How hard is Level II?

Lena Okafor, CFA, manages a government bond portfolio at Corvane Asset Management. She is preparing a briefing for a junior analyst, Theo Brandt, on how the par curve, the spot curve and the forward curve relate, and how the firm uses them to value bonds and to frame expected returns.

Okafor starts from the par yields on annual-coupon government bonds shown in Exhibit 1. She tells Brandt that each par yield is the coupon rate at which a bond of that maturity would price at exactly 100, and that the spot rates used to discount single cash flows must be extracted from these par yields one maturity at a time. All rates are annual rates with annual compounding.

Exhibit 1. Government par yields (annual coupons, annual compounding)

1-year: 2.50%

2-year: 3.00%

3-year: 3.40%

4-year: 3.70%

Brandt is also asked to value a 3-year government bond with a 5% annual coupon, paid at the end of each year, using the spot rates he derives. Okafor adds that a two-year forward rate starting two years from now is often quoted on the desk when the team discusses where medium-term rates are priced to be in the future.

Finally, Okafor asks Brandt to think about returns. She says: "Suppose that over the next year, interest rates evolve exactly as the current forward rates imply. I want you to tell me what one-year holding period return we would earn on the 3-year 5% bond under that scenario, and how it compares with the bond's yield to maturity." Brandt notes that the bond's yield to maturity, computed from the price he derives, is 3.39%.

Lena Okafor, CFA, manages a government bond portfolio at Corvane Asset Management. She is preparing a briefing for a junior analyst, Theo Brandt, on how the par curve, the spot curve and the forward curve relate, and how the firm uses them to value bonds and to frame expected returns.

Okafor starts from the par yields on annual-coupon government bonds shown in Exhibit 1. She tells Brandt that each par yield is the coupon rate at which a bond of that maturity would price at exactly 100, and that the spot rates used to discount single cash flows must be extracted from these par yields one maturity at a time. All rates are annual rates with annual compounding.

Exhibit 1. Government par yields (annual coupons, annual compounding)

1-year: 2.50%

2-year: 3.00%

3-year: 3.40%

4-year: 3.70%

Brandt is also asked to value a 3-year government bond with a 5% annual coupon, paid at the end of each year, using the spot rates he derives. Okafor adds that a two-year forward rate starting two years from now is often quoted on the desk when the team discusses where medium-term rates are priced to be in the future.

Finally, Okafor asks Brandt to think about returns. She says: "Suppose that over the next year, interest rates evolve exactly as the current forward rates imply. I want you to tell me what one-year holding period return we would earn on the 3-year 5% bond under that scenario, and how it compares with the bond's yield to maturity." Brandt notes that the bond's yield to maturity, computed from the price he derives, is 3.39%.

Lena Okafor, CFA, manages a government bond portfolio at Corvane Asset Management. She is preparing a briefing for a junior analyst, Theo Brandt, on how the par curve, the spot curve and the forward curve relate, and how the firm uses them to value bonds and to frame expected returns.

Okafor starts from the par yields on annual-coupon government bonds shown in Exhibit 1. She tells Brandt that each par yield is the coupon rate at which a bond of that maturity would price at exactly 100, and that the spot rates used to discount single cash flows must be extracted from these par yields one maturity at a time. All rates are annual rates with annual compounding.

Exhibit 1. Government par yields (annual coupons, annual compounding)

1-year: 2.50%

2-year: 3.00%

3-year: 3.40%

4-year: 3.70%

Brandt is also asked to value a 3-year government bond with a 5% annual coupon, paid at the end of each year, using the spot rates he derives. Okafor adds that a two-year forward rate starting two years from now is often quoted on the desk when the team discusses where medium-term rates are priced to be in the future.

Finally, Okafor asks Brandt to think about returns. She says: "Suppose that over the next year, interest rates evolve exactly as the current forward rates imply. I want you to tell me what one-year holding period return we would earn on the 3-year 5% bond under that scenario, and how it compares with the bond's yield to maturity." Brandt notes that the bond's yield to maturity, computed from the price he derives, is 3.39%.

Lena Okafor, CFA, manages a government bond portfolio at Corvane Asset Management. She is preparing a briefing for a junior analyst, Theo Brandt, on how the par curve, the spot curve and the forward curve relate, and how the firm uses them to value bonds and to frame expected returns.

Okafor starts from the par yields on annual-coupon government bonds shown in Exhibit 1. She tells Brandt that each par yield is the coupon rate at which a bond of that maturity would price at exactly 100, and that the spot rates used to discount single cash flows must be extracted from these par yields one maturity at a time. All rates are annual rates with annual compounding.

Exhibit 1. Government par yields (annual coupons, annual compounding)

1-year: 2.50%

2-year: 3.00%

3-year: 3.40%

4-year: 3.70%

Brandt is also asked to value a 3-year government bond with a 5% annual coupon, paid at the end of each year, using the spot rates he derives. Okafor adds that a two-year forward rate starting two years from now is often quoted on the desk when the team discusses where medium-term rates are priced to be in the future.

Finally, Okafor asks Brandt to think about returns. She says: "Suppose that over the next year, interest rates evolve exactly as the current forward rates imply. I want you to tell me what one-year holding period return we would earn on the 3-year 5% bond under that scenario, and how it compares with the bond's yield to maturity." Brandt notes that the bond's yield to maturity, computed from the price he derives, is 3.39%.