15: Asset Valuation: Debt Investments: Analysis and Valuation

15: Asset Valuation: Debt Investments: Analysis and Valuation 1.A: Introduction to the Valuation of Fixed Income Securities Question ID: 12975

What is the present value of a three-year security that pays a fixed annual coupon of 6 percent using a discount rate of 7 percent?

A. 92.48.

B. 97.38.

C. 100.00.

D. 101.75.

B This value is computed as follows:

Present Value = 6/1.07 + 6/1.072 + 106/1.073 = 97.38

The value 92.48 results if the coupon payment at maturity of the bond is neglected. The coupon rate and the discount rate are not equal so 100.00 cannot be the correct answer.

Question ID: 13009

If a bond's coupon is greater than the prevailing market rate on new issues, the bond is called a:

A. par bond.

B. term bond.

C. premium bond.

D. discount bond.

Question ID: 22342

By purchasing a noncallable, nonputable, U.S. Government 30-year bond, an investor is entitled to:

A. annuity of coupon payments.

B. monthly payments depending on the principal prepayment behavior of individual homeowners.

1 C. annuity of coupon payments plus recovery of principal at maturity.

D. full recovery of face value at maturity or when the bond is retired.

Bond investors are entitled to two distinct types of cash flows: (1) the periodic receipt of coupon income over the life of the bond, and (2) the recovery of principal (or face value) at the end of the bond’s life.

Question ID: 13010

Using the present-value method, which of the following is NOT needed to value a bond?

A. Coupon payment.

B. Term to maturity.

C. Par value.

D. Bond rating.

Question ID: 13011

The value of a bond is NOT affected by:

A. current yield.

B. coupon rate.

C. required rate of return.

D. year to maturity.

Question ID: 22343

Which of the following is NOT one of the steps in a valuation process for a noncallable bond?

A. Estimate the bond's cash flows.

B. Calculate the present value of the estimated cash flows.

2 C. Determine the appropriate discount rate.

D. Evaluate the probability of the issuer retiring the bond prematurely.

The three fundamental steps in the bond valuation process are (1) estimate the bond’s cash flows, (2) determine the appropriate discount rate, and (3) calculate the present value of the estimated cash flows. Since the bond has a noncallable feature, the issuer does not have the right to retire the bond prematurely.

Question ID: 22345

Zeta Corp. has outstanding a $10 million, 14 percent coupon bond that is noncallable. The bond pays quarterly coupon payments. The value of each cash coupon is closest to:

A. $700,000.

B. $350,000.

C. $1,000,000.

D. $1,400,000.

The cash coupon is ($10,000,000*0.14)/4 = $350,000. Note that while the coupon rate is stated as an annual percentage, the cash coupon payments are made on a quarterly basis.

Question ID: 22346

An investor gathers the following information about a 12-year bond:

· Par value of $10,000

· Semiannual coupon rate of 6 %

· Current price of $9,543

· Yield to maturity of 6.56 %

The value of each cash coupon is closest to:

A. $300.

B. $328.

3 C. $600.

D. $656.

The cash coupon is ($10,000*0.06)/2 = $300. Note that while the coupon rate is stated as an annual percentage, the cash coupon payments are made on a semiannual basis.

Question ID: 22344

If an investor purchases a 30-year semiannual bond with a coupon rate of 5 percent and par value of $100,000, the value of each cash coupon received is closest to:

A. $2,500.

B. $5,000.

C. $100,000.

D. $83.

The cash coupon is ($100,000*0.05)/2 = $2,500. Note that while the coupon rate is stated as an annual percentage, the cash coupon payments are made on a semiannual basis.

Question ID: 22348

Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows?

A. Conversion privilege.

B. Sinking fund provisions.

C. Fixed coupon rate.

D. Callable bond.

Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: (1) increased credit risk, (2) the presence of embedded options (i.e., call/put features

4 or sinking fund provisions), (3) the use of variable rather than fixed coupon rate, and (4) the presence of a conversion or exchange privilege.

Question ID: 22349

Which of the following characteristics would create the most difficulty in estimating a bond's cash flows?

A. Exchange privilege.

B. Noncallable bond.

C. Fixed coupon rate.

D. High credit quality bond.

Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: (1) increased credit risk, (2) the presence of embedded options (i.e., call/put features or sinking fund provisions), (3) the use of variable rather than fixed coupon rate, and (4) the presence of a conversion or exchange privilege.

Question ID: 22347

Which of the following characteristics would create the least difficulty in estimating a bond’s cash flows?

A. Exchange privilege.

B. Variable coupon rate.

C. Noncallable bond.

D. Putable bond.

Normally, estimating the cash flow stream is straightforward for a high quality, option-free bond due to the high degree of certainty in the timing and amount of the payments. The following four conditions could lead to difficulty in forecasting the bond’s future cash flow stream: (1) increased credit risk, (2) the presence of embedded options (i.e., call/put features or sinking fund provisions), (3) the use of variable rather than fixed coupon rate, and (4) the presence of a conversion or exchange privilege.

5 Question ID: 13014

What value would an investor place on a 20-year, 10 percent annual coupon bond, if the investor required an 11 percent rate of return?

A. $945.

B. $1,035

C. $920.

D. $879.

C N = 20, I/Y = 11, PMT = 100, FV = 1000, CPT PV Question ID: 13024

A coupon bond that pays interest annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10 percent. What is the intrinsic value of the bond today if the coupon rate is 8 percent?

A. $924.18.

B. $1,000.00.

C. $1,500.00.

D. $2,077.00.

A FV=1000

PMT=80

Compute PV=924.18.

Question ID: 13012

Using the following spot rates for pricing the bond, what is the present value of a three-year security that pays a fixed annual coupon of 6 percent?

Year 1: 5.0%

6 Year 2: 5.5% Year 3: 6.0%

A. 100.00.

B. 100.10.

C. 102.46.

D. 95.07.

B This value is computed as follows:

Present Value = 6/1.05 + 6/1.0552 + 106/1.063 = 100.10

The value 95.07 results if the coupon payment at maturity of the bond is neglected.

Question ID: 13020

A coupon bond that pays interest annually has a par value of $1,000, matures in 5 years, and has a yield to maturity of 10 percent. What is the intrinsic value of the bond today if the coupon rate is 12 percent?

A. $1,000.00.

B. $1,075.82.

C. $2,077.00

D. $650.00.

B FV=1000

PMT=120

PV=1,075.82.

