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FIN 4453 – PROJECT 3 (10 Questions)

Fall 2024

1. (10 Points) A bond has just been issued.  The bond will mature in 8 years and has a yield to maturity of 6%.  The bond’s annual coupon rate is 7% and the face value of the bond is $1,000.  Coupons will be paid quarterly.

a. Compute the bond’s duration using the basic duration formula, i.e., the Macaulay duration formula (DO NOT use Excel’s Duration function or the VBA function dduration).

2. (10 Points) A bond has just been issued.  The bond is currently selling for $848.  The bond will mature in 9 years.  The bond’s annual coupon rate is 9% and the face value of the bond is $1,000.  Coupons will be paid semi-annually.  The bond is callable in 6 years and the call price is $1090.

a. Compute the bond’s annual yield to call.

b. Compute the bond’s current yield.

c. Compute the bond’s annual yield to maturity.

3. (5 Points) A stock is selling today for $56.  The stock has an annual volatility of 42 percent, and the annual nominal risk-free interest rate is 8 percent.  A 14-month European call option with an exercise price of $48 is available to an investor.

a. Use Excel’s data table feature to construct a Two-Way Data Table to demonstrate the impact of the exercise price and the option’s duration on the price of this call option:

i. Option durations of 2 months, 4 months, 6 months, 8 months, and 10 months.

ii. Exercise prices of $50, $52, $58, $60, and $62.

b. How is the call option price impacted by varying the exercise price?

c. How is the call option price impacted by varying the duration of the option?

4. (10 Points) A bond has just been issued.  The bond has an annual coupon rate of 6% and coupons are paid annually.  The bond has a face value of $1,000 and will mature in 8 years.  The bond’s yield to maturity is 4%.

a. Calculate the actual currency change in the bond’s price as the yield to maturity changes from 4% to 5%.

b. Use the bond’s duration to calculate the bond’s approximate currency price change as the yield to maturity changes from 4% to 5%.

5. (5 Points) A bond has just been issued.  The bond will mature in 14 years.  The bond’s annual coupon rate is 16% and the face value of the bond is $1,000.  The bond’s (annual) yield to maturity is 12%.

a. Compute the bond’s duration if coupons are paid quarterly:

i. Using the VBA dduration function.

6. (20 Points) The Excel file Portfolio Bond Immunization Data contains information about three bonds.  Coupons are paid annually.  Use this data to:

a. Compute the amount to be invested to meet the future liability noted in the data.  This future liability is due in 9 years.

b. Find a combination of Bond 1 and Bond 2 having a target duration of 9 years.

c. Find a combination of Bond 1 and Bond 3 having a target duration of 9 years.

d. Perform an analysis using a data table and an accompanying graph to determine which of the following options (i.e., a portfolio consisting of Bond 1 and Bond 2, a portfolio consisting of Bond 1 and Bond 3, or a portfolio consisting of Bond 2) would be preferred to attempt to immunize this obligation.

i. Construct a data table by varying the yield to maturity that shows the value of each option at the end of 9 years.  Use yield to maturity values ranging from 0% to 15% in 1% increments.

ii. Based on your data table, construct a graph that demonstrates the performance of these 3 options.

iii. Analyze each option’s performance in attempting to achieve immunization.

7. (10 Points) The Excel file Portfolio Bond Weight Calculation Data contains information about three bonds. Coupons are paid annually.  Use matrix algebra and this data to construct a portfolio consisting of Bond 1, Bond 2, and Bond 3 that has a duration of 9 years, subject to the condition that the proportion invested in Bond 1 is 25% larger than the proportion invested in Bond 2.

8. (10 Points) A bond has just been issued.  The bond has an annual coupon rate of 8% and coupons are paid semi-annually.  The bond has a face value of $1,000 and will mature in 9 years.  The bond’s annual yield to maturity is 9%.

a. Use Excel’s Data Table feature to construct a Two-Way Data Table to demonstrate the impact of the coupon rate and the time to maturity on the bond’s duration using:

i. Coupon Rates of 0%, 4%, 8%, and 12%.

ii. Maturities of 4 years, 8 years, 12 years, 16 years, and 20 years.

b. What four (4) duration principles or relationships are demonstrated in this table?

9. (10 Points) Using EXCEL’s Text Box Feature, explain the principle of immunization when used with a bond portfolio.

a. What is bond portfolio immunization attempting to achieve?

b. How is bond portfolio immunization achieved?

c. Which two (2) bond risk components interact to make immunization successful?

i. Explain how these bond risk components interact to immunize a bond portfolio as interest rates change.

10. (10 Points) Using EXCEL’s Text Box Feature,

a. Explain how investors could apply Macaulay duration principles to make bond investment decisions.

b. Explain the relationship between a bond’s coupon rate and yield to maturity, and the bond’s price.