Chapter 14 Quiz: Binary Outcome Trading Strategies

Instructions: Select the best answer for each question. Some questions may have multiple parts. A score of 18/25 (72%) or higher indicates solid understanding of the material.

Question 1

In a binary prediction market, the expected profit from buying a YES contract at price $p$ when you estimate the true probability at $q$ is:

  • A) $q \times p - (1 - q) \times (1 - p)$
  • B) $q - p$
  • C) $p - q$
  • D) $q \times (1 - p) + (1 - q) \times p$

Question 2

Which strategy is MOST appropriate when a binary prediction market has 48 hours until expiry, the outcome is almost certain, but the price has not fully converged to 0 or 1?

  • A) Momentum trading
  • B) Event-driven trading
  • C) Closing-the-gap strategy
  • D) News and sentiment trading

Question 3

The Kelly Criterion for buying YES on a binary contract at price $p$ with estimated true probability $q$ is:

  • A) $f^* = \frac{q - p}{q}$
  • B) $f^* = \frac{q - p}{1 - p}$
  • C) $f^* = \frac{p - q}{p}$
  • D) $f^* = q - p$

Question 4

In a fundamental analysis approach to an election prediction market, which of the following is NOT a typical input?

  • A) Weighted polling averages
  • B) Economic conditions (GDP, unemployment)
  • C) Recent price momentum in the prediction market
  • D) Historical base rates for similar candidates

Question 5

A contrarian strategy fires a signal to buy when:

  • A) The price has been rising steadily with high volume
  • B) The price has dropped sharply, likely beyond what new information warrants
  • C) A scheduled catalyst is approaching
  • D) The price is converging toward its expiry value

Question 6

When adapting Bollinger Bands for binary prediction markets, why must the band width be adjusted based on the price level?

  • A) Binary prices are always more volatile than equity prices
  • B) The variance of a binary variable depends on its probability ($p(1-p)$), so prices near 0.50 have higher variance than prices near 0 or 1
  • C) Bollinger Bands do not work for binary markets
  • D) The sample size changes as the price moves

Question 7

Which pair of strategies has the MOST negative expected correlation?

  • A) Fundamental and event-driven
  • B) Momentum and contrarian
  • C) Closing-the-gap and fundamental
  • D) News/sentiment and event-driven

Question 8

A prediction market contract for "Will Team A win the championship?" is trading at 0.85 with 2 days until the final game. Your model estimates the true probability at 0.92. Transaction costs are 2 cents per contract.

What is the net edge per contract?

  • A) 0.10
  • B) 0.07
  • C) 0.05
  • D) 0.03

Question 9

In event-driven trading, "buy the rumor, sell the news" in prediction markets means:

  • A) Buy contracts based on insider information and sell after the news becomes public
  • B) Anticipation of a positive catalyst drives the price up gradually, and the actual event, even if positive, may already be "priced in"
  • C) Always sell contracts before any scheduled event
  • D) News is unreliable in prediction markets, so you should ignore it

Question 10

A mean-reversion signal fires when a binary contract's Z-score exceeds 2.0 on low volume. Which of the following would make you REJECT the signal?

  • A) The price change occurred during off-hours with minimal news
  • B) A major, credible news story broke simultaneously with the price move
  • C) The contract still has 3 months until expiry
  • D) The Z-score is exactly 2.1

Question 11

The closing-the-gap strategy is most effective in markets that exhibit which characteristic?

  • A) High volume and many active traders
  • B) Low attention, few traders, and infrequent trading (stale markets)
  • C) Prices near 0.50 with high uncertainty
  • D) Strong momentum trends

Question 12

When combining signals from multiple strategies, what does high conflict between strategy signals indicate?

  • A) You should definitely trade because one strategy must be right
  • B) You should increase position size because the opportunity is rare
  • C) You should reduce position size or avoid trading because uncertainty is high
  • D) You should only follow the fundamental strategy

Question 13

A trader uses half-Kelly sizing. If the full Kelly fraction recommends risking 20% of the bankroll, how much should the trader actually risk?

  • A) 5%
  • B) 10%
  • C) 15%
  • D) 20%

Question 14

In the context of binary market backtesting, "walk-forward testing" means:

  • A) Testing the strategy on the most recent data only
  • B) Optimizing parameters on one period, testing on the next, then rolling forward
  • C) Walking through each trade manually to verify correctness
  • D) Testing the strategy on increasingly longer time periods

Question 15

Which of the following is a form of lookahead bias in binary market backtesting?

  • A) Using the contract's resolution outcome to select which trades to make in the backtest
  • B) Using historical price data to calculate moving averages
  • C) Accounting for transaction costs in the backtest
  • D) Using a walk-forward methodology

Question 16

A binary contract is trading at 0.65. You believe the true probability is 0.75. The Kelly fraction for buying YES is:

  • A) $\frac{0.75 - 0.65}{1 - 0.65} = 0.286$ (28.6% of bankroll)
  • B) $\frac{0.75 - 0.65}{0.75} = 0.133$ (13.3% of bankroll)
  • C) $\frac{0.65}{0.75} = 0.867$ (86.7% of bankroll)
  • D) $0.75 - 0.65 = 0.10$ (10% of bankroll)

Question 17

In a momentum strategy for binary markets, volume-weighted momentum is preferred over simple price momentum because:

  • A) It is always more accurate
  • B) It gives more weight to price moves accompanied by high volume, filtering out noise
  • C) It is easier to calculate
  • D) It eliminates the need for other indicators

Question 18

The primary risk of a closing-the-gap strategy is:

  • A) The price may not converge before expiry
  • B) Transaction costs may consume the small edge
  • C) A "nearly certain" outcome may not occur, causing a large loss relative to the small expected gain
  • D) Other traders may front-run your trades

Question 19

When a fundamental model disagrees with a momentum signal, which approach is generally recommended for longer time horizons?