Question ID: 13017

7 An investor purchased a 6-year annual interest coupon bond one year ago. The coupon rate of interest was 10 percent and par value was $1,000. At the time she purchased the bond, the yield to maturity was 8 percent. The amount paid for this bond one year ago was:

A. $1,215.51.

B. $1,092.46.

C. $1,125.53.

D. $1,198.07.

PMT=(.10)(1000)=100

FV=1000

PV=1092.46

Question ID: 13026

Consider a bond that pays an annual coupon of 5 percent and that has three years remaining until maturity. Suppose the term structure of interest rates is flat at 6 percent. How much does the bond price change if the term structure of interest rates shifts down by 1 percent instantaneously.?

A. -2.67.

B. 3.76.

C. 2.67.

D. 0.00.

C This value is compute as follows:

Bond Price Change = New Price – Old Price = 100 – (5/1.06 + 5/1.062 + 105/1.063 = 2.67.

8 -2.67 is the correct value but the wrong sign. The value 0.00 is incorrect because the bond price is not insensitive to interest rate changes.

Question ID: 13031

Deep discount bonds have:

A. greater price volatility than bonds selling at par.

B. less call protection than bonds selling at par.

C. less coupon protection than bonds selling at par.

D. greater reinvestment risk than bonds selling at par.

Question ID: 13029

A year ago a company issued a bond with a face value of $1,000 an 8 percent coupon. Now the prevailing market yeild is 10 percent. What happens to the bond? The:

A. bond is traded at a market price higher than $1,000.

B. company has to issue a new 2-percent coupon bond.

C. bond price is not affected by the change in market yield, and will continue to trade at $1,000.

D. bond is traded at a market price of less than $1,000.

Question ID: 13039

A 5-year bond with a 10 percent coupon has a present yield to maturity of 8 percent. If interest rates remain constant one year from now, the rice of the bond will be:

A. higher.

B. cannot be determined.

C. lower.

D. the same.

Consider a bond that pays an annual coupon of 5 percent and that has three years remaining until maturity. Assume the term structure of interest rates is flat at 6 percent. How much does the bond price change over the next twelve-month interval if the term structure of interest rates does not change?

A. -0.56.

B. 0.00.

C. 0.84.

D. -0.84.

C The bond price change is computed as follows:

Bond Price Change = New Price – Old Price = (5/1.06 + 105/1.062) - 5/1.06 + 5/1.062 + 105/1.063 = 0.84.

The value -0.84 is the correct price change but the sign is wrong. The value 0.00 is incorrect because although the term structure of interest rates does not change the bond price increases since it is selling at a discount relative to par.

Question ID: 13035

A discount bond (nothing changes except the passage of time)

A. price is not related to time passing.

B. has a steady value as time passes.

C. falls in value as time passes.

D. rises in value as time passes.

Question ID: 13033

If market rates do not change, as time passes the price of a zero-coupon bond will:

A. move randomly about the purchase price.

B. approach par.

10 C. approach zero.

D. approach the purchase price.

Question ID: 13045

If the required rate of return is 12 percent, what is the value of a zero coupon bond with a face value of $1,000 that matures in 20 years?

A. $99.33.

B. $175.30.

C. $202.67.

D. $103.67.

D I=12

FV=1,000

PV=103.67

Question ID: 13040

What is the value of a zero-coupon bond if the term structure of interest rates is flat at 6 percent and the bond has two years remaining to maturity?

A. 88.85.

B. 100.00.

C. 83.75.

D. 91.76.

11 The bond price is computed as follows:

Zero-Coupon Bond Price = 100/1.034 = 88.85.

The value 83.75 is incorrect because the principal is discounted over a three-year period but the bond has only two years remaining to maturity. The value 100.00 is incorrect because the principal received at maturity has to be discounted over a period of two years.

Question ID: 13043

A 15-year zero coupon bond that has a par value of $1,000 and a required return of 8 percent would be priced at:

A. $464.

B. $308.

C. $315.

D. $555.

C N=15

FV=1,000

PV=315.24

Question ID: 13046

What is the accrued interest for a 5 percent coupon bond that that pays coupons semi- annually assuming that there are 84 days remaining until the next coupon payment and that 182 days in the coupon period?

A. $2.6923.

B. $1.3462.

C. $1.1538.

D. $1.2764.

12 B The amount is calculated as follows:Accrued Interest = (182 – 84)/182 x $5/2 = $1.3462.

The value $1.1538 is incorrect because 84 days instead of 182 minus 84 days is used in the formula. The value $2.6923 is incorrect because this would result for a semi-annual coupon of 5% which is, however, the annual coupon rate.

Question ID: 13050

A coupon bond is reported as having an ask price of 113 percent of the $1,000 par value. If the last interest payment was made two months ago and the coupon rate is 12 percent, the invoice price of the bond will be:

A. $1,200.

B. $1,150.

C. $1,400.

D. $1,300.

B (1.13)(1000)+2(120/12)=1,130+20=1,150 Question ID: 22350

An investor gathers the following information about a 2-year bond:

· Semiannual coupon rate of 6%

· 180 days in the coupon period

· 86 days between the settlement and the next coupon payment date

The dirty price of the bond is closest to:

A. $10,156.

B. $10,000.

C. $4,778.

D. $9,844.

The first step is to find the appropriate fractional payment period (w), w=86/180=0.4778. The easiest way to compute the dirty price on your financial calculator is to add up the present values of each of the four cash flows:

N=0.4778, I/Y=3, FV=300, PMT=0: Compute PV=295.79.

N=3.4778, I/Y=3, FV=10,300, PMT=0: Compute PV=9,293.77.

The present sum of the cash flows is $10,155.55.

Question ID: 22351

The use of a single discount rate to value all of a bond's cash flows assumes:

A. a flat term structure.

B. an upward sloping term structure.

C. a downward sloping term structure.

D. an unknown yield curve.

The use of a single discount factor (i.e., YTM) to value all of a bond’s cash flows assumes a flat term structure. This means that the interest rate is the same across all maturities, a very rare occurrence in reality.

Question ID: 13051

An amortizing security has two years remaining to maturity with a par value of $100,000 , a coupon rate of 6 percent, its expected cash flow per year is $26,765.98, and there are no prepayments. Using the following term structure of interest rates, what is the price of this security?

