karoliukas

Assume that a callable bond's call period starts two years from now with a call price of $102.50. Also assume that the bond pays an annual coupon of 6% and the term structure is flat at 5.5%. Which of the following is the price of the bond assuming that it is called on the first call date?

A) $100.00.

B) $102.50.

C) $103.17.

---

The bond price is computed as follows:
Bond price = 6/1.055 + (102.50 + 6)/1.0552 = $103.17

karoliukas

Can spot interest rates be used to value a callable bond?

A) Yes.

B) No.

C) It depends on the slope of the term structure.

---

Any complex debt instruments (like callable bonds, putable bonds, and mortgage-backed securities) can be viewed as the sum of the present value of its individual cash flows where each of those cash flows are discounted at the appropriate zero-coupon bond spot rate. It should be noted that while the appropriate spot interest rate can be used to discount each cash flow, determining the actual pattern of cash flows is uncertain due to the possibility of the bond being called away.

Kingpin804

One of the most commonly used yield spread measures is the nominal spread. Which of the following is NOT a limitation of nominal spread? The nominal spread:

A) assumes a flat yield curve.

B) assumes all cash flows can be discounted at the same rate.

C) is difficult to calculate.

---

The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond's YTM or its BEY).

Kingpin804

One of the most commonly used yield spread measures is the nominal spread. Which of the following is a limitation of nominal spread? The nominal spread assumes:

A) an upward sloping yield curve.

B) all coupon payments are reinvested at a rate equal to the risk free rate.

C) a flat yield curve.

---

The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond’s YTM or its BEY).

Kingpin804

The zero volatility spread (Z-spread) is the spread that:

A) is added to the yield to maturity of a similar maturity Treasury bond to equal the yield to maturity of the risky bond.

B) is added to each spot rate on the Treasury yield curve that will cause the present value of the bond's cash flows to equal its market price.

C) results when the cost of the call option in percent is subtracted from the option adjusted spread.

---

The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value. The nominal spread is the spread that is added to the YTM of a similar maturity Treasury bond that will then equal the YTM of the risky bond. The zero volatility spread (Z-spread) is the spread that results when the cost of the call option in percent is added to the option adjusted spread.

Kingpin804

Which of the following statements regarding the option adjusted spread (OAS) is least accurate? The option adjusted spread:

A) is the spread added to the Treasury spot rate curve that the bond would have if it were option-free.

B) is the spread that accounts for non-option characteristics like credit risk, liquidity risk, and interest rate risk.

C) for a putable bond is the Z-spread minus the cost of the option.

---

Since the buyer of a putable bond must pay extra for the put option, the OAS spread for a putable bond is the Z-spread plus the put option cost in percent.

Kingpin804

Which of the following statements regarding the option adjusted spread (OAS) is least accurate? The option adjusted spread:

A) is the spread added to the Treasury spot rate curve that the bond would have if it were option-free.

B) is the spread that accounts for non-option characteristics like credit risk, liquidity risk, and interest rate risk.

C) for a putable bond is the Z-spread minus the cost of the option.

---

Since the buyer of a putable bond must pay extra for the put option, the OAS spread for a putable bond is the Z-spread plus the put option cost in percent.

Kingpin804

One of the most commonly used yield spread measures is the nominal spread. Which of the following is least likely a limitation of nominal spread? The nominal spread assumes:

A) all cash payments will be received in a prompt and timely manner.

B) all cash flows can be discounted at the same rate.

C) an upward sloping yield curve.

---

The nominal spread is easy to calculate – it is simply the yield to maturity on a bond minus the yield to maturity on a Treasury security of a similar maturity. Because the nominal yield is based on the yield to maturity, it suffers the same shortcomings as yield to maturity. The yield measures assume that all cash flows can be discounted at the same rate (i.e., assumes a flat yield curve). They also assume that all coupon payments will be received in a prompt and timely fashion, and reinvested to maturity, at a rate of return that is equal to the appropriate solving rate (i.e., the bond’s YTM or its BEY).

Kingpin804

The zero volatility spread (Z-spread) is the spread that:

A) is added to the yield to maturity of a similar maturity Treasury bond to equal the yield to maturity of the risky bond.

B) is added to each spot rate on the Treasury yield curve that will cause the present value of the bond's cash flows to equal its market price.

C) results when the cost of the call option in percent is subtracted from the option adjusted spread.

---

The zero volatility spread (Z-spread) is the interest rate that is added to each zero-coupon bond spot rate that will cause the present value of the risky bond's cash flows to equal its market value. The nominal spread is the spread that is added to the YTM of a similar maturity Treasury bond that will then equal the YTM of the risky bond. The zero volatility spread (Z-spread) is the spread that results when the cost of the call option in percent is added to the option adjusted spread.

Kingpin804

The following information is available for two bonds:

• Bond X is callable and has an option-adjusted spread (OAS) of 55bp. Similar bonds have a Z-spread of 68bp and a nominal spread of 60bp.

• Bond Y is putable and has an OAS of 100bp. Similar bonds have a Z-spread of 78bp and a nominal spread of 66bp.

The embedded option cost for Bond:

A) X is 5bp.

B) X is 13bp.

C) X is 8bp.

---

Option cost (Bond X) = Z-spread – OAS = 68bp – 55bp = 13bp
Option cost (Bond Y) = Z-spread – OAS = 78bp – 100bp = - 22bp