Exam 3: Basics of Interest Rate Risk Management

Calculate the Modified Duration for the same security.

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

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.

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.

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?

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%.

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?

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 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: 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.

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.

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.

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: 2-year ?xed coupon pay- ing 5% quarterly.

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?