One-year rate: 6.5% Two-year rate: 7.0%

A. $49,645.53.

14 B. $49,072.55.

C. $48,393.38.

D. $48,510.82.

D The present value is computed as follows:Present Value = $26,765.98/1.065 + $26,765.98/1.072 = $48,510.82

The value $48,393.38 is incorrect because the two-year interest rate is used to discount both cash flows. The value $49,072.55 is incorrect because the coupon rate is used in order to discount the cash flows.

Question ID: 22352

Assume the term structure of interest rates is upward sloping. In this situation, will the use of a single discount rate in a bond valuation model, most likely lead to a mispricing?

A. Yes, the single factor rate will merely be a weighted average of a set of spot rates.

B. Yes, however, more mispricing will occur if a series of spot rates that reflect the current term structure are used in the valuation.

C. No, the bond model will be properly priced.

D. It depends on whether the slope of the term structure is steep or gradually rising.

The use of a single discount factor (i.e., YTM) to value all of a bond’s cash flows assumes a flat term structure. Unless the term structure is actually flat, the use of single discount rate will result in a mispricing of the bond.

Question ID: 22353

Which of the following approaches in determining the discount factor will lead to more accurate bond pricing when the term structure is upward sloping? The:

A. arithmetic average of the spot interest rates.

B. use of a single discount factor.

C. geometric average of the spot interest rates.

15 D. use of a series of spot interest rates that reflect the current term structure.

The use of multiple discount rates (i.e., a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in so doing, will eliminate any meaningful arbitrage opportunities. That is why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.

Question ID: 22354

The arbitrage-free bond valuation approach can best be described as the:

A. geometric average of the spot interest rates.

B. use of a single discount factor.

C. arithmetic average of the spot interest rates.

D. use of a series of spot interest rates that reflect the current term structure.

The use of multiple discount rates (i.e., a series of spot rates that reflect the current term structure) will result in more accurate bond pricing and in so doing, will eliminate any meaningful arbitrage opportunities. That is why the use of a series of spot rates to discount bond cash flows is considered to be an arbitrage-free valuation procedure.

Question ID: 13052

Which of the following packages of securities is equivalent to a three-year 8 percent coupon bond with semi-annual coupon payments? A three-year zero-coupon bond:

A. and six 8 % coupon bonds with a maturity equal to the time to each coupon payment of the above bond.

B. with a par of 100 and six zero-coupon bonds with a par value of 8 and maturities equal to the time to each coupon payment of the coupon bond.

C. with a par of 100 and six zer-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

D. with a par of 100 and six zero-coupon bonds with a par value of 4 and maturities equal to the time to each coupon payment of the coupon bond.

16 This combination of zero-coupon bonds has exactly the same cash flows as the above coupon bond and therefore it is equivalent to it. Question ID: 22355

An investor gathers the following information about three U.S. Treasury annual coupon bonds:

Bond #1 Bond #2 Bond #3 Maturity 2-year 1-year 2-year Price $10,000 $476.19 $9,500 Coupon 5% 0% 0% Par Value $10,000 $500 $10,500 Misvaluation $0 $0 ?

If bond price converge to their arbitrage-free value, what should happen to the price of bond #3?

A. Selling pressure should increase its value.

B. Buying pressure should decrease its value.

C. Selling pressure should decrease its value.

D. Buying pressure should increase its value.

Currently, an arbitrage opportunity exists with the three bonds. An investor could purchase bonds #2 and #3 and sell bond #1 for an arbitrage-free profit of $23.81 (-10,000 + 476.19 + 9,500). This action will result in positive income today in return for no future obligation – an arbitrage opportunity. Hence, buying pressure on bond #3 should increase its value to the point where the arbitrage opportunity would cease to exist.

Question ID: 22357

Which of the following statements concerning arbitrage-free bond prices is FALSE?

A. Credit spreads are affected by time to maturity.

B. The riskier the bond, the greater is its credit spread.

C. It is not possible to strip coupons from U.S. Treasuries and resell them.

D. The determination of spot rates is usually done using risk-free securities.

It is possible to both strip coupons from U.S. Treasuries and resell them, as well as to aggregate stripped coupons and reconstitute them into U.S. Treasury coupon bonds. Therefore, arbitrage arguments ensure that U.S. Treasury securities sell at or very near their arbitrage free values. For valuing non-Treasury securities, a credit spread is added to each treasury spot yields. The credit spread is a function of default risk and the term to maturity.

Question ID: 22356

Which of the following statements concerning the arbitrage-free valuation of non-Treasury securities is TRUE? The credit spread is:

A. only a function of the volatility of past interest rates.

B. a function of default risk and the term to maturity.

C. only a function of the bond's default risk.

D. only a function of the bond's term to maturity.

For valuing non-Treasury securities, a credit spread is added to each treasury spot yields. The credit spread is a function of default risk and the term to maturity.

Question ID: 22359

Bond #1 Bond #2 Bond #3 Maturity 2-year 1-year 2-year Price $10,000 $374.62 $9,560 Coupon 4% 0% 0% Par Value $10,000 $400 $10,400

Given the above information, how can the investor generate an arbitrage profit?

A. Purchase bonds #2 and #3 while selling bond #1.

B. No arbitrage profit exists.

C. Purchase bond #1 while selling bonds #2 and #3.

D. Purchase bonds #1 and #3 while selling bond #2.

By purchasing bonds #2 and 3 and selling bond #1, the investor could obtain a arbitrage profit of $65.38 (10,000-374.62-9,560). This action will result in positive income today in return for no future obligation – an arbitrage opportunity. Notice that in year 1, the principal payment from bond #2 will cover the bond #1 coupon obligation. In year 2, the coupon payment and principal obligation for bond #1 will be covered by the principal payment from bond #3

Question ID: 13053

Assume that there are no transaction costs and that securities are infinitely divisible. If an 8 percent coupon paying bond (with semi-annual coupon payments) that has six months left to maturity trades at 97.54, and there is a zero-coupon bond with six months remaining to maturity that is correctly priced using a discount rate of 9 percent, is there an arbitrage opportunity?

A. Yes, the coupon bond price is too high.

B. Yes, the coupon bond price is too low.

C. The coupon bond is not correctly priced but no arbitrage trade can be set up using the zero-coupon bond.

D. No, the coupon bond is correctly priced.

B The coupon bond has a cash flow at maturity of 104, which discounted at 9% results in a bond price of 99.52. Therefore, the bond is underpriced. An arbitrage trade can be set up by short-selling 1.04 units of the zero-coupon bond at 99.52 and then using the proceeds to buy 1.02 units of the coupon bond. The arbitrage profit at maturity calculated as follows:

Arbitrage Profit = 1.02 x 104 – 1.04 x 100 = $2.08

Question ID: 22358

Bond #1 Bond #2 Bond #3 Maturity 2-year 1-year 2-year Price $10,000 $384.62 $9,660 Coupon 4% 0% 0%

19 Par Value $10,000 $400 $10,400

Given the above information, how can the investor generate an arbitrage profit?

