reading 5

• What is the formula for the expected return of a portfolio?

  Expected return = Σ(wi * Ri)
• How is the weight of Asset i in a portfolio calculated?

  Weight = market value of Asset i / total portfolio value
• What is covariance in finance?

  Covariance measures how two assets move together
• What is the common symbol for covariance between random variables X and Y?

  Cov(X,Y)
• What does a positive covariance indicate?

  Both variables tend to move above their means
• What does a negative covariance indicate?

  One variable tends to move below its mean
• What is the formula for sample covariance?

  Cov(X,Y) = Σ[(Xi - X̄)(Yi - Ȳ)] / (n - 1)
• What does a covariance matrix show?

  Covariances between returns on a group of assets
• What do the diagonal terms in a covariance matrix represent?

  Variances of each asset's returns
• How many unique covariance terms are there for n assets?

  n(n − 1) / 2 unique covariance terms
• What is the formula for calculating portfolio variance?

  Portfolio variance = Σ(wi^2 * Var(Ri)) + ΣΣ(wi * wj * Cov(Ri, Rj))
• What is the variance of a portfolio composed of two risky assets A and B?

  Var(Rp) = wA^2 * Var(RA) + wB^2 * Var(RB) + 2 * wA * wB * Cov(RA, RB)
• What is the relationship between portfolio variance and covariance terms?

  Lower covariance terms lead to lower portfolio variance
• What is the formula for the correlation coefficient?

  Correlation = Cov(X,Y) / (σX * σY)
• How can a correlation matrix be used in portfolio variance calculations?

  It substitutes for covariances in variance formulas
• What is shortfall risk?

  Probability portfolio value falls below a target
• What does Roy's safety-first criterion aim to minimize?

  Minimizes probability of returns below a threshold
• What is the threshold level in Roy's safety-first criterion?

  Minimum acceptable return level for the portfolio
• How is the safety-first ratio calculated?

  Safety-first ratio = (Expected return - Threshold return) / Standard deviation
• What does a higher safety-first ratio indicate?

  Indicates a smaller shortfall probability
• How do you determine the most desirable portfolio using Roy's safety-first criterion?

  Choose the portfolio with the largest safety-first ratio
• What is the threshold return for the college endowment example?

  Threshold return = 3% or 0.03
• What is the probability of Portfolio A falling below $123.6 million?

  Probability is 30.85%
• What are the key concepts related to expected return and variance in a portfolio?

  • Expected return formula: Σ(wi * Ri)
  • Weight of Asset i: market value of Asset i / total portfolio value
  • Variance formula for two assets: Var(Rp) = wA^2 * Var(RA) + wB^2 * Var(RB) + 2 * wA * wB * Cov(RA, RB)
  • Covariance properties: Cov(RA,RA) = Var(RA), Cov(RA,RB) = Cov(RB,RA)
  • Safety-first criterion: minimizes shortfall risk
• What are the steps to apply Roy's safety-first criterion?

  1. Calculate the safety-first ratio
  2. Choose the portfolio with the largest safety-first ratio
• What is the relationship between covariance and portfolio variance?

  • Lower covariance terms lead to lower portfolio variance
  • Covariance affects the risk profile of the portfolio
• What is the significance of the covariance matrix?

  • Shows covariances between returns on multiple assets
  • Diagonal terms represent variances of individual assets
  • Unique covariance terms are essential for portfolio risk assessment