Advanced · Lessons 45–84

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Statistical assumptions, derivatives, execution diagnostics, physical-market risk and evidence audits.

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Advanced concept review

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Quantitative evidence & stress

1. What does multiplying daily volatility by sqrt(252) establish?
2. Does zero Pearson correlation rule out every relationship?
3. An event window reaches 2030 and 1990. Can its extrema alone identify a tradable round trip?
4. You inspect a final holdout and then change the rule based on it. What has changed?
5. The worst two of ten equally weighted scenario losses are USD 200 and USD 400. What is the worst-20% tail mean?

Options & conditional gold exposure

6. What is simplified expiry breakeven for the same call?
7. With gamma 0.01, what is the local second-order estimate for that rise?
8. Can a purchased call lose value while its underlying rises?
9. Must the ten-dollar calendar spread also be subtracted as an immediate USD 1000 loss?
10. Gold rises to 2200, unit cost to 1650 and output falls to 90000. What is the simplified spread?

Indicator definitions & decision timing

11. What does moving a VWAP anchor change?
12. Does a two-deviation rolling price band automatically guarantee about 95% future coverage?
13. MACD is +4 and signal is +4.2. What does a −0.2 histogram mean?
14. A new candle reaches 2017 but closes at 2014. Did it close above the prior 2015 boundary?
15. The low anchor changes to 2000 while the high remains 2080. What is the new 61.8% level?

Position state & execution diagnostics

16. Buy 10 at 2000, sell 4 at 2010, mark at 2005. What is combined gross price P&L under the stated single-price assumptions?
17. Two ounces of the six-ounce long exit at target. What is the remaining open position before another entry fill?
18. Does observing an MFE of 1.8R prove a trader could identify that exit live?
19. Add fees of USD 4 and opportunity cost USD 10. What is total shortfall on USD 20000 intended notional?
20. Finalized programs earn +1.8R before −0.9R total costs. What is net average across 18 programs?

Contract mechanics & relative prices

21. A new long trades with a new short. How many outstanding contracts are added per one-contract trade?
22. With a hypothetical 100-ounce multiplier, what is depth cost relative to the original best ask?
23. If equal-multiplier legs both rise by exactly 30, what is their combined gross price change?
24. Physical-minus-futures basis changes from −10 to −15 on 100 hedged ounces. What is the basis contribution?
25. At an agreed 2000 dollars per ounce conversion input, what is the cash equivalent of that interest?

Physical evidence & hedge practice

26. At USD 80 per fine gram, what is the reference-value difference?
27. A fixed USD 20000 valuation has a 0.6% annual storage charge plus USD 40 administration. What is stated annual total?
28. Physical and futures both fall USD 40 with no basis change. What is residual price P&L?
29. An idealized USD 20000 forward sells dollars at 0.90 against maturity spot 0.85. What is its local settlement-equivalent gain?
30. Add USD 100 trading and USD 150 custody costs not already included. What is net scenario result?

Performance metrics & uncertainty

31. After USD 10 costs per trade, what is net profit factor?
32. With sample deviation 1.4142 pp, what is the unannualized Sharpe ratio?
33. With a 0.5% target, what is the stated period Sortino ratio?
34. What is the approximate nominal 95% Wilson interval in the example?
35. What is maximum drawdown for that fixed-R path starting at zero?

Research design & evidence audits

36. How does bootstrap sampling differ from a permutation?
37. What is the sum of test-only fixed-R contributions +2, −1 and +1.5?
38. What mean appears if the failed product is silently removed?
39. Thirty A trades and ten B trades at the same subgroup means give what overall mean?
40. What is economic P&L after separating the deposit?

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