A. Purchase bond #1 while selling bonds #2 and #3.

B. Purchase bonds #1 and #3 while selling bond #2.

C. Purchase bonds #2 and #3 and selling bond #1.

D. No arbitrage profit exists.

By purchasing bond #1 and selling bonds #2 and #3, the investor could obtain an arbitrage profit of $44.62 (-10,000+384.62+9,660). This action will result in positive income today in return for no future obligation – an arbitrage opportunity. Notice that in year 1, the coupon payments from bond #1 will cover the bond #2 par value obligation. In year 2, the coupon payment and principal payment from bond #1 will cover the bond #3 obligation.

Question ID: 22360

Which of the following features is NOT common to embedded option bond valuation models?

A. Develop a fundamental model to derive a single discount factor.

B. Estimate the volatility of interest rates.

C. Develop rules for the exercise for the embedded options.

D. Develop an interest rate tree of future interest rates.

Generally, models that can handle embedded options (i.e., callable, putable) have the following five characteristics: (1) a fundamental model to derive estimates of treasury spot rates, (2) ability to estimate the volatility of interest rates, (3) development of an interest rate tree of future rates, (4) model probabilities are set such that the model correctly predicts the current treasury bond price, and (5) development of rules for the exercise of the embedded options.

Question ID: 13055

How does the valuation of a callable bond differ from the option-free bond valuation method? To price the callable bond:

20 A. a lower duration has to be used.

B. the term structure of interest rates used has to be shifted down by the price of the option as a proportion of the option-free bond price.

C. the term structure of interest rates used has to be shifted up by the price of the option as a proportion of the option-free bond price.

D. different possible future interest rate paths have to be considered.

D Different future interest rate paths have to be considered in order to determine how likely it is the bond is going to be called and to determine the bond present value under such a scenario.

The duration of a bond is not used to price it.

Question ID: 22361

Which of the following features is common to embedded option bond valuation models?

A. Develop an interest rate tree of future interest rates.

B. Assume firms will not exercise embedded call options.

C. Develop a fundamental model to derive a single discount factor.

D. Assume no volatility in future interest rates.

Generally, models that can handle embedded options (i.e., callable, putable) have the following five characteristics: (1) a fundamental model to derive estimates of treasury spot rates, (2) ability to estimate the volatility of interest rates, (3) develop an interest rate tree of future rates, (4) model probabilities are set such that the model correctly predicts the current treasury bond price, and (5) develop rules for the exercise of the embedded options.

Question ID: 13027

Suppose the term structure of interest rates makes an instantaneous parallel upward shift of 100 basis points. Which of the following securities experiences the largest change in value? A five-year:

A. coupon bond with a coupon rate of 6%.

B. floating rate bond.

21 C. coupon bond with a coupon rate of 5%.

D. zero-coupon bond.

D The duration of a zero-coupon bond is equal to its time to maturity since the only cash flows made is the principal payment at maturity of the bond. Therefore, it has the highest interest rate sensitivity among the four securities.

A floating rate bond is incorrect because the duration, which is the interest rate sensitivity, is equal to the time until the next coupon is paid. So this bond has a very low interest rate sensitivity.

A coupon bond with a coupon rate of 5% is incorrect because the duration of a coupon paying bond is lower than a zero-coupon bond since cash flows are made before maturity of the bond. Therefore, its interest rate sensitivity is lower.

Question ID: 13034

A 10 percent, 10-year bond is selling at par. If interest rates do not change, how much will the bond be selling for in 2 years?

A. more than par.

B. cannot be determined.

C. par.

D. less than par.

Question ID: 13047

The clean price of a bond is $98.65 and the accrued interest is $1.23. What is the dirty price of the bond?

A. $97.42.

B. $99.88.

C. $98.65.

D. $100.00.

22 The accrued interest has to be added to the clean price of the bond in order to get the dirty price. Question ID: 13025

A bond with a 12 percent coupon, 10 years to maturity and selling at 88 has a YTM of:

A. over 14%.

B. between 13% and 14%.

C. between 10% and 12%.

D. between 12% and 13%.

PMT = 120, N = 10, PV = 880, FV = 1000

Compute I = 14.3

Question ID: 13013

What value would an investor place on a 20-year, 10 percent annual coupon bond, if the investor required a 10 percent rate of return?

A. $1,000.

B. $920.

C. $1,052.

D. $1,104.

Question ID: 13018

A bond with a face value of $1,000 pays a semi-annual coupon of $60. It has 15 years to maturity and a yield to maturity of 16 percent per year. What's the value of the bond?

A. $774.84.

B. $697.71.

C. $832.88.

D. $943.06.

23 A FV=1000

PMT=60

PV= 774.84

Question ID: 13008

It is easier to value bonds than to value equities because:

A. there is no maturity value for common stock.

B. the required rate of return for bonds is more stable.

C. All of these choices are correct.

D. the future cash flows of bonds are more stable.

Question ID: 13030

The price and yield on a bond have:

A. sometimes positive and sometimes negative relation.

B. no relation.

C. positive relation.

D. inverse relation.

Question ID: 13044

A zero-coupon bond has a yield to maturity of 9.6 percent and a par value of $1,000. If the bond matures in 10 years, today's price of the bond would be:

A. $422.41.

24 B. $399.85.

C. $483.49.

D. $512.23.

B I=9.6

FV=1,000

PV=399.85

Question ID: 13041

What is the yield to maturity(YTM)of a 20-year, U.S. zero-coupon bond selling for $300?

A. 7.20%.

B. 6.11%.

C. 3.06%.

D. 5.90%.

B n=40, PV=300, FV=1000, compute i=3.055*2=6.11.

