Reference no: EM131138610

Answer the following question given below:

1. What is the difference between book value accounting and market value accounting? How do interest rate changes affect the value of bank assets and liabilities under the two methods? What is marking to market?

2. What are the two different general interpretations of the concept of duration, and what is the technical definition of this term? How does duration differ from maturity?

3. A one-year, $100,000 loan carries a coupon rate and a market interest rate of 12 percent. The loan requires payment of accrued interest and one-half of the principal at the end of six months. The remaining principal and accrued interest are due at the end of the year.

a. What will be the cash flows at the end of six months and at the end of the year?

b. What is the present value of each cash flow discounted at the market rate? What is the total present value?

c. What proportion of the total present value of cash flows occurs at the end of 6 months? What proportion occurs at the end of the year?

d. What is the duration of this loan?

4. Two bonds are available for purchase in the financial markets. The first bond is a two-year, $1,000 bond that pays an annual coupon of 10 percent. The second bond is a two-year, $1,000, zero-coupon bond.

a. What is the duration of the coupon bond if the current yield-to-maturity (R) is 8 percent?10 percent? 12 percent? (Hint: You may wish to create a spreadsheet program to assist in the calculations.)

b. How does the change in the current yield to maturity affect the duration of this coupon bond?

c. Calculate the duration of the zero-coupon bond with a yield to maturity of 8 percent, 10 percent, and 12 percent.

d. How does the change in the yield to maturity affect the duration of the zero-coupon bond? Changing the yield to maturity does not affect the duration of the zero coupon bond.

e. Why does the change in the yield to maturity affect the coupon bond differently than it affects the zero-coupon bond?

5. A six-year, $10,000 CD pays 6 percent interest annually and has a 6 percent yield to maturity. What is the duration of the CD? What would be the duration if interest were paid semiannually? What is the relationship of duration to the relative frequency of interest payments?

6. An insurance company is analyzing three bonds and is using duration as the measure of interest rate risk. All three bonds trade at a yield to maturity of 10 percent, have $10,000 par values, and have five years to maturity. The bonds differ only in the amount of annual coupon interest that they pay: 8, 10, and 12 percent.

a. What is the duration for each five-year bond?
b. What is the relationship between duration and the amount of coupon interest that is paid?

7. How is duration related to the interest elasticity of a fixed-income security? What is the relationship between duration and the price of the fixed-income security?

8. You have discovered that the price of a bond rose from $975 to $995 when the yield to maturity fell from 9.75 percent to 9.25 percent. What is the duration of the bond?

9. What is dollar duration? How is dollar duration different from duration?

10. Suppose you purchase a five-year, 15 percent coupon bond (paid annually) that is priced to yield 9 percent. The face value of the bond is $1,000.

a. Show that the duration of this bond is equal to four years.

b. Show that if interest rates rise to 10 percent within the next year and your investment horizon is four years from today, you will still earn a 9 percent yield on your investment.

c. Show that a 9 percent yield also will be earned if interest rates fall next year to 8 percent.

11. Two banks are being examined by regulators to determine the interest rate sensitivity of their balance sheets. Bank A has assets composed solely of a 10-year $1 million loan with a coupon rate and yield of 12 percent. The loan is financed with a 10-year $1 million CD with a coupon rate and yield of 10 percent. Bank B has assets composed solely of a 7-year, 12 percent zero-coupon bond with a current (market) value of $894,006.20 and a maturity (principal) value of $1,976,362.88. The bond is financed with a 10-year, 8.275 percent coupon $1,000,000 face value CD with a yield to maturity of 10 percent. The loan and the CDs pay interest annually, with principal due at maturity.

a. If market interest rates increase 1 percent (100 basis points), how do the market values of the assets and liabilities of each bank change? That is, what will be the net affect on the market value of the equity for each bank?

b. What accounts for the differences in the changes in the market value of equity between the two banks?

c. Verify your results above by calculating the duration for the assets and liabilities of each bank, and estimate the changes in value for the expected change in interest rates. Summarize your results.

12. If you use only duration to immunize your portfolio, what three factors affect changes in the net worth of a financial institution when interest rates change?

13. Financial Institution XY has assets of $1 million invested in a 30-year, 10 percent semiannual coupon Treasury bond selling at par. The duration of this bond has been estimated at 9.94 years. The assets are financed with equity and a $900,000, two-year, 7.25 percent semiannual coupon capital note selling at par.

a. What is the leverage adjusted duration gap of Financial Institution XY?

b. What is the impact on equity value if the relative change in all market interest rates is a decrease of 20 basis points? Note: The relative change in interest rates is ?R/(1+R/2) =
-0.0020.

c. Using the information calculated in parts (a) and (b), what can be said about the desired duration gap for a financial institution if interest rates are expected to increase or decrease.

d. Verify your answer to part (c) by calculating the change in the market value of equity assuming that the relative change in all market interest rates is an increase of 30 basis points.

e. What would the duration of the assets need to be to immunize the equity from changes in market interest rates?

