Chapter 17 Quiz: Portfolio Construction and Risk Management

Instructions: Select the best answer for each question. Some questions involve calculations or multi-part reasoning. A score of 18/25 (72%) or higher indicates solid understanding of the material.

Question 1

Which of the following is NOT a reason why single-trade thinking is insufficient for prediction market traders?

  • A) Variance is enormous on single binary outcomes
  • B) Opportunities arise concurrently, requiring capital allocation decisions
  • C) Binary outcomes always follow normal distributions, simplifying portfolio analysis
  • D) Correlations between markets mean independent sizing can lead to overexposure

Question 2

For two binary events with marginal probabilities $p_X = 0.90$ and $p_Y = 0.10$, what is approximately the maximum feasible positive Pearson correlation?

  • A) 1.0
  • B) 0.75
  • C) 0.33
  • D) 0.10

Question 3

Which method is recommended for estimating correlations between prediction market events when historical data is unavailable?

  • A) Using the sample correlation from the last 30 days of price data
  • B) Structural analysis of common causal factors and conditional probability estimation
  • C) Assuming all events are independent
  • D) Using the implied volatility surface from the options market

Question 4

The Portfolio Kelly Criterion differs from applying the single-bet Kelly Criterion independently to each bet because:

  • A) Portfolio Kelly uses a different formula for expected value
  • B) Portfolio Kelly accounts for budget constraints, correlations, and interaction effects among simultaneous bets
  • C) Portfolio Kelly always produces larger position sizes
  • D) Portfolio Kelly ignores the risk-free rate

Question 5

In the Gaussian copula approach to generating correlated binary outcomes, what is the role of the Cholesky decomposition?

  • A) It computes the optimal Kelly fractions directly
  • B) It transforms independent standard normal variables into correlated normal variables that preserve the specified correlation structure
  • C) It converts binary outcomes into continuous returns
  • D) It calculates the maximum drawdown of the portfolio

Question 6

A portfolio of $n$ equally-weighted uncorrelated binary bets each with probability $p$ of success has variance that decreases as:

  • A) $1/n^2$
  • B) $1/n$
  • C) $1/\sqrt{n}$
  • D) $\log(n)$

Question 7

Two positive-edge bets have a correlation of $\rho = -0.3$. Compared to the independent case ($\rho = 0$), the Portfolio Kelly optimizer will likely:

  • A) Allocate less to both bets because negative correlation signals model error
  • B) Allocate more to both bets because their combined variance is lower
  • C) Allocate the same amount because correlation does not affect Kelly sizing
  • D) Refuse to include negatively correlated bets in the portfolio

Question 8

Which position sizing approach allocates the same fraction of bankroll to every bet regardless of edge?

  • A) Kelly-based sizing
  • B) Volatility targeting
  • C) Fixed fraction
  • D) Risk parity

Question 9

A trader has identified 8 opportunities. The raw half-Kelly fractions sum to 95% of bankroll, and the aggregate deployment cap is 70%. What should the trader do?

  • A) Ignore the cap since Kelly is theoretically optimal
  • B) Scale all positions proportionally so the total allocation equals 70%
  • C) Drop the 3 smallest positions to get below 70%
  • D) Double the bankroll to accommodate all positions

Question 10

Which combination of diversification dimensions is MOST effective for a prediction market portfolio?

  • A) Diversify only across platforms
  • B) Diversify across event types, time horizons, platforms, and strategies
  • C) Diversify only across time horizons
  • D) Concentrate in the single event type where you have the most expertise

Question 11

The diversification ratio of a portfolio equals 1.0. This means:

  • A) The portfolio is perfectly diversified
  • B) All positions are perfectly positively correlated, providing zero diversification benefit
  • C) The portfolio contains exactly one position
  • D) Both B and C would produce this result

Question 12

Value at Risk (VaR) at 95% confidence for a binary outcome portfolio represents:

  • A) The average loss in the worst 5% of scenarios
  • B) The loss level that is exceeded in only 5% of scenarios
  • C) The maximum possible loss
  • D) The standard deviation of portfolio returns

Question 13

Why is Expected Shortfall (CVaR) considered a better risk measure than VaR for prediction market portfolios?

