$3.00	6 cents	7.0 per cent of close

Ask. What is each friction ratio, and what is the factor between them?

4. One contract, and the move that ends it

The S&P 500 is at 5,200 and the Micro E-mini is worth $5 an index point. You hold one contract with $3,250 of equity behind it, and you are trading it with a 12-point stop.

Ask. What leverage are you carrying, what move takes the whole deposit, how many index points is that, and how many times the risk is the money standing behind the trade?

5. The price at which somebody else sells

You buy $30,000 of a stock, putting up $15,000 of your own money and borrowing the other $15,000, which is the most the initial rule allows. It is a volatile name, so your broker holds you to a 40 per cent house maintenance requirement rather than the 25 per cent floor.

Ask. At what position value does the call arrive, what fall from $30,000 is that, and how many average days is it for the small cap of lesson 12’s table?

6. The same trade, held for a month

Back to the trade lesson 10 priced: 200 shares of a $50 stock, a stop $0.60 away, so $120 at risk. Spread $2.00, commission $2.00, slippage $2.00, and $5,000 borrowed at 8 per cent a year. Lesson 10 held it three nights and the bill came to $9.29. Hold it thirty instead. A simulator then reports 80 of these trades at a 57.5 per cent win rate, wins and losses both one unit of risk, and puts you up $1,440.

Ask. On which night does financing alone pass the other three put together, what is the thirty-night bill, what breakeven win rate does it demand, and what do the simulator’s 80 trades actually net?

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. Four charges, one bill

The money at risk is the denominator for everything below: 400 × $0.40 = $160.

Charge	Arithmetic	Cost
Spread	$0.02 × 400, once for the round trip	$8.00
Commission	$0.005 × 400 each way, above the $1.00 floor	$4.00
Slippage	$0.01 × 400, on the entry only	$4.00
Financing	$5,000 × 9% × 5 ÷ 365	$6.16
Total		$22.16

Then s = $22.16 ÷ $160 = 0.1385, and lesson 10 showed that the breakeven formula never cared that s was a spread: (1 + 0.1385) ÷ 2 = 56.9 per cent.

The spread is $8.00 of $22.16, so the only charge on the chart is about a third of the bill. And the floor did nothing here, because 400 shares at half a cent is $2.00 a side. Run the same schedule at 100 shares and the $1.00 minimum binds on both sides, so the round trip costs two cents a share instead of one. The smaller account pays double.

Answer. $22.16, s = 13.9 per cent, and a 56.9 per cent breakeven win rate.

2. What the walk costs in a thin name

The order takes 400 at 20.00, 400 at 20.05, and 400 of the 500 at 20.10.

Price	Shares	Cost
20.00	400	$8,000.00
20.05	400	$8,020.00
20.10	400	$8,040.00
Total	1,200	$24,060.00

So the average fill is $24,060 ÷ 1,200 = $20.05. The midpoint was 19.975, so the entry cost 1,200 × $0.075 = $90.00.

Split it the way lesson 11 splits it. Half a spread on 1,200 shares is 1,200 × $0.025 = $30.00, and you would have paid that at any size. The remaining $60.00 is the walk, and it exists only because 1,200 was three times the 400 resting in front of you.

A 1 per cent stop is $0.20 a share, so the risk is 1,200 × $0.20 = $240. The entry alone has spent $90 ÷ $240 = 37.5 per cent of it, before commission, before financing and before the exit.

Answer. $20.05 average, $90.00 against the midpoint, of which $60.00 is the walk, and the entry has spent 37.5 per cent of the risk.

3. Which of the two is cheaper to be in

Both quantities go into basis points so that two instruments at different prices become comparable. One full spread is the round trip: half going in and half coming out.

Instrument	Round trip (bps)	Daily range (bps)	Friction ratio
X	$0.02 ÷ $80 × 10,000 = 2.5	160	1.56%
Y	$0.06 ÷ $3 × 10,000 = 200	700	28.6%

So X hands over 1.56 per cent of a typical day’s movement for the right to participate and Y hands over 28.6 per cent, a factor of 18.

