Question 1

Compute the 95% VaR for the following portfolio: 
i. A 1.5-year ?xed rate bond paying 2% quarterly. 
ii. A 0.75-year ?oating rate bond paying ?oat plus 80 basis points semi- annually. You know that the reference rate was set to 6% six months ago. 
iii. A 0.25 zero coupon bond. Additionally you know that ?dr =0and?dr =0.4233.

Accepted Answer

The 95%VaR=1.3116.

Question 2

Use the following discount factors when needed. 
-Calculate the duration of the following security: 5-year zero coupon bond.

Accepted Answer

The duration of the security is 5.00.

Question 3

What is the dollar duration of the following portfolio?
 i. Long a 1.5-year zero coupon bond. 
ii. Short a 2-year ?xed coupon bond paying 1% quarterly.

Accepted Answer

Dollar duration for the portfolio is -41.0462.

Question 4

What is the duration of the following portfolio? 
i. Long a 1.5-year zero coupon bond. 
ii. Short a 2-year ?xed coupon bond paying 1% quarterly.

Accepted Answer

The answer of What is the duration of the following...

Question 5

Use the following discount factors when needed. 
-Calculate the duration of the following security: 1.25-year ?oating coupon paying ?oat + 50 bps semiannually. You know that last quarter the semi- annual rate was 6.4%.

Accepted Answer

The answer of Use the following discount factors when needed....

Question 6

What is the PV01 of the following portfolio?
 i. Long a 1-year ?xed coupon bond paying 4% quarterly. 
ii. Long a 1.75-year ?oating rate bond paying ?oat plus 80 bps semian- nually. You know that the reference rate was set at 6% six months ago. 
iii. Short a 2-year zero coupon bond.

Accepted Answer

The answer of What is the PV01 of the following...

Question 7

Use the following discount factors when needed. 
-Calculate the duration of the following portfolio:
 i. 5 units of a 2-year ?xed rate bond paying 6% quarterly. 
ii. 2 units of a 1.75-year ?oating rate bond paying ?oat + 80 bps semi- annually. You know that the reference rate was 6.5% three months ago.
 iii. 6 units of a 1-year zero coupon bond. 
iv. 5 units of a 1.5-year ?oating rate bond with no spread paid semian- nually.

Accepted Answer

The answer of Use the following discount factors when needed....

Question 8

Calculate the Modiﬁed Duration for the same security.

Accepted Answer

The answer of Calculate the Modiﬁed Duration for the same...

Question 9

Use the following discount factors when needed. 
-Calculate the duration of the following portfolio:  
i. 3 units of a 0.75-year ?xed rate bond paying 6% quarterly. 
ii. 4 units of a 2-year ?xed rate bond paying 3% semiannually. 
iii. 7 units of a 1.75-year zero coupon bond.
 iv. 1 unit of a 2-year ?oating rate bond with no spread paid semiannually.

Accepted Answer

The answer of Use the following discount factors when needed....

Question 10

You have two bond coupon with the same maturity, one has a 9% coupon paid semiannually and the other a 8% coupon paid semiannually. Which one has a higher duration?

Accepted Answer

The answer of You have two bond coupon with the...

Question 11

What is the PV01 of the following portfolio? 
i. Long a 2-year ?xed coupon bond paying 7% quarterly. 
ii. Short three 1.25-year ?oating rate bonds paying ?oat plus 80 bps semiannually. You know that the reference rate was set at 7% six months ago. 
iii. Short two 0.5-year zero coupon bonds.

Accepted Answer

The answer of What is the PV01 of the following...

Question 12

Use the following discount factors when needed. 
-Calculate the duration of the following security: 2-year ?xed coupon pay- ing 5% quarterly.

Accepted Answer

The answer of Use the following discount factors when needed....

Question 13

Suppose that you calculate VaR from Duration. In your many results you ?nd that:
 i. using historical data (of whatever length) or a normal distribution does not a?ect the result; 11
 ii. you ?nd that kurtosis between historical data and the normal distri- bution is almost identical; 
iii. You ?nd the expected change in the portfolio ?P = 0, with very small standard errors. Given the above, can you say that this Duration based VaR is an appro- priate approach to measure risk?