  • A) Always trust momentum
  • B) Trust the fundamental model
  • C) Average the two signals equally
  • D) Exit all positions

Question 20

A trader has a portfolio of 20 binary positions, each with an estimated 5% edge. If the positions are perfectly correlated, the portfolio's risk is:

  • A) Reduced by diversification to near zero
  • B) The same as a single position scaled up 20x
  • C) Square root of 20 times a single position's risk
  • D) Impossible to calculate without more information

Question 21

In news and sentiment trading, the "speed advantage hierarchy" from most to least valuable is:

  • A) First to act, first to interpret, first to know
  • B) First to know, first to act, first to interpret
  • C) First to know, first to interpret, first to act
  • D) First to interpret, first to know, first to act

Question 22

A prediction market drops from 0.58 to 0.40 in 2 hours. The 20-period average is 0.56 with standard deviation 0.04. The Z-score is:

  • A) $(0.40 - 0.56) / 0.04 = -4.0$
  • B) $(0.56 - 0.40) / 0.04 = 4.0$
  • C) $(0.40 - 0.58) / 0.04 = -4.5$
  • D) $(0.40 - 0.56) / 0.56 = -0.286$

Question 23

For a binary market backtest to be statistically meaningful, approximately how many trades are needed at a 60% win rate to be 95% confident the edge is real?

  • A) 20-30 trades
  • B) 50-60 trades
  • C) 90-100 trades
  • D) 500+ trades

Question 24

Which of the following is the best reason to use fractional Kelly (e.g., half-Kelly) rather than full Kelly?

  • A) Full Kelly is mathematically incorrect for binary markets
  • B) Full Kelly maximizes expected growth but has high variance; fractional Kelly trades some growth for much lower variance and drawdown risk
  • C) Half Kelly always outperforms full Kelly in terms of total return
  • D) Fractional Kelly is required by prediction market platforms

Question 25

A trader combines three strategy signals with weights 0.40, 0.35, and 0.25. The signals are +0.70, -0.20, and +0.50 respectively. The weighted combined signal is:

  • A) $0.40 \times 0.70 + 0.35 \times (-0.20) + 0.25 \times 0.50 = 0.28 - 0.07 + 0.125 = 0.335$
  • B) $(0.70 - 0.20 + 0.50) / 3 = 0.333$
  • C) $0.40 + 0.35 + 0.25 = 1.00$
  • D) $0.70 \times 0.35 \times 0.50 = 0.1225$

Answer Key

  1. B - The expected profit is simply $q - p$, derived from $q(1-p) - (1-q)p = q - qp - p + qp = q - p$.

  2. C - Closing-the-gap is designed exactly for this scenario: near-certain outcome, approaching expiry, price not yet at terminal value.

  3. B - The Kelly fraction for buying YES is $(q - p)/(1 - p)$, representing the edge divided by the odds.

  4. C - Recent price momentum is a technical factor, not a fundamental input. Fundamental analysis uses external data like polls, economics, and base rates.

  5. B - Contrarian strategies buy into sharp drops (or sell into sharp rises) that appear to exceed the informational content of news.

  6. B - A Bernoulli random variable with parameter $p$ has variance $p(1-p)$, which is maximized at $p=0.50$ and approaches zero near the extremes.

  7. B - Momentum and contrarian are conceptual opposites: momentum follows the trend while contrarian fades it.

  8. C - Edge = $0.92 - 0.85 = 0.07$. Net edge = $0.07 - 0.02 = 0.05$.

  9. B - In prediction markets, gradual price appreciation in anticipation of a positive catalyst means the event itself may produce no further price movement.

  10. B - A major credible news story provides a fundamental reason for the price move, meaning it is likely information-driven rather than noise.

  11. B - Stale markets with low attention are most likely to have prices that have not converged to their true values.

  12. C - High conflict means strategies disagree, indicating uncertainty. The appropriate response is to reduce exposure or avoid trading.

  13. B - Half Kelly = $0.20 / 2 = 0.10 = 10\%$.

  14. B - Walk-forward testing involves rolling optimization and out-of-sample testing windows.

  15. A - Using the resolution outcome to select trades is the classic lookahead bias: using future information in past decisions.

  16. A - Kelly fraction = $(0.75 - 0.65) / (1 - 0.65) = 0.10 / 0.35 \approx 0.286$.

  17. B - Volume weighting emphasizes price moves that have market conviction behind them, filtering out low-volume noise.

  18. C - The asymmetric payoff is the key risk: small expected gains but large potential losses on the rare occasions the "certain" outcome does not materialize.

  19. B - For longer time horizons, fundamental analysis is generally more reliable than momentum signals.

  20. B - Perfect correlation means no diversification benefit; the portfolio behaves like a single concentrated position 20 times larger.

  21. C - First to know > first to interpret > first to act is the speed advantage hierarchy.

  22. A - Z-score = $(0.40 - 0.56) / 0.04 = -0.16 / 0.04 = -4.0$.

  23. C - Using the formula $n \geq z^2 p(1-p) / (p-0.5)^2$, we get approximately 92 trades, so roughly 90-100.

  24. B - Full Kelly has optimal expected logarithmic growth but very high volatility. Fractional Kelly sacrifices some growth for dramatically lower drawdowns and ruin probability.

  25. A - Weighted sum: $0.40(0.70) + 0.35(-0.20) + 0.25(0.50) = 0.28 - 0.07 + 0.125 = 0.335$.