2.7 Measures of Risk and Performance Flashcards
What are the applications / differences between these measures of risk?
1. Standard Deviation
2. Semivariance
3. Semistandard Deviation
4. Semivolatility
SD cannot be used for non-normal distribution
Semivariance measures only the negative deviations
Semistandard Deviation square root of SV
Similar to Semistandard Deviation
Define shortfall risk
probability that return will be less than TARGET RETURN
Define target semivariance
dispersion of data points below target return
Define target semistandard deviation
square root of target semivariance. low target return removes most of outcomes. high target return removes only the highest outcomes
Define tracking error
dispersion of returns relative to benchmark return
Define drawdown
loss in asset value between peak and trough
Define VaR
max loss expected under normal market conditions. determined for a specific time interval and level of confidence (probability that loss will not exceed VaR value)
- longer time interval = higher VaR, more time for negative event to occur
- higher level of confidence = larger VaR, higher the confidence, the more VaR accounts for EXTREME negative events
Parametric vs non-parametric approach to measuring VaR
Parametric: normal distribution
How to handle VaR with leptokurtic returns?
Leptokurtic distributions have fatter tails than normal:
1. probability distribution that incorporates fat tails like t-dist
2. increase SD for confidence level
Describe two non-parametric approach to estimating VaR
1. Using historical data
2. Monte Carlo
- Historical data: split time into periods, rank price changes. If 1% has price drops that exceeds 12%, estimated 99% VaR is 12%
- Monte Carlo: approximate future frequency distribution by simulating many potential paths
What are the four key properties of Sharpe ratio?
1. I____
2. Stand-alone and not S___ risk
3. Less useful for non-_____ return
4. Sensitive to d____
- Intuitive
- Stand-alone and not Systematic risk
- Less useful for non-normal return
- Sensitive to duration
Sharpe vs Treynor ratio
Excess return per unit of risk vs excess return for bearing systematic risk
Sortino
(Portfolio Return - Target Return) / Target Semistandard Risk or Downside Risk
Information Ratio
(Portfolio Return - Benchmark Return) / Tracking Error
Return on VaR
Average Return / VaR
Jensen’s Alpha
Jensen’s alpha is a direct measure of the absolute amount by which an asset is estimated to outperform, if positive, the return on efficiently priced assets of equal systematic risk in a single-factor market model.
Portfolio Return - Risk-free - Beta (Market - Risk-free)
Name the two primary approaches for estimating the volatility used in computing value-at-risk.
- asset’s historical standard deviation of returns
- implied volatilities from option prices
What are the steps involved in directly estimating VaR from historical data rather than through a parametric technique?
- Collect the percentage price changes
- Rank the gains/losses from the highest to the lowest
- Select the outcome (loss) reflecting the quantile specified by the VaR (e.g., for a VaR based on 95% confidence pick the observation with a loss larger than 95% of the other outcomes).
Define tracking error and average tracking error
- Tracking error indicates the dispersion of the returns of an investment relative to a benchmark return, where a benchmark return is the contemporaneous realised return on an index or peer group of comparable risk.
- Average tracking error simply refers to the average difference between an investment’s return relative to its benchmark. In other words, it is the numerator of the information ratio.
What is the difference between value at risk and conditional value-at-risk?
While VaR represents a worst-case loss associated with a probability and a time horizon, CVaR is the expected loss if that worst-case threshold is ever crossed. CVaR, in other words, quantifies the expected losses that occur beyond the VaR breakpoint.
What are the two main differences between the formula for variance and the formula for semivariance?
- negative deviations in the numerator
- smaller number of observations in the denominator.
