Deck 3: Basics of Interest Rate Risk Management

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.

Answer 1

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.

Answer 2

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.

Answer 3

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.

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%.

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.

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.

Question 8

Calculate the Modified Duration for the same security.

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.

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?

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.

Question 12

Use the following discount factors when needed.

-Calculate the duration of the following security: 2-year ?xed coupon pay- ing 5% quarterly.

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?

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

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.

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%.

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?