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Exam 4: Basic Refinements in Interest Rate Risk Management

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Exam 1: An Introduction to Fixed Income Markets17 Questionsadd course
Exam 2: Basics of Fixed Income Securities20 Questionsadd course
Exam 3: Basics of Interest Rate Risk Management17 Questionsadd course
Exam 4: Basic Refinements in Interest Rate Risk Management18 Questionsadd course
Exam 5: Interest Rate Derivatives: Forwards and Swaps15 Questionsadd course
Exam 6: Interest Rate Derivatives: Futures and Options15 Questionsadd course
Exam 7: Inflation, Monetary Policy, and the Federal Funds Rate15 Questionsadd course
Exam 8: Basics of Residential Mortgage Backed Securities21 Questionsadd course
Exam 9: One Step Binomial Trees15 Questionsadd course
Exam 10: Multi-Step Binomial Trees15 Questionsadd course
Exam 11: Risk Neutral Trees and Derivative Pricing18 Questionsadd course
Exam 12: American Options19 Questionsadd course
Exam 13: Monte Carlo Simulations on Trees18 Questionsadd course
Exam 14: Interest Rate Models in Continuous Time15 Questionsadd course
Exam 15: No Arbitrage and the Pricing of Interest Rate Securities17 Questionsadd course
Exam 16: Dynamic Hedging and Relative Value Trades13 Questionsadd course
Exam 17: Dynamic Hedging and Relative Value Trades18 Questionsadd course
Exam 18: The Risk and Return of Interest Rate Securities11 Questionsadd course
Exam 19: No Arbitrage Models and Standard Derivatives20 Questionsadd course
Exam 20: The Market Model for Standard Derivatives19 Questionsadd course
Exam 21: Forward Risk Neutral Pricing and the Libor Market Model14 Questionsadd course
Exam 22: Multifactor Models16 Questionsadd course
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You currently hold a 7-year ?xed rate bond paying 5% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 1-year zero coupon bond and a 7-year zero coupon bond. Use the following table to compute the adequate positions in the hedging instruments. You currently hold a 7-year ?xed rate bond paying 5% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 1-year zero coupon bond and a 7-year zero coupon bond. Use the following table to compute the adequate positions in the hedging instruments.

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Question 1
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The position in the short term bond should be -0.4651, while the position in the long term bond should be -1.1231.

What is the advantage of a factor model?

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A factor model has the advantage that it is adjusted to the data. The factors are not generated beforehand, but derived from the data itself. It so happens that embedded in the interest rate data there are three factors: slope, level and curvature (in addition to some more negligible factors). Additionally, by obtaining factors this way, they are automatically inde- pendent. This makes the hedging easier.

Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have? Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have?

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Question 3
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The term spread is 1% and the Butterfly Spread is -3%. The shape of the yield cure is an inverted hump.

Use the following discount factors when needed. Use the following discount factors when needed. -Calculate the convexity of the following security: a 3-year ?xed rate bond paying 4% coupon on a semiannual basis. -Calculate the convexity of the following security: a 3-year ?xed rate bond paying 4% coupon on a semiannual basis.

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Question 4

Suppose you hold a bond and interest rates suddenly fall. Duration says that bond prices will raise a given amount. If Convexity is included in this estimate, will bond prices go above or below what Duration predicts?

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Question 5

If you need three securities to hedge three factors, can you do the follow- ing? Take two securities and make a third "synthetic" security from these two (i.e. it is the average of both prices). Use it to solve the system of equations. Is this valid?

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Question 6

Compute the Term Spread and the Butter?y Spread for the following data. What shape does the yield curve have? Compute the Term Spread and the Butter?y Spread for the following data. What shape does the yield curve have?

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Question 7

Suppose you hold a bond and interest rates suddenly rise. Duration says that bond prices will fall a given amount. If Convexity is included in this estimate, will bond prices go above or below what Duration predicts?

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Question 8

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

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Question 9

Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have? Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have?

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Question 10

Use the following discount factors when needed. Use the following discount factors when needed. -Calculate the convexity of the following portfolio: i. 1 unit of a 2-year ?xed coupon bond paying 10% coupon quarterly. ii. 1 unit of a 2-year ?xed coupon bond paying 1% coupon semiannually. iii. 1 unit of a 2-year zero coupon bond. -Calculate the convexity of the following portfolio: i. 1 unit of a 2-year ?xed coupon bond paying 10% coupon quarterly. ii. 1 unit of a 2-year ?xed coupon bond paying 1% coupon semiannually. iii. 1 unit of a 2-year zero coupon bond.

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Question 11

Use the following discount factors when needed. Use the following discount factors when needed. -Calculate the convexity of the following portfolio: i. 2 units of a 1.5-year ?xed rate bond paying 6% quarterly. ii. 4 units of a 1.75-year ?oating rate bond paying ?oat + 80 bps semi- annually. You know that the reference rate was 7% three months ago. 13 iii. 6 units of a 2-year zero coupon bond. iv. 1 units of a 1.5-year ?oating rate bond with no spread paid semian- nually. -Calculate the convexity of the following portfolio: i. 2 units of a 1.5-year ?xed rate bond paying 6% quarterly. ii. 4 units of a 1.75-year ?oating rate bond paying ?oat + 80 bps semi- annually. You know that the reference rate was 7% three months ago. 13 iii. 6 units of a 2-year zero coupon bond. iv. 1 units of a 1.5-year ?oating rate bond with no spread paid semian- nually.

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Question 12

Use the following discount factors when needed. Use the following discount factors when needed. -Calculate the convexity of the following portfolio: i. 4 units of a 1.5-year ?xed rate bond paying 4% quarterly. ii. 5 units of a 1.5-year ?xed rate bond paying 5% semiannually. iii. 10 units of a 1.5-year zero coupon bond. iv. 3 units of a 1.5-year ?oating rate bond with no spread paid semian- nually. -Calculate the convexity of the following portfolio: i. 4 units of a 1.5-year ?xed rate bond paying 4% quarterly. ii. 5 units of a 1.5-year ?xed rate bond paying 5% semiannually. iii. 10 units of a 1.5-year zero coupon bond. iv. 3 units of a 1.5-year ?oating rate bond with no spread paid semian- nually.

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Question 13

You currently hold a 7-year fixed rate bond paying 1% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 2-year zero coupon bond and a 6-year zero coupon bond as hedging instruments. Use the following table to compute the adequate positions in the hedging instruments. You currently hold a 7-year fixed rate bond paying 1% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 2-year zero coupon bond and a 6-year zero coupon bond as hedging instruments. Use the following table to compute the adequate positions in the hedging instruments.

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Question 14

Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have? Compute the Term Spread and the Butterfly Spread for the following data. What shape does the yield curve have?

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Question 15

You currently hold a 2-year fixed rate bond paying 1% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 1-year zero coupon bond and a 8-year zero coupon bond as hedging instruments. Use the following table to compute the adequate positions in the hedging instruments. You currently hold a 2-year fixed rate bond paying 1% annually. You would like to hedge against changes in the level and the slope of the yield curve and you plan to use a 1-year zero coupon bond and a 8-year zero coupon bond as hedging instruments. Use the following table to compute the adequate positions in the hedging instruments.

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Question 16

How many securities do you need to hedge three factors? Why?

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Question 17

Use the following discount factors when needed. Use the following discount factors when needed. -Calculate the convexity of the following security: a 3-year ?oating rate bond with no spread paid quarterly. -Calculate the convexity of the following security: a 3-year ?oating rate bond with no spread paid quarterly.

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Question 18
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