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Answers and explanations for questions related to quantitative methods in the cfa level 1 exam, specifically covering expected portfolio return, covariance, and risk measures such as portfolio variance, shortfall risk, and roy's safety first criterion. Topics also include properties of covariance, monte carlo simulation, resampling, probability sampling, and various sampling techniques.
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Expected Return on a Portfolio - Correct Answer Composed of n assets with weights w and expected returns r Covariance of asset returns - Correct Answer Is a measure of how two assets move together. It is the expected value of the product of the deviations of the two random variables from their expected values Properties: The Covariance of a random variable with itself is its variance May range from - infinity to + infinity Positive Covariance means that when one random variable is above the mean, the other random variable also tends to be above the mean Negative Covariance is the opposite of Positive Covariance Portfolio Variance - Correct Answer Shortfall Risk - Correct Answer Probability that a portfolio value or return will fall below a particular target value or return over a given period Roy's Safety First Criterion - Correct Answer States that the optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level (Threshold level) We want to minimize P(Rp-RL) Rp is port. return & RL is thresholds level return Safety-First Ratio - Correct Answer When portfolio returns are normally distributed, then Roy's Safety First Criterion can be Lognormal Distribution - Correct Answer The function e^x where x is normally distributed Monte Carlo Simulation - Correct Answer A technique based on the repeated generation of one or more risk factors that affect security values to generate a distribution of security values.
Resampling - Correct Answer A method for generating data inputs to use in a simulation. We start with the observed sample and repeatedly draw subsamples from it, each with the same # of observations. From these samples we can infer parameters' for the population such as mean and variance. Probability Sampling - Correct Answer Refers to selecting a sample when we know the probability of each sample member in the overall pop. Random Sampling - Correct Answer Each item is assumed to have the same prob. of being selected Simple Random Sampling - Correct Answer Use a computer to randomly select a number of observations, each observation has the same prob of being selected Nonprobability Sampling - Correct Answer Based on either low cost and easy access to some data items, or on using the judgement of the researcher in selecting data items. Systematic Sampling - Correct Answer Selecting every nth member from a population Stratified Random Sampling - Correct Answer uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics Often used in bond indexes because of the difficulty and costs of replicating a bond portfolio Cluster Sampling - Correct Answer Based on subsets of a pop., but in this case, we are assuming that each subset (cluster) is representative of the overall pop. Ex. State's residents household income that is by County (County is the cluster) One-Stage Cluster Sampling - Correct Answer A random sample of clusters is selected, and all of the data in those clusters comprise the sample Two-Stage Cluster Sampling - Correct Answer random samples from each of the selected clusters comprise the sample Convenience Sampling - Correct Answer Refers to selecting data based on ease of access High sampling error Judgmental Sampling - Correct Answer Refers to samples for which each observation is selected from a larger data set by the researcher