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21 Sep 2018

You plan to buy a car 3 years from now and plan to take out a 3-year car loan. Given the following yield curve and assume that the spot rates are continuous compounded, what will be the interest rate for your car loan?

Yrs to Maturity

1

2

3

4

5

6

7

% yield

4

5

6

7

8

9

10

2. Given the following treasury bonds, calculate the 18-month zero rate. Assume face value of each bond is 100 and coupons are paid semi-annually.

Bond

Yrs to Maturity

Annual coupon rate%

Bond price

A

0.5

0

98

B

1

8

98

C

1.5

9

104

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Tod Thiel
Tod ThielLv2
23 Sep 2018

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Note: If not otherwise stated, assume that:

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

• Bonds have a face value of $1,000

• 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:

A

B

C

D

E

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

Select one:

A

B

C

D

E

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!

A bond portfolio named DEX, comprises four bonds (face value=$1000):

1)50 semi-annual bond, 5-year maturity, a coupon rate of 4%.

2)100 annual bonds, 30-year maturity, 8% coupon bond.

3)150 zero coupon bonds, 10-year maturity.

4)200 zero coupon bonds, 20-year maturity.

Given a 6% initial yield, what is the DEX’s duration (use Macaulay’s duration)?

The yield to maturity on two 10-year maturity bonds currently is 7%. Each bond has a call price of $1,100. One bond has a coupon rate of 6% and the other 8%. Assume for simplicity that bonds are called as soon as the present value of their remaining payments exceeds their call price. What will be the capital gain on each bond if the market interest rate suddenly falls to 6%. A 20-year maturity 9% coupon bond paying coupons semiannually is callable in 5 years at a call price of $1050. The bond currently sells at a yield to maturity of 8%. What is the yield to call?

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