  • A) Expected Shortfall is always smaller than VaR
  • B) Expected Shortfall accounts for the severity of tail losses beyond the VaR threshold, not just whether they occur
  • C) Expected Shortfall does not require Monte Carlo simulation
  • D) Expected Shortfall is easier to compute analytically for binary outcomes

Question 14

The Sortino ratio differs from the Sharpe ratio in that it:

  • A) Uses maximum drawdown instead of standard deviation
  • B) Uses only downside deviation rather than total standard deviation, focusing on harmful volatility
  • C) Ignores the risk-free rate
  • D) Is always larger than the Sharpe ratio

Question 15

In a Monte Carlo simulation of a prediction market portfolio, which statistic requires the MOST simulations for a stable estimate?

  • A) Mean return
  • B) Standard deviation
  • C) 95% VaR
  • D) Risk of ruin

Question 16

Your portfolio has dropped from a peak of $15,000 to $12,000. The current drawdown is:

  • A) 25.0%
  • B) 20.0%
  • C) 16.7%
  • D) 12.0%

Question 17

According to the chapter's drawdown management framework, when your drawdown reaches 20-30% (classified as "Serious"), you should:

  • A) No action needed
  • B) Reduce position sizes to 75% of normal
  • C) Halve position sizes and close marginal bets
  • D) Close all positions and reassess strategy

Question 18

A trader is in a 20% drawdown and normally earns 2% expected return per round. After scaling positions to 50% per drawdown rules, approximately how many rounds are needed to recover?

  • A) 6 rounds
  • B) 11 rounds
  • C) 22 rounds
  • D) 44 rounds

Question 19

In the chapter's recommended bankroll tier structure, Reserve Capital serves which primary purpose?

  • A) Active trading positions deployed on platforms
  • B) Personal safety net kept in a separate account
  • C) A buffer to replenish trading capital after drawdowns or to fund new opportunities
  • D) Collateral for leveraged positions

Question 20

When should you rebalance a prediction market portfolio?

  • A) On a fixed calendar schedule (monthly)
  • B) When a position resolves, when edge changes significantly, or when superior new opportunities appear
  • C) Only when the portfolio has a positive return for the month
  • D) Never; let positions run to resolution without adjustment

Question 21

During a correlation spike stress scenario, a portfolio that appeared well-diversified may behave as if it were:

  • A) More diversified than expected
  • B) A concentrated bet on a single narrative, because normally uncorrelated markets become correlated
  • C) Immune to losses because diversification always works
  • D) Generating higher returns due to increased volatility

Question 22

A stress test reveals that if all 8 of your political market positions lose simultaneously, you would lose 35% of your bankroll. This is:

  • A) Acceptable because individual political bets each have positive edge
  • B) A sign you need more political positions to diversify within the category
  • C) A sign of excessive concentration in correlated political positions, requiring reduced allocation to this group
  • D) Irrelevant because simultaneous loss is impossible

Question 23

The rule of thumb for rebalancing in prediction markets states: only rebalance when the expected improvement exceeds:

  • A) The transaction cost
  • B) Twice the transaction cost
  • C) Three times the transaction cost
  • D) The current portfolio return

Question 24

A Monte Carlo simulation of your portfolio produces these results: mean return +3.2%, P(profit) = 72%, 95% VaR = 8.5%, CVaR(95%) = 12.1%. The CVaR tells you that:

  • A) You will never lose more than 12.1%
  • B) In the worst 5% of scenarios, the average loss is 12.1%
  • C) 12.1% of your positions will lose money
  • D) The portfolio will lose 12.1% with 95% probability

Question 25

Which statement best captures the unifying theme of this chapter?

