Reading 2.7

Question 1

Drawbacks of st dev

Answer 1

Not appropriate measure of risk for asymmetrical (fat tailed) distributions. Because it measures distribution around the mean both ways.

Question 2

What is semi-variance? And semi-standard deviation?

Answer 2

Semivar = popular measure of downside risk. Uses only negative deviations feom the mean squared.

Semi st dev = sq root of samivar

Question 3

Formula for semivariance

Answer 3

1/ (T-1) Zsum (Rt- Rmean)

• for Rt<Rmean

Where T is the number of negative/total observations

Question 4

Why is semi-volatility better than semi-variance?

Answer 4

T is only negative (no ambuguitity as with semivar)

Question 5

Formula for semi-standard deviation

Answer 5

Sq root of: 1 / (T-0.5) * Zsum (Rt-Rmean)^2

Question 6

What is shortfall risk

Answer 6

Probability that return will be less than the target return.

Target return is usually constant.

Question 7

Target semi-variance definition

Answer 7

Dispersion of data points below target return. Similar to semi-variance, but uses target return instead of mean return

Question 8

When does semi-variance = variance

Answer 8

When target return = mean

Question 9

Tracking error definition

Answer 9

Dispersion of returns relative to benchmark return

Question 10

When is tracking error used:

Answer 10

For assets with relative return performance as their goal

Question 11

When is st dev of returns is used:

Answer 11

Used for assets with absolute return performance as their goal

Question 12

Drawdown definition

Answer 12

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.

Question 13

Max drawdown definition:

Answer 13

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.

Question 14

What is the problem of drawdowns bases on end of quarter values

Answer 14

Because it would miss the true highs and lows, unless they occur at the end of the quarter

Question 15

How to solve the problem of drawdowns based on quarterly values

Answer 15

Use daily drawdown values

Question 16

What is value at risk? (VAR)

Answer 16

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)

Question 17

How does VAR change over time?

Answer 17

All else equal, longer time period => higher VAR because more time for some negative event to occur

Question 18

How does confidence level impact VAR?

Answer 18

All else equal, higher levels of VAR => larger VAR because VAR accounts for more extreme negative events

Question 19

VAR strengths

Answer 19

• single measure can easily be computed
• useful when worst case scenario analysis makes no sense (derivatives that have unlimited downside risk)

Question 20

VAR (value at risk) weaknesses:

Answer 20

unless the distribution of losses (potential) is known, the info is limited

Question 21

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?

Answer 21

For conf level > 98,75%, VAR = 100k

Less than 98.75%, VAR=0

Question 22

Conditional Value at risk (CVAR) definition

Answer 22

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.