1.B: Yield Measures, Spot Rates, and Forward Rates Question ID: 13057

A 6-year annual interst coupon bond was purchased one year ago. The coupon rate is 10 percent and par value is $1,000. At the time the bond was bought, the yield to maturity (YTM) was 8 percent. If the bond is sold after receiving the first interest payment and the bond's yield to maturity had changed to 7 percent, the annual total rate of return on holding the bond for that year would have been:

A. 9.95%.

25 B. 7.00%.

C. 8.00%.

D. 11.95%.

D Price 1 year ago N=6, PMT=100, FV=1000, I=8, Compute PV=1092

Price now N=5, PMT=100, FV=1000, I=7, Compute PV=1123

% Return=(1123.00 흍 1092.46)/1092.46 x 100=11.95%

Question ID: 13056

An investor purchased a 6-year annual interest coupon bond one year ago. The coupon interest rate was 10 percent and the par balue was $1000. At the time he purchased the bond, the yield to maturity was 8 percent. If he sold the bond after receiving the first interest payment and the yield to maturity continued to be 8 percent, his annual total rate of return on holding the bond for that year would have been:

A. 8.00%

B. 6.00%

C. 9.95%

D. 7.82%

Purchase price N = 6, PMT = 100, FV = 1000, I = 8 compute PV = 1092.46

Sale price N = 5, PMT = 100, FV = 1000, I = 8 compute PV = 1079.85

% ruturn 1079.85 - 1092.46 x 100 = = +100 8% 1092.46

Question ID: 13062

26 A bond has a par value of $1,000, a time to maturity of 20 years, a coupon rate of 10% with interest paid annually, a current price of $850, and a yield to maturity (YTM) of 12 percent. If the interest payments are reinvested at 10 percent, the realized compounded yield on this bond is:

A. 10.00%.

B. 10.9%.

C. 12.0%.

D. 12.4%.

The realized yield would have to be between the reinvested rate of 10% and the yield to maturity of 12%.

Question ID: 13059

If an investor holds a bond for a period less than the life of the bond, the rate of return the investor can expect to earn is called:

A. promised yield.

B. expected return, or horizon return.

C. approximate yield.

D. bond equivalent yield.

Question ID: 13070

A 20-year, 10 percent semi-annual coupon bond selling for $925 has a promised yield to maturity(YTM)of:

A. 10.93%.

B. 11.23%.

C. 10.64%.

D. 9.23%.

27 N = 40, PMT = 5, PV = -925, FV = 1000, CPT I/Y. Question ID: 13087

A $1,000 bond with an annual coupon rate of 10 percent has 10 years to maturity and is currently priced at $800. What is the bond's approximate yield-to-maturity?

A. 11.7%.

B. 12.6%.

C. 13.8%.

D. 10.5%.

FV = 1000, PMT = 100, N = 10, PV = 850

Compute I = 13.8

Question ID: 13063

What is the current yield for a 5 percent three-year bond whose price is $93.19?

A. 5.37%.

B. 4.94%.

C. 5.00%.

D. 2.68%.

The current yield is computed as follows:

Current yield = 5% x 100 / $93.19 = 5.37%

Question ID: 13093

The yield to call is a less conservative yeild measure whenever the price of a callable bond i quoted at a value:

A. equal to par value less one year's interest.

B. more than par.

C. equal to or greater than par value plus one year's interst.

28 D. equal to par value.

Question ID: 13090

An 11 percent coupon bond, annual payment, 10 years to maturity is callable in 3 years at a call price of $1,000. If the bond is selling today for 4975, the yield to call is:

A. 10.26%.

B. 14.97%.

C. 10.00%.

D. 9.25%.

PMT = 110, N = 3, FV = 1,110, PV = 975

Compute I = 14.97

Question ID: 13068

A 20-year, 9 percent semi-annual coupon bond selling for $1,000 offers a yield of:

A. 10%.

B. 11%.

C. 9%.

D. 8%.

Question ID: 13080

Which of the following statements concerning the current yield is CORRECT? It:

A. is of great interest to aggressive bond investors seeking capital gains.

B. shows the rate of return an investor will receive by holding a bond to maturity.

C. can be deteremined by dividing coupon income by the face value of a bond.

29 D. is of great interest to conservative bond investors seeking current income.

Question ID: 13067

A 20-year, 9 percent semiannual coupon bond selling for $1,098.96 offers a yield of:

A. 11%

B. 8%.

C. 10%

B N = 20, PMT = 90, PV = -1098.96, FV = 1000, CPT I/Y Question ID: 13084

The current yield on a bond is equal to:

A. annual interest divided by the current market price.

B. the yield to maturity.

C. the internal rate of return

D. annual interest divided by the par value.

Question ID: 13079

A coupon bod which pays interest $100 annually hasa par value of $1,000, matures in 5 years, and is selling today at a $72 discount from par value. The yield to maturity on this bond is:

A. 7.00%

B. 9.00%

C. 12.00%

D. 8.33%

PMT = 100

FV = 1000

PV = 1000 - 72 = 928 compute I = 11.997% or 12.00%

Question ID: 13099

Which of the following statements concerning the yield-to-maturity on a bond is CORRECT? Yield to maturity (YTM) is:

A. based on the assumption that any payments recieved are reinvested at the current yield.

B. always larger than current yield of the bond.

C. the discount rate that will set the present value of the payments equal to the bond price.

D. below the current yield minus capital gain when the bond sells at a discount, and above the current yield plus capital loss when the bond sells at a premium.

Question ID: 13096

Which bond valuation measure takes into consideration both interest income and price appreciation?

A. yield to coupon

B. current return.

C. yield to maturity.

D. holding period yield.

A bond will sell at a discount when the coupon rate is:

A. greater than the current yield and the current yield is greater than the yield to maturity.

B. greater than the yield to maturity.

C. less than the current yield and the current yield is greater than the yield to maturity.

D. less than the current yield and the current yield is less than the yield to maturity.

Question ID: 13104

If the promised yield is equal to the realized yield then:

A. current yield is lesser than the yield to maturity.

B. promised yield is greater than current yield.

C. the coupon payments are reinvested at the promised yield during the life of the issue.

D. nominal yield is smaller than the promised yield.

Question ID: 22319

An investor purchases a 4-year, 6 percent, semiannual-pay Treasury note for $9,485. The security has a par value of $10,000. To realize a total dollar return equal to 7.515 percent (its yield to maturity), the investor must have which of the following reinvestment assumptions?

A. All payments must be reinvested at less than 7.515%.

B. Total dollar return is unaffected by the reinvestment assumption.

C. All payments must be reinvested at more than 7.515%.

D. All payments must be reinvested at 7.515%.

32 The reinvestment assumption that is embedded in any present value-based yield measure implies that all coupons and principal payments must be reinvested at the specific rate of return, in this case, the yield to maturity. Thus, to obtain a 7.515% total dollar return, the investor must reinvest all the coupons at a 7.515% rate of return. Total dollar return is made up of three sources, coupons, principal, and reinvestment income.