  • A) Maximizing expected returns is the most important goal
  • B) Survival is the prerequisite for success; portfolio construction and risk management ensure you stay in the game long enough for skill to compound
  • C) Prediction markets are too risky for portfolio approaches
  • D) The Kelly Criterion alone is sufficient for managing a prediction market portfolio

Answer Key

Click to reveal answers 1. **C** - Binary outcomes do NOT follow normal distributions; they are discrete, which is one of the challenges that makes portfolio construction more complex. All other options are genuine limitations of single-trade thinking. 2. **C** - For binary events where $p_X = 0.90$ and $p_Y = 0.10$, the maximum positive correlation is approximately $\sqrt{\frac{\min(0.9, 0.1) \cdot (1 - \max(0.9, 0.1))}{\max(0.9, 0.1) \cdot (1 - \min(0.9, 0.1))}} = \sqrt{\frac{0.1 \times 0.1}{0.9 \times 0.9}} = \sqrt{1/81} \approx 0.33$. 3. **B** - Since prediction market events are often one-time occurrences without historical data, structural analysis of causal factors and conditional probability estimation are the recommended approaches. 4. **B** - The key difference is that Portfolio Kelly jointly optimizes across all bets, respecting the budget constraint ($\sum f_i \leq 1$), accounting for correlations, and recognizing that the optimal size of one bet depends on all other allocations. 5. **B** - The Cholesky decomposition $L$ of the correlation matrix allows transformation $Z \cdot L^T$ to produce correlated normal variables from independent ones, which are then thresholded to generate correlated binary outcomes. 6. **B** - Portfolio variance for uncorrelated equally-weighted bets scales as $\sigma^2/n$, which is the classic $1/n$ diversification effect. 7. **B** - Negative correlation reduces combined portfolio variance, so the optimizer can afford to allocate more to each bet while maintaining the same risk level. 8. **C** - Fixed fraction sizing allocates $c/n$ to each bet regardless of edge, probability, or any other factor. 9. **B** - The aggregate deployment cap should be enforced by scaling all positions proportionally: multiply each fraction by $0.70 / 0.95 \approx 0.737$. 10. **B** - Maximum diversification benefit comes from spreading across all available dimensions: event types, time horizons, platforms, and analytical strategies. 11. **D** - A diversification ratio of 1.0 means portfolio volatility equals the weighted sum of individual volatilities, implying zero diversification benefit. This occurs with perfect positive correlation or with a single position. 12. **B** - VaR at 95% is the loss threshold such that only 5% of scenarios produce a worse outcome. It answers "how bad could it get in all but the worst 5% of cases?" 13. **B** - Expected Shortfall (CVaR) measures the average loss in the tail beyond VaR, capturing how severe the worst outcomes are, not just whether they cross a threshold. 14. **B** - The Sortino ratio replaces total standard deviation with downside deviation, which only penalizes negative returns. This is more relevant for traders who care about losses but welcome upside volatility. 15. **D** - Risk of ruin is a rare-event probability requiring at least 100,000 simulations for stability. Mean return needs only about 1,000; standard deviation about 5,000; 95% VaR about 10,000. 16. **B** - Drawdown = $(15{,}000 - 12{,}000) / 15{,}000 = 3{,}000 / 15{,}000 = 0.20 = 20\%$. 17. **C** - The 20-30% drawdown level is classified as "Serious" with the action to halve position sizes and close marginal bets. 18. **C** - Effective return per round = $0.02 \times 0.50 = 0.01$ (1%). Recovery rounds $= \log(1/0.80) / \log(1.01) \approx 0.223 / 0.00995 \approx 22$ rounds. 19. **C** - Reserve Capital (20-30% of total) provides a buffer for replenishing trading capital after losses and for deploying into new opportunities without dipping into the emergency fund. 20. **B** - Prediction market portfolio rebalancing should be event-driven: triggered by position resolution, significant edge changes, or the appearance of higher-quality opportunities. 21. **B** - Correlation spikes cause previously uncorrelated positions to move together, effectively transforming a diversified portfolio into a concentrated directional bet on a single macro factor. 22. **C** - A 35% loss from a single category wipeout indicates excessive concentration. The correlated group cap (recommended: 10-20%) should be enforced to limit exposure. 23. **B** - The chapter recommends rebalancing only when the expected improvement exceeds twice the transaction cost, to ensure the improvement is worth the friction. 24. **B** - CVaR (Conditional VaR) at 95% means: conditional on being in the worst 5% of scenarios, the average loss is 12.1%. 25. **B** - The chapter's unifying theme is explicitly stated: "Survival is the prerequisite for success. The best edge in the world is worthless if a drawdown wipes you out before it can compound."