14. Hands Insurance Company issued a $90 million, one-year, zero-coupon note at 8 percent add-on annual interest (paying one coupon at the end of the year) or with an 8 percent yield. The proceeds were used to fund a $100 million, two-year commercial loan with a 10 percent coupon rate and a 10 percent yield. Immediately after these transactions were simultaneously closed, all market interest rates increased 1.5 percent (150 basis points).

a. What is the true market value of the loan investment and the liability after the change in interest rates?

b. What impact did these changes in market value have on the market value of the FI's equity?

c. What was the duration of the loan investment and the liability at the time of issuance?

d. Use these duration values to calculate the expected change in the value of the loan and the liability for the predicted increase of 1.5 percent in interest rates.

e. What is the duration gap of Hands Insurance Company after the issuance of the asset and note?

f. What is the change in equity value forecasted by this duration gap for the predicted increase in interest rates of 1.5 percent?

g. If the interest rate prediction had been available during the time period in which the loan and the liability were being negotiated, what suggestions would you have offered to reduce the possible effect on the equity of the company? What are the difficulties in implementing your ideas?

15. Identify and discuss three criticisms of using the duration model to immunize the portfolio of a financial institution.

16. In general, what changes have occurred in the financial markets that would allow financial institutions to restructure their balance sheets more rapidly and efficiently to meet desired goals? Why is it critical for an investment manager who has a portfolio immunized to match a desired investment horizon to rebalance the portfolio periodically? What is convexity? Why is convexity a desirable feature to capture in a portfolio of assets?

17. A financial institution has an investment horizon of two years 9.33 months (or 2.777 years). The institution has converted all assets into a portfolio of 8 percent, $1,000, three-year bonds that are trading at a yield to maturity of 10 percent. The bonds pay interest annually. The portfolio manager believes that the assets are immunized against interest rate changes.

a. Is the portfolio immunized at the time of bond purchase? What is the duration of the bonds?

b. Will the portfolio be immunized one year later?

c. Assume that one-year, 8 percent zero-coupon bonds are available in one year. What proportion of the original portfolio should be placed in these bonds to rebalance the portfolio?

18. Consider a 12-year, 12 percent annual coupon bond with a required return of 10 percent. The bond has a face value of $1,000.

a. What is the price of the bond?

b. If interest rates rise to 11 percent, what is the price of the bond?

c. What has been the percentage change in price?

d. Repeat parts (a), (b), and (c) for a 16-year bond.

e. What do the respective changes in bond prices indicate?

19. Consider a five-year, 15 percent annual coupon bond with a face value of $1,000. The bond is trading at a yield to maturity of 12 percent.

a. What is the price of the bond?

b. If the yield to maturity increases 1 percent, what will be the bond's new price?

c. Using your answers to parts (a) and (b), what is the percentage change in the bond's price as a result of the 1 percent increase in interest rates?

d. Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates.

e. What do the differences in your answers indicate about the rate-price relationships of fixed-rate assets?

20. Estimate the convexity for each of the following three bonds, all of which trade at yield to maturity of 8 percent and have face values of $1,000.

A 7-year, zero-coupon bond.
A 7-year, 10 percent annual coupon bond.
A 10-year, 10 percent annual coupon bond that has a duration value of 6.994 years (i.e., Approximately 7 years).
Market Value ?Market Value Capital Loss + Capital Gain at 8.01 percent at 7.99 percent Divided by Original Price
7-year zero -0.37804819 0.37832833 0.00000048
7-year coupon -0.55606169 0.55643682 0.00000034
10-year coupon -0.73121585 0.73186329 0.00000057

Convexity = 108 * (Capital Loss + Capital Gain) ÷ Original Price at 8.00 percent

7-year zero CX = 100,000,000*0.00000048 = 48
7-year coupon CX = 100,000,000*0.00000034 = 34
10-year coupon CX = 100,000,000*0.00000057 = 57

An alternative method of calculating convexity for these three bonds using the following equation is illustrated at the end of this problem and onto the following page.

Rank the bonds in terms of convexity, and express the convexity relationship between zeros and coupon bonds in terms of maturity and duration equivalencies.

Ranking, from least to most convexity: 7-year coupon bond, 7-year zero, 10-year coupon

Academic requirements:

• Your work must be submitted as  pages 16 -19 of pages

• Your work should be submitted in the formats outlined for each questionin the assignment.