Module 5 Quiz: Context
This module asked when a reading means anything, and answered with measurements rather than impressions: a regime is a ratio, a timeframe is a grouping rule with two settings, a filter is an exchange with a price, an auction is one equation solved once, and an announcement is quoted out loud by the option chain. Six questions, all arithmetic. The last regroups the twenty bars this course has carried since lesson 32 and watches a summary move eight-fold while the highest price in the sample never moves at all.
Covers: Lessons 36 to 47, and the twenty bars the last two modules have been built on.
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. One ratio, three windows
Eleven closes: 100.0, 100.8, 100.3, 101.4, 100.9, 102.2, 101.6, 102.8, 102.1, 103.4 and 102.9. Lesson 36’s ratio is the distance travelled that ended up as net progress: the absolute change from first close to last, divided by the sum of the absolute changes between consecutive closes.
Ask. What is the ratio over all eleven, over the first six, and over the last six?
2. What a filter has to clear, twice
A method takes 100 trades, wins 40 of them, and its winners pay 2.5 times its losers. You are considering a filter that would have removed 40 per cent of the losing trades. It also removes some winners, because every filter does.
Ask. What does the method make now? What happens to the expectancy per trade and to the total if the filter takes 20 per cent of the winners, and what if it takes 30? At what share of winners does the money stop improving?
3. Clearing an opening auction by hand
An opening auction. At each price, how much wants to buy at that price or better, and how much wants to sell at that price or better.
| Price | Demand at or above | Supply at or below |
|---|---|---|
| 50.00 | 5,000 | 400 |
| 50.10 | 4,400 | 900 |
| 50.20 | 3,800 | 1,600 |
| 50.30 | 3,200 | 2,400 |
| 50.40 | 2,800 | 3,000 |
| 50.50 | 2,200 | 3,800 |
Two thousand of the demand is one market-on-open buy.
Ask. Where does it clear, how much matches, what does the market buyer pay, and what would the same 2,000 shares have cost walking a continuous ladder made of the identical offers?
4. Three numbers inside one straddle
A stock at 80.00 reports after the close. The call is 2.90 and the put is 2.70, so the straddle costs 5.60.
Ask. What move is being quoted, where does the long call break even, and what do the call, the put and the straddle make on a five per cent move each way?
5. Scaling a volatility, a hedge and a book
An instrument whose daily returns have a standard deviation of 1.20 per cent. A hedge whose correlation with your position is 0.60. And a book of twelve positions of the same size.
Ask. What is the annualised volatility, how much of the standard deviation does the hedge leave standing, and how many independent positions is the book at an average pairwise correlation of 0.40 and of 0.15?
6. The same twenty bars, grouped three ways
The series this course has carried since lesson 32, with its closes. The closes are 100.7, 101.5, 100.4, 102.8, 101.5, 104.1, 102.6, 102.1, 105.3, 103.7, 106.7, 104.6, 103.0, 105.7, 102.2, 104.9, 100.8, 103.2, 99.4 and 101.6. The highs reach 106.8 at bar 11 and the lows reach 99.2 at bar 19.
Ask. What is lesson 36’s ratio on the twenty closes? Now group the bars four at a time from bar 1 and compute it again, along with the sample high and low. Then keep the width and start at bar 2 instead.
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. One ratio, three windows
The path is the same in every case: add up every step without regard to sign. The net is one subtraction.
| Window | Net progress | Distance travelled | Ratio |
|---|---|---|---|
| All eleven closes | 2.9 | 8.5 | 0.34 |
| First six | 2.2 | 4.2 | 0.52 |
| Last six | 0.7 | 4.3 | 0.16 |
The two halves travelled almost exactly the same distance, 4.2 against 4.3, and kept three times as much of it in the first as in the second. That is the whole content of the measurement: not how far price went, but how much of the going it held on to.
