You need to use Excel for the calculations (with cells containing formulas) and Word for the Essay questions and the Bloomberg portions. If certain functions in Bloomberg have changed since this exam was prepared, please try to find a comparable function. In worst case-scenario, you should identify on the exam that you were not able to find that portion.

1. Given a 6year, 9% coupon bond with semiannual payments, $1,000 face value, and currently trading at par, calculate the total return for an investor with a 4-year horizon date, given the following interest rate scenarios:

a. Yields on such bonds stay at 9% on all maturities until the investor sells the bond at her horizon date. b. Immediately after the investor buys the bond, yields on such bonds drop to 6% on all maturities and remain there until the investor sells the bond at her horizon date.

c. Immediately after the investor buys the bond, yields on such bonds increase to 12% on all maturities and remain there until the investor sells the bond at her horizon date.

Comment on the relation between ARR and interest rates. Please show your calculations in a spreadsheet with coupon value, interest-on-interest, horizon value, present value and total return.

2. Given the following spot rates on 1-year to 5-year zero coupon bonds:

Year Spot market

1 4.0%

2 4.5%

3 5.0%

4 5.5%

5 6.0%

a. What is the equilibrium price of a five-year, 7% coupon bond paying a principal of $100 at maturity and coupons annually?

b. If the market prices the five-year bond such that it yields 6%, what is the bonds market price?

c. What would arbitrageurs do given the prices you determined in (a) and (b)? What impact would their actions have on the market price?

d. What would arbitrageurs do if the market price exceeded the equilibrium price? What impact would their actions have on the market price?

3. Assume the following Treasury spot rates:

Period Years to maturity Spot rate

1 0.5 5.0%

2 1.0 5.4

3 1.5 5.8

4 2.0 6.4

5 2.5 7.0

6 3.0 7.2

7 3.5 7.4

8 4.0 7.8

Please show the entire matrix in Excel from f11 to f17 (28 calculations in total) and highlight the following cells

• The 6-month forward rate six months from now.

The 6-month forward rate one year from now.

The 6-month forward rate three years from now.

The 2-year forward rate one year from now.

The 1-year forward rate two years from now.

4. Calculate Macaulays duration, the modified duration, and the convexity of the following bonds (annualize the parameters). Assume all of the bonds pay principal at their maturity. Please show all your calculations in Excel.

a. Six-year, 8% coupon bond with a principal of $1,000 and annual coupon payments trading at par.

b. Six-year, zero coupon bond with a principal of $1,000 and priced at $812.43 to yield 8%.

c. Five-year, 9% coupon bond with a principal of $1,000 and annual coupon payments trading at par.

d. Twenty-year, 6.5% coupon bond with a principal of $1,000 and semiannual coupon payments (3.25%) and priced at par.

e. Three-year, 7% coupon bond with a principal of $1,000 and semiannual coupon payments (3.5%) and priced at par.

f. Three-year zero-coupon bond with a principal of $1,000 and priced at $816.30 to yield 7%

Given your duration and convexity calculations in Question 4, answer the following:

a. Which bond has the greatest price sensitivity to interest rate changes?

b. For an annualized 1% decrease in rates what would be the approximate percentage change in the price of Bond a?

c. Which bond has the greatest non-symmetrical capital gain and capital loss feature? 3

d. If you were a speculator and expected yields to decrease in the near future by the same amount across all maturities (a parallel downward shift in the yield curve), which bond would you select?

e. If you were a bond portfolio manager and expected yields to increase in the near future by the same amount across all maturities (a parallel upward shift in the yield curve), which bond would you select?

f. Comment on the relation between maturity and a bonds price sensitivity to interest rate changes.

g. Comment on the relation between coupon rate and a bonds price sensitivity to interest rate changes.

5. Using the Market Segmentation Theory, outline the impacts on the term structure of interest rates of the following cases

a. Economic Recession

b. Fed purchase of long-term Treasury bonds.