Question ID: 13103

Which of the following is an incorrect statement when zero-coupon bonds are compared to coupon-paying bonds with the same maturity? Zero coupon bonds:

A. have a higher duration.

B. are sold at a lower price.

C. have a higher convexity.

D. are less sensitive to interest rate changes.

D Since zero-coupon bonds have a higher duration than coupon-paying bonds of the same maturity, they are more sensitive to interest rate changes. Question ID: 13111

If the coupon payments are reinvested at the coupon rate during the life of the issue, then the:

A. yield to maturity cannot be determined from the information given.

B. yield to maturity is greater than the realized yeild.

C. nominal yield declines.

D. yield to maturity is less than the realized yield.

Question ID: 22322

All else being equal, which of the following bond characteristics will lead to higher levels of coupon reinvestment risk?

A. Longer maturities and lower coupon levels.

B. Shorter maturities and higher coupon levels.

C. Longer maturities and higher coupon levels.

33 D. Shorter maturities and lower coupon levels.

Other things being equal, the amount of reinvestment risk embedded in a bond will increase with higher coupons, because there is a greater dollar amount to reinvest, and longer maturities because the reinvestment period is longer.

Question ID: 22323

All else being equal, which of the following bond characteristics will lead to lower levels of coupon reinvestment risk?

A. Shorter maturities and higher coupon levels.

B. Longer maturities and lower coupon levels.

C. Shorter maturities and lower coupon levels.

D. Longer maturities and higher coupon levels.

Other things being equal, the amount of reinvestment risk embedded in a bond will decrease with lower coupons because the there will be a lesser dollar amount to reinvest and shorter maturities because the reinvestment period is shorter.

Question ID: 22324

The yield to maturity for a semiannual-pay, 10-year corporate bond is 5.25 percent. What is the bond's annual equivalent yield?

A. C. 5.25%.

B. D. It is not possible to determine from the data given.

C. A. 5.32%.

D. B. 5.00%.

The annual equivalent yield is equal to [1+(nominal yield/number of payments per year)]number of payments per year –1 = (1+0.0525/2)2-1=5.32%.

What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yield to maturity of 12.51 percent?

A. A. 12.14%.

B. D. 12.51%.

C. B. 12.00%.

D. C. 11.49%.

The semiannual-pay bond equivalent yield of an annual-pay bond = 2*[(1 + yield to maturity on the annual-pay bond)0.5 – 1]=12.14%.

Question ID: 13112

The yield to maturity on an annual-pay bond 5.6 percent, what is the bond equivalent yield for this bond?

A. 5.43%.

B. 5.60%.

C. 5.52%.

D. 11.20%.

The bond-equivalent yield is computed as follows:

Bond-equivalent yield = 2[(1 + 0.056)0.5 – 1] = 5.52% Question ID: 13112

The yield to maturity on an annual-pay bond 5.6 percent, what is the bond equivalent yield for this bond?

A. 5.60%.

B. 11.20%.

C. 5.43%.

D. 5.52%.

The bond-equivalent yield is computed as follows:

Bond-equivalent yield = 2[(1 + 0.056)0.5 – 1] = 5.52% Question ID: 22324

The yield to maturity for a semiannual-pay, 10-year corporate bond is 5.25 percent. What is the bond's annual equivalent yield?

A. C. 5.25%.

B. B. 5.00%.

C. D. It is not possible to determine from the data given.

D. A. 5.32%.

The annual equivalent yield is equal to [1+(nominal yield/number of payments per year)]number of payments per year –1 = (1+0.0525/2)2-1=5.32%.

Question ID: 22325

What is the semiannual-pay bond equivalent yield on an annual-pay bond with a yield to maturity of 12.51 percent?

A. C. 11.49%.

B. D. 12.51%.

C. B. 12.00%.

D. A. 12.14%.

The semiannual-pay bond equivalent yield of an annual-pay bond = 2*[(1 + yield to maturity on the annual-pay bond)0.5 – 1]=12.14%.

Question ID: 22328

An investor gathers the following information about a semiannual-pay, 6-year corporate bond:

36 - Current price is $875

- Par value of $1,000

- Coupon is 86 basis points over the London interbank offered rate (LIBOR)

- LIBOR is currently 9%

The corporate bond’s discount margin is closest to:

A. 3.06%.

B. 12.92%.

C. 9.00%.

D. 3.92%.

The bond has an expected coupon of $1,000 * (0.09+0.0086)/2 = 49.3. Solving for YTM with a hand-held calculator: N=12 (6*2), PMT=49.3, PV=-875, FV=1,000, compute I/Y=6.46*2 = 12.92%. Recall that the difference between the YTM and the reference rate is the discount margin. Hence, the discount margin = 12.92% - 9.00% = 3.92%.

Question ID: 22327

A floating-rate bond has a yield to maturity of 5.25 percent and pays 100 basis points over the London interbank offered rate (LIBOR). If LIBOR is currently 3.00 percent, the bond’s discount margin is closest to:

A. 2.25%.

B. 2.15%.

C. 4.25%.

D. 1.25%.

The difference between the yield to maturity and the reference rate is the discount margin. Hence, the discount margin = 5.25% - 3.00% = 2.25%.

An investor gathers the following information about a corporate bond:

- 4-year maturity

- Semiannual-pay

- Current price is $9,875

- Par value of $10,000

- Coupon is 225 basis points over the London Interbank Offered Rate (LIBOR)

- London interbank offered rate (LIBOR) is currently 6.15%

The corporate bond’s discount margin is closest to:

A. 1.76%.

B. 2.63%.

C. 8.78%.

D. 0.38%.

The bond has an expected coupon of $10,000 * (0.0615+0.0225)/2 = 420. Solving for YTM with a hand-held calculator: N=8 (4*2), PMT=420, PV=-9,875, FV=10,000, compute I/Y=4.39*2 = 8.78%. Recall that the difference between the YTM and the reference rate is the discount margin. Hence, the discount margin = 8.78% - 6.15% = 2.63%.

Question ID: 13119

The price of a two-year bond with annual coupon payments of 5 percent is $97.34. The one- year spot rate is 4.76 percent. What is the implied three-year spot rate?

