Deck 26: Value at Risk

Question 1

Matt owns 5,000 share of Matrix at $52.50.To arbitrage this he shorts 5,000 calls and longs 5,000 puts at a strike of $50.00.Assume = 0.16,σ = 0.30,rf = 0.06,and the options expire in 170 days.What is the value at risk for 1 week at a 95% confidence level?

A) $0
B) $16,433
C) $18,433
D) $20,433

Answer 1

A

Question 2

Why is recent data more relevant than older data when calculating volatility?

Answer 2

Research shows that future near term volatility more closely approximates the recent past volatility.

Question 3

You own two bonds; 25% of a 30-year bond with σ = 0.02 and 75% of a 20-year bond with ?σ = 0.015.The correlation coefficient is 0.82.What is the 2-week value at risk at a 95% confidence level? (Assume portfolio value = $15 million.)

A) $0
B) $234,357
C) $734,357
D) $1,734,357

Answer 3

D

Question 4

How is VaR used in credit risk scenarios?

Question 5

Use VaR techniques to determine the cost of insurance on a risky investment.The investment asset has a value of $80 and pays no dividend.The historical standard deviation of the asset is 15% and the expected return on the asset is 8%.At the 95% confidence level,what is the price of a put option that insures the asset over the next year?

A) $2.56
B) $1.25
C) $0.86
D) $0.15

Question 6

What is a default swap and what is its use?

Question 7

Your $1 million portfolio consists of 50% of Jacko with = 0.14,σ = 0.20 and 50% of Macko with = 0.10,σ = 0.15.The correlation coefficient is 0.25.What is the value at risk over 1 week at a 95% confidence level?

A) $23,447
B) $26,447
C) $29,447
D) $32,447

Question 8

Your portfolio is worth $200,000.The standard deviation of its annual returns is 0.20 and the expected return is 11.0%.What is the 2-week value at risk at a 95% confidence level?

A) $12,058
B) $13,058
C) $14,058
D) $15,058

Question 9

What is bootstrapping and what is its use?

Question 10

Your portfolio is worth $200,000.The standard deviation of its annual returns is 0.20 and the expected return is 11.0%.What is the probability of a loss over 10 business days?

A) 39.84%
B) 49.84%
C) 59.84%
D) 69.84%

Question 11

Kelly owns 50,000 shares of Microsoft at $63.60 per share.She buys 20,000 $60 strike calls.Assume = 0.12,σ = 0.23,rf = 0.05,and the options expire in 170 days.What is the value at risk for 2 weeks,using the delta approximation at a 99% confidence level?

A) $311,463
B) $411,463
C) $511,463
D) $611,463

Question 12

Harold owns 10,000 shares of IBM at $54.50 per share.He writes $55 strike covered call on all the shares.Assume = 0.14,σ = 0.18,rf = 0.04,and the options expire in 90 days.What is the value at risk for 1 day,using the delta approximation at a 95% confidence level?

A) $4,717
B) $5,717
C) $6,717
D) $7,717

Question 13

Your $2 million portfolio consists of 25% Evans stock with = 0.16,σ = 0.22 and 75% Indy stock with = 0.09,σ = 0.12.The correlation coefficient is 0.13.What is the value at risk over 1 day at a 99% confidence level? Assume 252 days per year.

A) $21,792
B) $31,792
C) $41,792
D) $51,792

Question 14

A stock has a price of $42.63 and pays no dividend.The historical standard deviation of the stock is 18% and the expected return on the stock is 11%.At the 95% confidence level,what is the Tail VaR over the next 270 days?

A) $2.13
B) $6.56
C) $9.71
D) $40.50

Question 15

Use VaR techniques to determine the cost of insurance on a risky investment.The investment asset has a value of $150 and pays no dividend.The historical standard deviation of the asset is 20% and the expected return on the asset is 15%.At the 95% confidence level,what is the price of a put option that insures the asset over the next 6 months?

A) $0.33
B) $1.25
C) $2.65
D) $6.56

Question 16

You own $4 million of Jacko Corp.The expected return is 14.0% and σ = 0.20.What is the value at risk over 4 weeks at a 99% confidence level?

A) $383,000
B) $413,000
C) $453,000
D) $473,000

Question 17

What is implied volatility?

Question 18

Your $2 million portfolio consists of 25% Evans stock with = 0.16,σ = 0.22 and 75% Indy stock with = 0.09,σ = 0.12.The correlation coefficient is 0.65.What is the value at risk over 1 day at a 99% confidence level? Assume 252 days per year.

A) $27,976
B) $37,976
C) $47,976
D) $57,976

Question 19

A stock has a price of $50 and pays no dividend.The historical standard deviation of the stock is 25% and the expected return on the stock is 12%.At the 95% confidence level,what is the Tail VaR over the next 6 months?

A) $2.50
B) $13.63
C) $22.36
D) $47.50

Question 20

A bond maturing in 5 years has a YTM = 0.065 and an annual yield volatility of 2.0%.Given a $15 million portfolio,what is the value at risk over 2 weeks at a 95% confidence level?

A) $283,917
B) $383,917
C) $483,917
D) $583,917

Question 21

Why is VaR an important tool in measuring risk? What are some of its shortcomings? Ask the class to explain the rationale for a company to rely heavily on VaR in the absence of other measurement tools.