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Mathematical Finance

This quiz covers the fundamental concepts and techniques used in Mathematical Finance.

14 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

What is the formula for calculating the present value of a future cash flow?

  1. PV = FV / (1 + r)^n
  2. PV = FV * (1 + r)^n
  3. PV = FV / (1 - r)^n
  4. PV = FV * (1 - r)^n
Question 2 Multiple Choice (Single Answer)

What is the relationship between the price of a bond and its yield to maturity?

  1. As the price of a bond increases, the yield to maturity decreases.
  2. As the price of a bond decreases, the yield to maturity increases.
  3. The price of a bond and its yield to maturity are not related.
  4. The relationship between the price of a bond and its yield to maturity is unpredictable.
Question 3 Multiple Choice (Single Answer)

What is the formula for calculating the duration of a bond?

  1. Duration = (PV of cash flows / Price of bond) / (1 + r)
  2. Duration = (PV of cash flows / Price of bond) * (1 + r)
  3. Duration = (Price of bond / PV of cash flows) / (1 + r)
  4. Duration = (Price of bond / PV of cash flows) * (1 + r)
Question 4 Multiple Choice (Single Answer)

What is the Black-Scholes model used for?

  1. Pricing options
  2. Pricing stocks
  3. Pricing bonds
  4. Pricing commodities
Question 5 Multiple Choice (Single Answer)

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

  1. Expected return = (Weight of asset 1 * Expected return of asset 1) + (Weight of asset 2 * Expected return of asset 2) + ...
  2. Expected return = (Weight of asset 1 * Expected return of asset 1) - (Weight of asset 2 * Expected return of asset 2) - ...
  3. Expected return = (Weight of asset 1 / Expected return of asset 1) + (Weight of asset 2 / Expected return of asset 2) + ...
  4. Expected return = (Weight of asset 1 / Expected return of asset 1) - (Weight of asset 2 / Expected return of asset 2) - ...
Question 6 Multiple Choice (Single Answer)

What is the Sharpe ratio used for?

  1. Measuring the risk-adjusted return of an investment
  2. Measuring the volatility of an investment
  3. Measuring the correlation between two investments
  4. Measuring the beta of an investment
Question 7 Multiple Choice (Single Answer)

What is the formula for calculating the beta of an asset?

  1. Beta = Covariance(Asset returns, Market returns) / Variance(Market returns)
  2. Beta = Correlation(Asset returns, Market returns) / Variance(Market returns)
  3. Beta = Covariance(Asset returns, Market returns) / Standard deviation(Market returns)
  4. Beta = Correlation(Asset returns, Market returns) / Standard deviation(Market returns)
Question 8 Multiple Choice (Single Answer)

What is the formula for calculating the value at risk (VaR) of a portfolio?

  1. VaR = (Expected return of portfolio - Minimum return of portfolio) * (1 + Confidence level)
  2. VaR = (Expected return of portfolio + Minimum return of portfolio) * (1 + Confidence level)
  3. VaR = (Expected return of portfolio - Minimum return of portfolio) / (1 + Confidence level)
  4. VaR = (Expected return of portfolio + Minimum return of portfolio) / (1 + Confidence level)
Question 9 Multiple Choice (Single Answer)

What is the formula for calculating the expected shortfall (ES) of a portfolio?

  1. ES = (Expected return of portfolio - Minimum return of portfolio) / (1 - Confidence level)
  2. ES = (Expected return of portfolio + Minimum return of portfolio) / (1 - Confidence level)
  3. ES = (Expected return of portfolio - Minimum return of portfolio) * (1 - Confidence level)
  4. ES = (Expected return of portfolio + Minimum return of portfolio) * (1 - Confidence level)
Question 10 Multiple Choice (Single Answer)

What is the formula for calculating the optimal portfolio weights using the mean-variance optimization approach?

  1. w = (Σ^-1 μ) / (μ^T Σ^-1 μ)
  2. w = (Σ μ) / (μ^T Σ μ)
  3. w = (Σ^-1 μ) / (μ^T Σ μ)
  4. w = (Σ μ) / (μ^T Σ^-1 μ)
Question 11 Multiple Choice (Single Answer)

What is the formula for calculating the Sharpe ratio of a portfolio?

  1. Sharpe ratio = (Expected return of portfolio - Risk-free rate) / Standard deviation of portfolio returns
  2. Sharpe ratio = (Expected return of portfolio + Risk-free rate) / Standard deviation of portfolio returns
  3. Sharpe ratio = (Expected return of portfolio - Risk-free rate) / Variance of portfolio returns
  4. Sharpe ratio = (Expected return of portfolio + Risk-free rate) / Variance of portfolio returns
Question 12 Multiple Choice (Single Answer)

What is the formula for calculating the Jensen's alpha of a portfolio?

  1. Jensen's alpha = Expected return of portfolio - (Risk-free rate + Beta of portfolio * Market risk premium)
  2. Jensen's alpha = Expected return of portfolio + (Risk-free rate + Beta of portfolio * Market risk premium)
  3. Jensen's alpha = Expected return of portfolio - (Risk-free rate - Beta of portfolio * Market risk premium)
  4. Jensen's alpha = Expected return of portfolio + (Risk-free rate - Beta of portfolio * Market risk premium)
Question 13 Multiple Choice (Single Answer)

What is the formula for calculating the Treynor ratio of a portfolio?

  1. Treynor ratio = Excess return of portfolio / Beta of portfolio
  2. Treynor ratio = Expected return of portfolio / Beta of portfolio
  3. Treynor ratio = Excess return of portfolio / Standard deviation of portfolio returns
  4. Treynor ratio = Expected return of portfolio / Standard deviation of portfolio returns
Question 14 Multiple Choice (Single Answer)

What is the formula for calculating the Information ratio of a portfolio?

  1. Information ratio = (Expected return of portfolio - Benchmark return) / Standard deviation of portfolio returns
  2. Information ratio = (Expected return of portfolio + Benchmark return) / Standard deviation of portfolio returns
  3. Information ratio = (Expected return of portfolio - Benchmark return) / Variance of portfolio returns
  4. Information ratio = (Expected return of portfolio + Benchmark return) / Variance of portfolio returns
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