Read where the factor comes from. Y moves 4.4 times as much as X, which is the part a chart shows you. It also costs 80 times as much to cross as a fraction of its own price, which no chart shows you at all. The second number is the larger one, and that is the whole of lesson 12 in one line: the ranking a chart suggests runs backwards.

Answer. 1.56 per cent for X and 28.6 per cent for Y, a factor of 18.

4. One contract, and the move that ends it

One contract controls 5,200 × $5 = $26,000, and that notional does not change with your deposit. Leverage is notional over the equity behind it: $26,000 ÷ $3,250 = 8 times.

Lesson 14’s consequence follows exactly, with no estimation in it. At leverage L an adverse move of 1 ÷ L is the whole deposit, so 1 ÷ 8 = 12.5 per cent, and 12.5 per cent of 5,200 is 650 index points.

Now the other number. A 12-point stop at $5 a point risks 12 × $5 = $60, so the money standing behind the trade is $3,250 ÷ $60 = 54.2 times what the trade actually risks.

Neither figure tells you the other, and only one of them is yours. The clearing house set the collateral without ever seeing your stop.

Answer. 8 times leverage, wiped by a 12.5 per cent move, which is 650 index points, against a trade risking $60 — so the deposit is 54.2 times the risk.

5. The price at which somebody else sells

The loan is $15,000 and it does not fall with the position. Only your equity absorbs the loss, which is why the threshold arrives sooner than the requirement suggests: the call comes at $15,000 ÷ (1 − 0.40) = $25,000, where your $10,000 of remaining equity is exactly 40 per cent of the position.

From $30,000 that is a fall of 1 − $25,000 ÷ $30,000 = 16.7 per cent. Note what is not in the arithmetic: not your entry, not your reasoning, and not your stop.

Lesson 12 gave the small cap a daily range of 500 basis points, so 16.7 per cent is 16.7 ÷ 5 = 3.3 average days. Three ordinary sessions in one direction and the decision stops being yours — their timing, and whichever position is easiest to sell rather than the one you would have picked.

Answer. $25,000, a fall of 16.7 per cent, which is 3.3 average days.

6. The same trade, held for a month

Three of the four charges are paid per trip and do not care how long you stay: $2.00 + $2.00 + $2.00 = $6.00. The fourth is paid for the staying, at $5,000 × 8% ÷ 365 = $1.0959 a night. So financing equals the other three after $6.00 ÷ $1.0959 = 5.5 nights, which means the sixth night is where the column you cannot see becomes the larger one.

Thirty nights of it is 30 × $1.0959 = $32.88, so the bill is $6.00 + $32.88 = $38.88.

Held	Financing	Whole bill	s	Breakeven win rate
Three nights, as lesson 10 held it	$3.29	$9.29	7.7%	53.9%
Thirty nights	$32.88	$38.88	32.4%	66.2%

Nothing about the setup changed. The instrument is the same, the stop is the same, the entry technique is rounding error at this holding period, and the win rate the trade needs has gone from 53.9 to 66.2 per cent because of a decision that felt like patience.

Which is what the simulator declined to charge. Eighty round trips at $38.88 is $3,110.40, so the $1,440 it reported is really $1,440 − $3,110.40 = −$1,670.40. And 57.5 per cent never cleared 66.2 per cent, so the strategy did not stop working somewhere between the simulator and the broker. It was losing money the whole time.

Answer. The sixth night. $38.88 a round trip, a 66.2 per cent breakeven win rate, and the 80 trades net −$1,670.40.

What this quiz was testing

Whether you can put a number on the seat before you sit in it. Handed a schedule and a holding period, you produce a bill; handed a book and an order, you produce the walk; handed a price and a range, you produce the share of the day’s movement the instrument takes for itself; handed a loan and a requirement, you produce the price at which the decision stops being yours. Every one of those was available before the trade, and every one of them was arithmetic.

Notice what the module never did. It never told you what to buy. Cost sets the bar and clearing it is a different subject, which is where module 3 starts: a setup winning seven times in ten can lose 0.125 units of risk on every trade, while one winning four times in ten makes 1.40. The win rate is not the thing.

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