2.7 Measures of Risk and Performance

Question 1

What are the applications / differences between these measures of risk?
1. Standard Deviation
2. Semivariance
3. Semistandard Deviation
4. Semivolatility

Answer 1

SD cannot be used for non-normal distribution

Semivariance measures only the negative deviations

Semistandard Deviation square root of SV

Similar to Semistandard Deviation

Question 2

Define shortfall risk

Answer 2

probability that return will be less than TARGET RETURN

Question 3

Define target semivariance

Answer 3

dispersion of data points below target return

Question 4

Define target semistandard deviation

Answer 4

square root of target semivariance. low target return removes most of outcomes. high target return removes only the highest outcomes

Question 5

Define tracking error

Answer 5

dispersion of returns relative to benchmark return

Question 6

Define drawdown

Answer 6

loss in asset value between peak and trough

Question 7

Define VaR

Answer 7

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

Question 8

Parametric vs non-parametric approach to measuring VaR

Answer 8

Parametric: normal distribution

Question 9

How to handle VaR with leptokurtic returns?

Answer 9

Leptokurtic distributions have fatter tails than normal:
1. probability distribution that incorporates fat tails like t-dist
2. increase SD for confidence level

Question 10

Describe two non-parametric approach to estimating VaR
1. Using historical data
2. Monte Carlo

Answer 10

1. Historical data: split time into periods, rank price changes. If 1% has price drops that exceeds 12%, estimated 99% VaR is 12%
2. Monte Carlo: approximate future frequency distribution by simulating many potential paths

Question 11

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____

Answer 11

1. Intuitive
2. Stand-alone and not Systematic risk
3. Less useful for non-normal return
4. Sensitive to duration

Question 12

Sharpe vs Treynor ratio

Answer 12

Excess return per unit of risk vs excess return for bearing systematic risk

Question 13

Sortino

Answer 13

(Portfolio Return - Target Return) / Target Semistandard Risk or Downside Risk

Question 14

Information Ratio

Answer 14

(Portfolio Return - Benchmark Return) / Tracking Error

Question 15

Return on VaR

Answer 15

Average Return / VaR

Question 16

Jensen’s Alpha

Answer 16

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)

Question 17

Name the two primary approaches for estimating the volatility used in computing value-at-risk.

Answer 17

1. asset’s historical standard deviation of returns
2. implied volatilities from option prices

Question 18

What are the steps involved in directly estimating VaR from historical data rather than through a parametric technique?

Answer 18

1. Collect the percentage price changes
2. Rank the gains/losses from the highest to the lowest
3. 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).

Question 19

Define tracking error and average tracking error

Answer 19

1. 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.
2. 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.

Question 20

What is the difference between value at risk and conditional value-at-risk?

Answer 20

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.

Question 21

What are the two main differences between the formula for variance and the formula for semivariance?

Answer 21

1. negative deviations in the numerator
2. smaller number of observations in the denominator.