Accepted Answer

The answer of Suppose that you calculate VaR from Duration....

Question 14

What is the dollar duration of the following portfolio: 
i. Long a 1-year ?xed coupon bond paying 4% quarterly.
 ii. Long a 1.75-year ?oating rate bond paying ?oat plus 80 bps semian- nually. You know that the reference rate was set at 6% six months ago. 
iii. Short a 2-year zero coupon bond. 10

Accepted Answer

The answer of What is the dollar duration of the...

Question 15

What is the dollar duration of the following portfolio: 
i. Long a 2-year ?xed coupon bond paying 7% quarterly. 
ii. Short three 1.25-year ?oating rate bonds paying ?oat plus 80 bps semiannually. You know that the reference rate was set at 7% six months ago. 
iii. Short two 0.5-year zero coupon bonds.

Accepted Answer

The answer of What is the dollar duration of the...

Question 16

Calculate the MacCaulay Duration for the following security: 1-year ﬁxed rate coupon bond paying 6% semiannually. You know that the yield of the bond is 6.72%.

Accepted Answer

The answer of Calculate the MacCaulay Duration for the following...

Question 17

Mr. Brown wants to invest $100,000 for the next ?ve years. He purchases an annuity from a ?nancial institution. Currently the term structure is ?at at 10% (yearly compounded). 
i. If the payments are made yearly, what is the amount that the ?nan- cial institution will agree to pay Mr. Brown?
 ii. Assume that there is a 5-year ?xed coupon bond that pays 12% coupon every year. What is the price and duration of the bond? 
iii. How much must the ?nancial institution invest in the long-term bond in order to hedge the position? What should it do with the remainder of the money?

Accepted Answer

The answer of Mr. Brown wants to invest $100,000 for...

Quiz 3: Basics of Interest Rate Risk Management

Use the following discount factors when needed. -Calculate the duration of the following security: 5-year zero coupon bond.

What is the dollar duration of the following portfolio? i. Long a 1.5-year zero coupon bond. ii. Short a 2-year ?xed coupon bond paying 1% quarterly.

What is the duration of the following portfolio? i. Long a 1.5-year zero coupon bond. ii. Short a 2-year ?xed coupon bond paying 1% quarterly.

Use the following discount factors when needed. -Calculate the duration of the following security: 1.25-year ?oating coupon paying ?oat + 50 bps semiannually. You know that last quarter the semi- annual rate was 6.4%.

What is the PV01 of the following portfolio? i. Long a 1-year ?xed coupon bond paying 4% quarterly. ii. Long a 1.75-year ?oating rate bond paying ?oat plus 80 bps semian- nually. You know that the reference rate was set at 6% six months ago. iii. Short a 2-year zero coupon bond.

Calculate the Modiﬁed Duration for the same security.

You have two bond coupon with the same maturity, one has a 9% coupon paid semiannually and the other a 8% coupon paid semiannually. Which one has a higher duration?

What is the PV01 of the following portfolio? i. Long a 2-year ?xed coupon bond paying 7% quarterly. ii. Short three 1.25-year ?oating rate bonds paying ?oat plus 80 bps semiannually. You know that the reference rate was set at 7% six months ago. iii. Short two 0.5-year zero coupon bonds.

Use the following discount factors when needed. -Calculate the duration of the following security: 2-year ?xed coupon pay- ing 5% quarterly.

What is the dollar duration of the following portfolio: i. Long a 1-year ?xed coupon bond paying 4% quarterly. ii. Long a 1.75-year ?oating rate bond paying ?oat plus 80 bps semian- nually. You know that the reference rate was set at 6% six months ago. iii. Short a 2-year zero coupon bond. 10

What is the dollar duration of the following portfolio: i. Long a 2-year ?xed coupon bond paying 7% quarterly. ii. Short three 1.25-year ?oating rate bonds paying ?oat plus 80 bps semiannually. You know that the reference rate was set at 7% six months ago. iii. Short two 0.5-year zero coupon bonds.

Calculate the MacCaulay Duration for the following security: 1-year ﬁxed rate coupon bond paying 6% semiannually. You know that the yield of the bond is 6.72%.