Question

Note: If not otherwise stated, assume that:

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

• Bonds have a face value of $1,000

• Coupon bonds make semi-annual coupon payments; however, coupon rates (rc) are annual rates, i.e., bonds make a semi-annual coupon payment of rc/2

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

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

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

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

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

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

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

Select one:

ABCDE

CAEDB

CEABD

DBAEC

BDEAC

AECDB

EACBD

CDEAB

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

Select one:

A

B

C

D

E

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

Select one:

A

B

C

D

E

d) What is the duration (in years) of the bond you chose in 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 by step with equations) Thanks!

Answer 1

a)

Rule 1: The longer the maturity of a bond, the higher the interest rate sensitivity (as longer time is needed to recover the investment and therefore and probability of adverse movement in interest rates over a longer time is higher)

Rule 2: Bonds with lower coupon rates have higher interest rate sensitivity (as lower interest rates will fall less and higher interest rates will fall more in adverse movement of interest rates)

Rule 3: The Bonds with higher coupon frequency will have lower interest rates (investment is recovered more frequently than in a less frequent manner carrying higher risk.

Based on above, the ranking is CAEDB

b) Bond 'B', the one paying highest coupon

c) Bond 'B', the one with lowest interest rate sensitivity

d) 2.76 years

Duration = Sum of present values of future cash flows weighted to their time of receipt and divided by the present value of the future cashflows