FNCE30001 Study Guide - Final Guide: Interest Rate Swap, Yield Curve, Current Yield

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lavendermoose527

21 Nov 2018

School

University of Melbourne

Department

Finance

Course

FNCE30001

Professor

Brown

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Document Summary

Note: this tutorial has to cover two topics and is therefore longer than usual. It is most unlikely that tutors will be able to cover all questions in class but full answers will be provided on the lms. Problem 1 [question 9 on page 278 of bodie, et al principles of investments] Find the duration of a 6% coupon bond making annual coupon payments if it has three years until maturity and a yield to maturity of 6%. What is the duration if the yield to maturity is. Consider a 7-year 12% coupon bond, with a par value of , and which has just paid a coupon. The yield curve is flat at 9. 25% pa. coupons are paid annually. Use the duration to make a first approximation of the percentage capital gain or loss if the yield increases by 25 basis points.

Related Questions

Please use Excel to complete the problem below.

Immunization

Your company has just built and patented a laser defense system and is planning on installing the equipment in various locations around the country. To finance the installations, you, the CFO, have borrowed $1 billion, which your company will need to repay in five years. The market interest rate is 8%, so the present value of this obligation is $680,583,197. You decide to fund the obligation using three-year zero-coupon bonds and perpetuities that make annual coupon payments.

1. How can you immunize the obligation? (Here, you need to construct an immunized portfolio that consists of the zero-coupon bonds and the perpetuities.)

2. Now suppose that one year has passed and that the market rate is still 8%. You need to ensure that the obligation is still fully-funded and immunized. Is the obligation still fully-funded and immunized? If not, what do you need to do to fully fund and immunized the obligation?

Duration

1. What is the duration of a 10-year, 6% bond if the market rate on bonds of similar quality is 5.8%?

2. Now suppose that the yield to maturity has changed to 5.81%. Using Macaulay duration, what is the approximate percent change in the price of the bond? (You do not need to recalculate Macaulay duration using 5.81%. Use the duration value that you found in Problem 1.)

3. Using convexity, what is the approximate percent change in the price of the bond?

azurewater-buffalo769

Note: If not otherwise stated, assume that:

â¢ Yield-to-maturity (YTM) is an APR, semi-annuallycompounded

â¢ Bonds have a face value of $1,000

â¢ Coupon bonds make semi-annual coupon payments; however, couponrates (rc) are annual rates, i.e., bonds make a semi-annual couponpayment of rc/2

You must invest $100,000, and the bonds listed below from Ato E are the only investments available today (assume that it ispossible to buy a fraction of a bond in order to invest the full$100,000). The same 6% market interest rate (APR, compoundedsemi-annually) applies to all of these bonds and they have thefollowing additional characteristics:

A. 6 years to maturity and 4% coupon rate (coupons paidannually)

B. 3 years to maturity and 7% coupon rate (coupons paidsemi-annually)

C. 6 years to maturity and 0% coupon rate (discount orzero-coupon bond)

D. 3 years to maturity and 4% coupon rate (coupons paidsemi-annually)

E. 6 years to maturity and 4% coupon rate (coupons paidsemi-annually)

a) Rank these bonds according to their interest ratesensitivities, from the most interest rate sensitive to the leastinterest rate sensitive.

Select one:

ABCDE

CAEDB

CEABD

DBAEC

BDEAC

AECDB

EACBD

CDEAB

b) If you want to benefit from an unexpected decrease inmarket interest rates, which bond would you purchase?

Select one:

c) If you want to minimize interest rate risk, whichbond would you purchase?

Select one:

d) What is the duration (in years) of the bond you chosein part c)?

Select one:

0.32 years

2.76 years

2.84 years

5.68 years

5.52 years

2.34 years

1.98 years

3.96 years

NOTE: Please show all the work, without using excel (step bystep with equations) Thanks!

coraldeer83

2a) The following prices and maturities of zero coupon bonds are given below:

Maturity (Years)	Price ($)
1	925.38
2	890.00
3	816.30
4	735.03

i) A 10% coupon bond with a maturity of 3 years is currently selling at $1,080.07 in the market. The coupons are paid annually.
Strip the bond and determine whether there is an arbitrage opportunity. Clearly explain how you would profit from the arbitrage.

ii) Use the given zero coupon bonds to design a synthetic forward loan that starts 2 years from now (at the end of year 2), and is paid back 2 years later (at the end of year 4). Assume you are the lender in this transaction. How is the interest that you charge over the two years of this loan related to the implied forward rates?

2b) A pension plan will pay me $12,000 per year for a 6-year period, starting next year. My pension fund wants to immunize its position.

i) What is the duration of its obligation to me if the yield curve is flat at 5%?

ii) If the pension fund uses a 4-year zero coupon bonds and a perpetuity with yield to maturity of 5% p.a. to construct the immunized position, calculate the fraction of wealth that needs to be placed in each bond.

coffeetoad602

FNCE30001 Study Guide - Final Guide: Interest Rate Swap, Yield Curve, Current Yield

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