A. 6.50%.

B. 6.23%.

C. 4.76%.

D. 5.00%.

The two-year spot rate is computed as follows:

Two-year spot rate = - 1 = 6.50%

97.34- 5 1.0476

Question ID: 13122

There is a one-year T-Bill yielding 10 percent and a two-year 11 percent annual coupon bond selling for $985. What is the two-year annualized spot rate?

A. 13.0%

B. 11.0%.

C. 12.5%.

D. 12.0%.

D [square root of 1110/885]-1 Question ID: 13120

The current 6-month T-Bill rate is 10 percent (5 percent semi-annually) and the one-year T- Bill rate is 11 percent (5.5 percent semi-annually). If there is an existing 1.5-year 12 percent coupon bond selling for $1,010 what is the annualized 1.5-year spot rate?

A. 12.00%

B. 12.30%

C. 11.30%.

D. 12.75%

C [[1060/(1010-57-54)].333-1](2) Question ID: 22329

An investor gathers the following information about a 2-year, annual-pay bond:

39 - Par value of $1,000

- Coupon of 4%

- 1-year spot interest rate is 2%

- 2-year spot interest rate is 5%

Using the above spot rates, the current price of the bond is closest to:

A. B. $1,000.

B. D. $990.

C. A. $983.

D. C. $1,010.

The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $40 (0.04*1,000). The bond price = 40/(1.02) + 1040/(1.05)2 = $982.53.

Question ID: 22330

An investor gathers the following information about a 3-year, annual-pay bond:

· Coupon of 8%

· Current price of $1,100

· 1-year spot interest rate is 5%

· 2-year spot interest rate is 6%

Using the above information, the 3-year spot rate is closest to:

A. A. 4.27%.

B. B. 8.00%.

40 C. C. 8.20%.

D. D. 4.37%.

The value of the bond is simply the present value of discounted future cash flows, using the appropriate spot rate as the discount rate for each cash flow. The coupon payment of the bond is $80 (0.08*1,000) and the face value is $1,000. Hence, bond price of 1100= 80/(1.05)+ 80/(1.06)2 + 1080/(1 + 3-year spot rate)3. Using the yx key on our calculator, we can solve for the 3-year spot rate of 4.27%.

Question ID: 13131

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 percent and the term structure is flat at 5.5 percent. Which of the following is the price of the bond assuming that it is called on the first call date?

A. $102.50.

B. $103.17.

C. $100.00.

D. $104.54.

The bond price is computed as follows:

Bond price = 6/1.055 + (102.50 + 6)/1.0552 = $103.17 Question ID: 22331

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 all cash flows can be discounted at the same rate.

B. assumes all coupon payments are reinvested to maturity.

C. is difficult to calculate.

D. assumes a flat yield curve.

41 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).

Question ID: 22333

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. a flat yield curve.

C. a downward sloping yield curve.

D. all coupon payments are reinvested at a rate equal to the risk free rate.font>

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).

Question ID: 22332

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 assumes:

A. all coupon payments are reinvested at the yield to maturity.

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

C. an upward sloping yield curve.

D. all cash flows can be discounted at the same rate.

42 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).

Question ID: 22334

Which of the following best describes the zero-volatility bond spread?

A. Issuer's yield to maturity plus the yield to maturity of a Treasury security.

B. The constant required spread added to each of the Treasury spot rates in a term structure.

C. Issuer's yield to maturity assuming zero volatility in future interest rates.

D. Issuer's yield to maturity minus the yield to maturity of a Treasury security.

The zero-volatility spread is the constant required spread added to each of the Treasury spot rates in a given Treasury term structure. The zero-volatility spread is based upon arbitrage- free spot rates rather than the given yield to maturity, making it more accurate than the nominal spread.

Question ID: 22335

Which of the following statements correctly illustrates a major difference between the zero- volatility spread (Z-spread) and the nominal spread for bonds? The:

A. nominal spread is an issuer's yield to maturity minus each Treasury spot rate in a given Treasury term structure.

B. Z-spread is an issuer's yield to maturity minus the yield to maturity of a Treasury security.

C. nominal spread is more accurate since it is based upon the arbitrage-free spot rates.

D. Z-spread is more accurate since it is based upon the arbitrage-free spot rates.

43 The zero-volatility spread is the constant required spread added to each of the Treasury spot rates in a given Treasury term structure.. Since the zero-volatility spread is based upon arbitrage-free spot rates rather than the given yield to maturity, it is believed to be more accurate than the nominal spread. The nominal spread is simply an issuer’s YTM minus the YTM of a Treasury security of similar maturity.

Question ID: 13138

A non-treasury bond has a zero-volatility spread of 1 percent and pays annual coupons of 5 percent with two years remaining to maturity. Using the following spot rates, what is the price of the bond?

One-year spot rate: 4.5% Two-year spot rate: 5.5%

A. $99.12.

B. $97.31.

C. $100.00.

D. $97.22.

The bond price is computed as follows:

Bond price = 5/1.055 + 105/1.0652 = $97.31 Question ID: 22337

To compute the zero-volatility bond spread, which of the following steps is needed?

A. Assume a flat term structure to obtain the bond's yield to maturity.

B. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate spread.

C. Calculate the value of the bond's embedded options.

D. Set the present value of the bond's cash flows equal to the bond's call price.

To compute the Z-spread, set the present value of the bond’s cash flows equal to today’s market price, not the call price. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate, or static spread (SS). By solving for the SS component, you have

44 the Z-spread. Notice that this spread is obtained by trial-and-error, not a hand-held calculator. Recall that you use the zero-volatility spread for bonds that do not contain embedded options.

Question ID: 22338

To compute the zero-volatility bond spread, which of the following steps is NOT needed?

A. Calculate the value of the bond's embedded options.

B. Set the present value of the bond's cash flows equal to today's price.

C. Solve for the fixed rate spread using trial and error.

D. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate spread.

To compute the Z-spread, set the present value of the bond’s cash flows equal to today’s market price. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate, or static spread (SS). By solving for the SS component, you have the Z-spread. Notice that this spread is obtained by trial-and-error, not a hand-held calculator. Recall that you use the zero-volatility spread for bonds that do not contain embedded options.

Question ID: 22336

To compute the zero-volatility bond spread, which of the following steps is NOT needed?

A. Solve for the fixed rate spread using trial and error.

B. Make cash flow adjustments for embedded bond call options.

C. Set the present value of the bond's cash flows equal to today's price.

D. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate spread.

