Ch 13 - Risk management and value at risk models

Question 1

What are some problems of measuring risk?

Answer 1

Measure of risk differs based on the investor’s expectations and risk preferences
There may be no single number that can summarize the risk of an investment decision

Question 2

What is the alpha % VaR?

Answer 2

Cut off such that there’s only a alpha % probability that we will see a return as low or lower. It is a measure of the probability that the return on an asset will fall below a certain threshold where the threshold is and the alpha % of the VAR within a given number of days

Question 3

What is meant by ‘support’?

Answer 3

The set of all possible values that a random variable can take

Question 4

What are the 2 key inputs to VaR?

Answer 4

The probability and the time horizon

Question 5

What is a drawback of variance as a measure of risk?

Answer 5

It penalizes large positive returns in the same way as large negative returns. VaR overcomes this by focusing on the lower tail of the distribution of returns only as investors are usually only interested in the probability of the value of the portfolio falling

Question 6

What are some shortcomings of VaR?

Answer 6

Extreme losses are ignored
Assumes that the portfolio value is constant over time
Not clear on how alpha and the number of observations should be chosen

Question 7

What is an advantage of the historical simulation method of estimating VaR?

Answer 7

Simple to implement

Does not require us to specify the distribution of returns

Question 8

What are some disadvantages of the historical simulation method of estimating VaR?

Answer 8

Requires us to assume returns are iid through time, ruling out empirical regularities such as volatility clustering
Arbitrary choice of m
Equal weight is given to all m observations

Question 9

What is the difference between historical simulation and weighted historical simulation?

Answer 9

Historical simulation assigns zero weight to observations older than m and equal weight to observations more recent than m.
Weighted historical simulation assigns higher weight to more recent observations and a lower weight to older observations

Question 10

Increasing _________ can either increase or decrease VaR

Answer 10

Kurtosis