Reading 2.7 Flashcards
Drawbacks of st dev
Not appropriate measure of risk for asymmetrical (fat tailed) distributions. Because it measures distribution around the mean both ways.
What is semi-variance? And semi-standard deviation?
Semivar = popular measure of downside risk. Uses only negative deviations feom the mean squared.
Semi st dev = sq root of samivar
Formula for semivariance
1/ (T-1) Zsum (Rt- Rmean)
- for Rt<Rmean
Where T is the number of negative/total observations
Why is semi-volatility better than semi-variance?
T is only negative (no ambuguitity as with semivar)
Formula for semi-standard deviation
Sq root of: 1 / (T-0.5) * Zsum (Rt-Rmean)^2
What is shortfall risk
Probability that return will be less than the target return.
Target return is usually constant.
Target semi-variance definition
Dispersion of data points below target return. Similar to semi-variance, but uses target return instead of mean return
When does semi-variance = variance
When target return = mean
Tracking error definition
Dispersion of returns relative to benchmark return
When is tracking error used:
For assets with relative return performance as their goal
When is st dev of returns is used:
Used for assets with absolute return performance as their goal
Drawdown definition
Max % loss in the value of an asset in a given time period. = difference between RELATIVE peak and a RELATIVE low
Example: individual drawdown of 22% in 2017.
Max drawdown definition:
Largest drop in value over a time interval in the observation period. Max drop from relative peak to relative low.
Ex: max drawdown of 25% between 2008 and 2019.
What is the problem of drawdowns bases on end of quarter values
Because it would miss the true highs and lows, unless they occur at the end of the quarter
How to solve the problem of drawdowns based on quarterly values
Use daily drawdown values
What is value at risk? (VAR)
Max loss expected from an investment under normal market conditions.
Determined for a specific time period, level of confidence (representing the probability that the loss will not exceed VAR)
How does VAR change over time?
All else equal, longer time period => higher VAR because more time for some negative event to occur
How does confidence level impact VAR?
All else equal, higher levels of VAR => larger VAR because VAR accounts for more extreme negative events
VAR strengths
- single measure can easily be computed
- useful when worst case scenario analysis makes no sense (derivatives that have unlimited downside risk)
VAR (value at risk) weaknesses:
unless the distribution of losses (potential) is known, the info is limited
Exercise!
Binary option has 1.25% chance of losing 100k and 98.75% chance of earning 20k.
For 99% VAR (or any confidence level > 98.75%) what is the VAR?
For conf level > 98,75%, VAR = 100k
Less than 98.75%, VAR=0
Conditional Value at risk (CVAR) definition
Information on situations when VAR is exceeded (extreme conditions when return fall into the tail)
Gives the average of all losses that are equal or more than VAR.