And notice that the eleven-close reading sits between the two, which is what an average of two regimes looks like and is not a regime anything was ever in. Lesson 36 changed a window from ten closes to thirty and got two readings that disagreed about the state of the market on twenty-two bars out of thirty. This is the same effect on eleven closes.
Answer. 0.34 over all eleven, 0.52 over the first six and 0.16 over the last six.
2. What a filter has to clear, twice
Unfiltered the method wins 40 × 2.5 = 100R and loses 60R, so it makes 40R over 100 trades, or 0.40R a trade.
| Filter removes | Trades kept | Total | Per trade |
|---|---|---|---|
| Nothing | 100.0 | 40.0R | 0.40R |
| 40% of losers, 20% of winners | 68.0 | 44.0R | 0.65R |
| 40% of losers, 30% of winners | 64.0 | 34.0R | 0.53R |
Both filters raise the expectancy per trade, and they raise it for the same trivial reason: they remove a higher share of losers than of winners. That test is easy to pass and it is the one every filter is sold on.
The second test is the one that decides whether you have more money. The gross win is 100R and the gross loss is 60R, so the profit factor is 100 ÷ 60 = 1.67, and the money only improves while the share of winners removed divided by the share of losers removed stays under 1 ÷ 1.67 = 0.60. The first filter is at 20 ÷ 40 = 0.50 and passes. The second is at 30 ÷ 40 = 0.75 and fails, and it fails while its expectancy per trade still looks better than it started.
The exact break-even is 24 per cent of the winners: 30.4 winners and 36 losers is 30.4 × 2.5 − 36 = 40R, the same money on 66 trades instead of 100. Between 24 and 30 per cent the filter is charging you trades for a better-looking average and no more money at all.
Answer. 40R now at 0.40R a trade. At 20 per cent the filter makes 44R at 0.65R; at 30 per cent it makes 34R at 0.53R. The money stops improving at 24 per cent.
3. Clearing an opening auction by hand
At each price the auction can match the smaller of the two sides, and it picks the price where that is largest.
| Price | Shares that can trade | Leftover |
|---|---|---|
| 50.00 | 400 | +4,600 |
| 50.10 | 900 | +3,500 |
| 50.20 | 1,600 | +2,200 |
| 50.30 | 2,400 | +800 |
| 50.40 | 2,800 | −200 |
| 50.50 | 2,200 | −1,600 |
2,800 is the most that can trade, so the auction clears at 50.40 with 200 shares left unfilled on the sell side. Every filled order gets that one price, so the market buyer pays 2,000 × 50.40 = $100,800.
Now walk the identical offers as a continuous ladder. 400 rest at 50.00, another 500 at 50.10, another 700 at 50.20 and another 800 at 50.30. The order takes 400, 500, 700 and 400, which is $100,310, an average of 50.155.
The auction charged 24.5 cents a share more, $490 in total, on the same orders in the same book. It did not save the buyer the walk. It charged him the top of the walk on every share, because the rule solves for the marginal order rather than for where trading has been. His 2,000 shares were 71 per cent of everything that matched, so the marginal order was very nearly his own.
Answer. 50.40, with 2,800 matched. The buyer pays $100,800. The same shares walking the ladder cost $100,310, an average of 50.155.
4. Three numbers inside one straddle
The straddle costs 5.60 on an 80.00 stock, so the quoted move is 5.60 ÷ 80 = 7.0 per cent. That is the number everyone repeats, and it is the break-even of the straddle rather than of anything inside it.
The call alone breaks even at 2.90 ÷ 80 = 3.6 per cent and the put alone at 2.70 ÷ 80 = 3.4 per cent. So the usual warning — that you have to beat the implied move — overstates a single option’s hurdle by nearly a factor of two.
| Realised move | Long call | Long put | Long straddle |
|---|---|---|---|
| +5% | +1.10 | −2.70 | −1.60 |
| −5% | −2.90 | +1.30 | −1.60 |
A five per cent move is well past either single option’s break-even and still loses the straddle 1.60, because the straddle paid for both sides and only one of them happened.
