reading 6

• What function generates the lognormal distribution?

  ex, where x is normally distributed
• Why are logarithms of lognormally distributed variables normally distributed?

  Because ln(ex) equals x
• What is the relationship between continuously compounded returns and asset prices?

  • Asset prices modeled as continuously compounded returns
  • Future price is based on current price
• How can we express the sum of continuously compounded returns over shorter periods?

  r0,T is the sum of returns
• What does the central limit theorem imply about the sum of returns?

  Their sum is approximately normally distributed
• What distribution is PT if it is proportional to a normally distributed variable?

  Lognormally distributed
• What assumption is made about returns in many pricing models in the CFA curriculum?

  Returns are independently and identically distributed
• What does it mean if returns are independently distributed?

  Past returns do not predict future returns
• What is stationarity in the context of returns?

  Mean and variance do not change over time
• What is Monte Carlo simulation used for in investment applications?

  To generate a distribution of security values
• What must an analyst specify for each risk factor in Monte Carlo simulation?

  The parameters of the probability distribution
• How does Monte Carlo simulation generate random values for risk factors?

  Based on assumed probability distributions
• What is done with each set of randomly generated risk factors in Monte Carlo simulation?

  Used with a pricing model to value the security
• What is the purpose of repeating the simulation many times in Monte Carlo simulation?

  To draw inferences about expected security values
• What can Monte Carlo simulation estimate about security values?

  The expected mean and variance of values
• What is one advantage of Monte Carlo simulation?

  Inputs are not limited to historical data
• What is a limitation of Monte Carlo simulation?

  It is complex and relies on assumptions
• How does bootstrap resampling generate data inputs for simulations?

  By repeatedly drawing subsamples from observed data
• What is the purpose of bootstrap resampling?

  To infer parameters for the population
• How does bootstrap resampling differ from Monte Carlo simulation?

  Bootstrap uses observed data, Monte Carlo does not
• What is calculated in bootstrap resampling to estimate the standard error?

  The standard deviation of sample means
• What are the applications of Monte Carlo simulation in finance?

  • Value complex securities
  • Simulate trading strategy profits/losses
  • Calculate value at risk (VaR)
  • Simulate pension fund assets and liabilities
  • Value portfolios with nonnormal return distributions
• What are the steps in bootstrap resampling?

  1. Start with observed sample
  2. Draw subsamples with same number of observations
  3. Infer population parameters (mean, variance)