6. Explain Expectations Theory intuitively and with an example. In your example assume a flat yield curve with one- and two-year bonds at 6% and an expectation of next year's yield curve being flat with one- and two-year bonds at 4%. Explain the theory only in terms of the response to the expectation by investors. Please use calculations and graphs to show the changes in the yield curve

You need to use Excel for the calculations (with cells containing formulas) and Word for the Essay questions and the Bloomberg portions. If certain functions in Bloomberg have changed since this exam was prepared, please try to find a comparable function. In worst case-scenario, you should identify on the exam that you were not able to find that portion. 1. Given a 6-year, 9% coupon bond with semiannual payments, $1,000 face value, and currently trading at par, calculate the total return for an investor with a 4-year horizon date, given the following interest rate scenarios: a. Yields on such bonds stay at 9% on all maturities until the investor sells the bond at her horizon date. b. Immediately after the investor buys the bond, yields on such bonds drop to 6% on all maturities and remain there until the investor sells the bond at her horizon date. c. Immediately after the investor buys the bond, yields on such bonds increase to 12% on all maturities and remain there until the investor sells the bond at her horizon date. Comment on the relation between ARR and interest rates. Please show your calculations in a spreadsheet with coupon value, interest-on-interest, horizon value, present value and total return. 2. Given the following spot rates on 1-year to 5-year zero coupon bonds: Year Spot market 1 4.0% 2 4.5% 3 5.0% 4 5.5% 5 6.0% a. What is the equilibrium price of a five-year, 7% coupon bond paying a principal of $100 at maturity and coupons annually? b. If the market prices the five-year bond such that it yields 6%, what is the bond's market price? c. What would arbitrageurs do given the prices you determined in (a) and (b)? What impact would their actions have on the market price? d. What would arbitrageurs do if the market price exceeded the equilibrium price? What impact would their actions have on the market price? 3. Assume the following Treasury spot rates: Period Years to maturity Spot rate 1 0.5 5.0% 2 1.0 5.4 3 1.5 5.8 4 2.0 6.4 5 2.5 7.0 6 3.0 7.2 7 3.5 7.4 8 4.0 7.8 Please show the entire matrix in Excel from f11 to f17 (28 calculations in total) and highlight the following cells The 6-month forward rate six months from now. The 6-month forward rate one year from now. The 6-month forward rate three years from now. The 2-year forward rate one year from now. The 1-year forward rate two years from now. 4. Calculate Macaulay's duration, the modified duration, and the convexity of the following bonds (annualize the parameters). Assume all of the bonds pay principal at their maturity. Please show all your calculations in Excel. a. Six-year, 8% coupon bond with a principal of $1,000 and annual coupon payments trading at par. b. Six-year, zero coupon bond with a principal of $1,000 and priced at $812.43 to yield 8%. c. Five-year, 9% coupon bond with a principal of $1,000 and annual coupon payments trading at par. d. Twenty-year, 6.5% coupon bond with a principal of $1,000 and semiannual coupon payments (3.25%) and priced at par. e. Three-year, 7% coupon bond with a principal of $1,000 and semiannual coupon payments (3.5%) and priced at par. f. Three-year zero-coupon bond with a principal of $1,000 and priced at $816.30 to yield 7% Given your duration and convexity calculations in Question 4, answer the following: a. Which bond has the greatest price sensitivity to interest rate changes? b. For an annualized 1% decrease in rates what would be the approximate percentage change in the price of Bond a? c. Which bond has the greatest non-symmetrical capital gain and capital loss feature? 3 d. If you were a speculator and expected yields to decrease in the near future by the same amount across all maturities (a parallel downward shift in the yield curve), which bond would you select? e. If you were a bond portfolio manager and expected yields to increase in the near future by the same amount across all maturities (a parallel upward shift in the yield curve), which bond would you select? f. Comment on the relation between maturity and a bond's price sensitivity to interest rate changes. g. Comment on the relation between coupon rate and a bond's price sensitivity to interest rate changes. 5. Using the Market Segmentation Theory, outline the impacts on the term structure of interest rates of the following cases a. Economic Recession b. Fed purchase of long-term Treasury bonds. 6. Explain Expectations Theory intuitively and with an example. In your example assume a flat yield curve with one- and two-year bonds at 6% and an expectation of next year's yield curve being flat with oneand two-year bonds at 4%. Explain the theory only in terms of the response to the expectation by investors. Please use calculations and graphs to show the changes in the yield curve