READING 4 PROBABILITY TREES AND CONDITIONAL EXPECTATIONS Flashcards
What is the expected value of a random variable?
A) The median outcome
B) The maximum possible outcome
C) The weighted average of all possible outcomes
D) The probability of the most likely event
C) The weighted average of all possible outcomes
The expected value is the probability-weighted average of all possible outcomes.
What do variance and standard deviation measure?
A) Average return
B) Time horizon
C) Dispersion around the expected value
D) Cumulative probability
C) Dispersion around the expected value
They measure how much outcomes deviate from the expected value, reflecting volatility.
Variance is calculated as:
A) Weighted sum of deviations from the mean
B) Weighted sum of squared deviations from the mean
C) Average probability of outcomes
D) Weighted probability of the maximum return
B) Weighted sum of squared deviations from the mean
Variance uses squared deviations to account for both upside and downside variability.
How is the standard deviation related to the variance?
A) It is the square of the variance
B) It is half the variance
C) It is the positive square root of the variance
D) It is the variance divided by two
C) It is the positive square root of the variance
Standard deviation = √(variance).
In probability models of returns, returns and probabilities are often shown using:
A) Regression analysis
B) Probability trees
C) Normal distribution
D) Moving averages
B) Probability trees
Probability trees map out the probabilities of different outcomes visually.
What is a conditional expected value?
A) An expected value based on historical data
B) An expected value depending on another event occurring
C) A fixed outcome regardless of conditions
D) The weighted sum of unconditional probabilities
B) An expected value depending on another event occurring
Conditional expected values adjust based on the occurrence of another event.
Analysts use conditional expected values to:
A) Create random models
B) Revise expectations when new information arrives
C) Build portfolios without risk
D) Identify arbitrage opportunities
B) Revise expectations when new information arrives
New information affects conditional expected returns.
If a government imposes a steel tariff, the conditional expected return for domestic steel producers will likely:
A) Stay the same
B) Decrease
C) Increase
D) Be zero
C) Increase
Tariffs favor domestic producers, increasing their expected returns.
What formula is used to update prior probabilities with new information?
A) Bayes’ Formula
B) CAPM
C) Black-Scholes Formula
D) Variance-Covariance Formula
A) Bayes’ Formula
Bayes’ formula updates prior probabilities after observing new events.
Bayes’ Formula is derived from which fundamental rule?
A) Central Limit Theorem
B) Law of Large Numbers
C) Multiplication Rule of Probability
D) Law of One Price
C) Multiplication Rule of Probability
Bayes’ formula stems from the multiplication rule and joint probability properties.
The joint probability of events A and B can be written as:
A) P(A) + P(B)
B) P(A) / P(B)
C) P(A) × P(B|A)
D) P(B) × P(A+B)
C) P(A) × P(B|A)
Joint probability = P(A) × P(B given A).
Bayes’ Formula calculates the probability of:
A) An event given no conditions
B) An event given another event has occurred
C) The mean return
D) The maximum probable outcome
B) An event given another event has occurred
It updates the probability for an event after incorporating new evidence.
What represents the denominator in Bayes’ formula?
A) Joint probability of A and B
B) Sum of conditional probabilities
C) Unconditional probability of event B
D) Probability of event A
C) Unconditional probability of event B
The denominator is the total (unconditional) probability of event B.
What is the numerator in Bayes’ formula?
A) Sum of unconditional probabilities
B) Product of prior probability and conditional probability
C) Difference between two probabilities
D) Square root of variance
B) Product of prior probability and conditional probability
Bayes’ numerator = prior probability × conditional probability.