And read the last figure against a stop. A stop one per cent away, into a print the market has publicly priced at seven per cent, is a stop inside a move quoted at seven times its own distance. That is the arithmetic behind trading the reaction rather than the announcement.
Answer. A 7.0 per cent move. The call breaks even at 3.6 per cent, about half. Five per cent either way pays one leg 1.10 or 1.30 and loses the straddle 1.60.
5. Scaling a volatility, a hedge and a book
There are 252 trading days in a year and volatility scales with the square root of time, so 1.20 × √252 = 1.20 × 15.87 = 19.0 per cent. That 15.87 is also the entire origin of the habit of dividing a volatility index by sixteen to get a daily figure.
The hedge is the one most people get backwards. A hedge removes the square of the correlation from the variance, not the correlation from the standard deviation. At 0.60 it removes 0.36 of the variance and leaves √0.64 = 0.80, so 80 per cent of the standard deviation is still there after a hedge most people would describe as taking out well over half the risk.
| Average pairwise correlation | Positions | Independent positions |
|---|---|---|
| 0.40 | 12 | 2.22 |
| 0.15 | 12 | 4.53 |
The book comes from n ÷ (1 + (n − 1)ρ). Twelve positions at 0.40 carry the risk of 2.22 of them, and dropping the average correlation to 0.15 doubles that to 4.53. Not one position size changed in between.
One thing survives all of this untouched, and lesson 44 is right to end on it: share count is inversely proportional to volatility, exactly. Double the volatility, halve the size, and no square root or correlation enters it.
Answer. 19.0 per cent a year. The hedge leaves 80 per cent standing. The book is 2.22 independent positions at 0.40 and 4.53 at 0.15.
6. The same twenty bars, grouped three ways
On the twenty closes the net progress is 101.6 − 100.7 = 0.9 and the distance travelled is 43.1, so the ratio is 0.021. On this measurement the series barely went anywhere.
Group the bars four at a time from bar 1 and the closes become 102.8, 102.1, 104.6, 104.9 and 101.6 — the last close of each group. Net progress 1.2, distance travelled 6.8, ratio 0.176.
| How the tape is grouped | Ratio | Sample high | Sample low |
|---|---|---|---|
| Bar by bar | 0.021 | 106.8 | 99.2 |
| Four at a time, from bar 1 | 0.176 | 106.8 | 99.2 |
| Four at a time, from bar 2 | 0.084 | 106.8 | 100.2 |
Nothing about the tape changed. The same trades printed in the same order, and the highest and lowest prices in the sample are identical, because a group’s high is the highest of the four highs inside it. What moved by a factor of eight is the summary, and it moved because the intermediate wiggles stopped being counted as distance travelled.
Then the setting nobody quotes. Keep the width at four and start one bar later, and the ratio halves to 0.084 on identical tape. It also drops bar 1 and bars 18 to 20 out of any complete group, which is why the sample low reads 100.2 instead of 99.2: where the first group starts decides which bars are in the sample at all.
Every chart you have ever read was one of these three, and the platform told you the width and never told you the offset.
Answer. 0.021 on the twenty closes, 0.176 grouped from bar 1, and 0.084 grouped from bar 2. The sample high never moves.
What this quiz was testing
Whether you can put a number on the context before you read anything into it. Handed eleven closes, you produce a regime; handed a filter, you produce both of its break-even points and notice they are not the same one; handed a book of limit orders, you produce a clearing price and the money the auction charged over the ladder; handed a straddle, you produce the move the market has quoted out loud; handed a correlation, you produce how much of the risk is genuinely still there.
Module 6 turns to the instruments people put on the chart instead, and lesson 48 opens with the fact that governs all of them: every indicator is a function of prices you already have, so none of them adds information. The only questions worth asking are what it discards, how long it takes to discard it, and whether it quietly rewrites its own history.
Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.