Week 3 - Value at Risk and Volatility

Question 1

VaR asks the question:

Answer 1

“How bad can things get?” ES asks: “If things do get bad, what is the expected loss?”

Question 2

ES asks:

Answer 2

“If things do get bad, what is the expected loss?”

Question 3

What is the Expected Shortfall ES?

Answer 3

ES is the expected loss during time T conditional on the loss being greater than the VaR.

Question 4

What are the criteria for a Coherent Risk Measure? SOS

Answer 4

1. Monotonicity: If one portfolio always produces a worse outcome than another its risk measure should be greater
2. Translation Invariance: If an amount of cash K is added to a portfolio, its risk measure should go down by K.
3. Homogeneity: Changing the size of a portfolio by L should result in the risk measure being multiplied by L
4. Subadditivity: The risk measure for two portfolios after they have been merged should be no greater than the sum of their risk measures before they were merged 𝑅𝑖𝑠𝑘(𝐴+𝐵)≤𝑅𝑖𝑠𝑘(𝐴)+𝑅𝑖𝑠𝑘(𝐵). (Satisfied by ES but not VaR)

Question 5

Explain Subadditivity SOS!

Answer 5

Subadditivity criterion refers to the risk measure for two portfolios after they have been merged should NOT be greater than the sum of their risk measures seperetly.

Question 6

ES, has better properties than VaR in the sense that it always recognizes the benefits of….

Answer 6

Diversification

Question 7

Monotonicity is:

Answer 7

If one portfolio always produces a worse outcome than another its risk measure should be greater

Question 8

Translation Invariance is:

Answer 8

If an amount of cash K is added to a portfolio, its risk measure should go down by K.

Question 9

Homogeneity is:

Answer 9

Changing the size of a portfolio by L should result in the risk measure being multiplied by L

Question 10

Wich risk three measure conditions VaR satisfies ?

Answer 10

1. Monotonicity: If one portfolio always produces a worse outcome than another its risk measure should be greater
2. Translation Invariance: If an amount of cash K is added to a portfolio, its risk measure should go down by K.
3. Homogeneity: Changing the size of a portfolio by L should result in the risk measure being multiplied by L