To compute the Z-spread, set the present value of the bond’s cash flows equal to today’s market price. Discount each cash flow at the appropriate zero coupon bond spot rate plus a fixed rate, or static spread (SS). By solving for the SS component, you have the Z-spread. Notice that this spread is obtained by trial-and-error, not a hand-held calculator. Recall that you use the zero-volatility spread for bonds that do not contain call options.

Question ID: 24164

45 An analyst gathered the following information on a U.S. corporate bond:

- 5 years until maturity - 12 percent yield to maturity (YTM) - 10 percent yield to maturity on 5-year U.S. Treasury Security - Nominal spread is 200 basis points

Why should the bond’s zero-volatility spread (Z-spread) differ from its nominal spread?

The bond’s Z-spread:

A. will always be less than its nominal spread.

B. is the spread over each of the spot rates in a given Treasury structure, not simply the spread over the Treasury's YTM.

C. is always equal to the nominal spread for the same bond.

D. will always be greater than its nominal spread.

The nominal spread is the issue’s YTM minus the YTM of a Treasury security of similar maturity. The Z-spread is the spread not over the Treasury’s YTM but over each of the spot rates in a given Treasury term structure. In other words, the Z-spread is the same spread added to all risk-free spot rates. The Z-spread is inherently more accurate (and will usually differ from) the nominal spread, since it is based upon arbitrage-free spot rates, rather than the issue’s YTM.

Question ID: 24170

An analyst gathered the following information on a U.S. corporate bond:

· 8 years until maturity · 14 percent yield to maturity (YTM) · 13 percent yield to maturity on 8-year U.S. Treasury Security · Zero-volatility spread of 167 basis points

The difference between the bond’s zero-volatility spread (Z-spread) and its nominal spread is the closest to which of the following?

A. 100 basis points.

B. 167 basis points.

46 C. 0 basis points.

D. 67 basis points.

The nominal spread is the issue’s YTM minus the YTM of a Treasury security of similar maturity. In this case, the nominal spread is 100 basis points (14% - 13%). The Z-spread is the spread not over the Treasury’s YTM but over each of the spot rates in a given Treasury term structure. The Z-spread is 167 basis points. Hence, the difference between the two spreads is 67 basis points (167 basis points – 100 basis points).

Question ID: 24173

A U.S. corporate bond has a 10 percent yield to maturity (YTM) compared to a 9.55 percent YTM on a U.S. Treasury security of similar maturity. The bond has a 1.04 percent zero- volatility spread. Which of the following is the closest to the difference between the bond’s zero-volatility spread (Z-spread) and its nominal spread?

A. 59 basis points.

C. 45 basis points.

D. 900 basis points.

The nominal spread is the issue’s YTM minus the YTM of a Treasury security of similar maturity. In this case, the nominal spread is 45 basis points (10% - 9.55%). The Z-spread is the spread not over the Treasury’s YTM but over each of the spot rates in a given Treasury term structure. The Z-spread is 104 basis points. Hence, the difference between the two spreads is 59 basis points (104 basis points – 45 basis points).

Question ID: 22340

An investor gathers the following information on a callable corporate bond:

· Option-adjusted spread of 120 basis points

· Bond is call protected until 2005

· Maturity of 10-years

47 · Par value of $1,000,000

· Similar option-free bonds have a zero-volatility spread of 250 basis points

Given the above information, the cost of the embedded option is closest to:

A. 120 basis points.

C. It is not possible to determine from the data given.

D. 0 basis points.

For the exam, remember the following relationship between the zero-volatility spread (Z- spread), the option-adjusted spread (OAS), and the embedded option cost: Z-Spread – OAS = Option Cost in Percentage Terms. Hence, the option cost is 250 – 120 = 130 basis points.

Question ID: 22339

Which of the following best illustrates the relationship between the zero-volatility spread (Z- spread), the option-adjusted spread (OAS), and the embedded option cost?

A. Z-Spread + OAS = Option Cost in Percentage Terms.

B. Z-Spread - OAS = Option Cost in Percentage Terms.

C. OAS / Z-Spread = Option Cost in Percentage Terms.

D. Z-Spread / OAS = Option Cost in Percentage Terms.

The option adjusted spread (OAS) is used when a bond has embedded options. The OAS can be thought of as the difference between the Z-spread and the option cost. For the exam, remember the following relationship between the zero-volatility spread (Z-spread), the option- adjusted spread (OAS), and the embedded option cost: Z-Spread – OAS = Option Cost in Percentage Terms.

Question ID: 13141

48 There are two bonds:

 a two-year straight bond with a 5 percent coupon (paid annually)  a callable bond which is otherwise equivalent

The option adjusted spread over treasury rates is 2 percent for the callable bond. Using the following treasury spot rates, what is the value of the call option?

One-year rate: 5.5% Two-year rate: 6%

A. $94.67.

B. $98.19.

C. $2.65.

D. $3.52.

The option value is computed as the difference between the option free and the callable bond price. So we have:

Option free bond = 5/1.055 + 105/1.062 = $98.19 Callable bond = 5/1.075 + 105/1.082 = $94.67

So the option value is $98.19 - $94.67 = $3.52 Question ID: 24175

An analyst finds a callable, corporate bond with a very large zero-volatility spread value. The large zero-volatility spread value could be due to which of the following?

A. Only the option cost.

B. Only the option-adjusted spread.

C. Cannot be determined by the information provided.

D. Both the option-adjusted spread and the option cost.

A large Z-spread value can result from either the option adjusted spread (OAS) or the option cost. Therefore, a large Z-spread could be the result of a large option cost, implying that the

49 investor may not be receiving as much compensation for default, and other risks as might have initially been perceived.

Question ID: 24176

· 10-year maturity · Putable in two years · 8% coupon rate · Semiannual-pay · $10,000 par value

Given the information, which of the following statements regarding option-adjusted spread (OAS) and zero-volatility spread (Z-spread) are TRUE?

A. Cannot be determined by the information provided.

B. OAS = Z-spread.

C. OAS > Z-spread.

D. Z-spread > OAS.

For embedded long puts (i.e., putable bonds), the option value < 0. That means that the holder of the bond must pay for the option. Hence, the OAS will be greater than the Z-spread. In other words, you require less yield on a putable bond than for an option-free bond.

Question ID: 24178

· 10-year maturity · Callable in two years · 12% coupon rate · Annual-pay · $1,000 par value

Given the information, which of the following statements regarding option-adjusted spread (OAS) and zero-volatility spread (Z-spread) are TRUE?

A. OAS = Z-spread.

B. Cannot be determined with the information provided.

50 C. Z-spread > OAS.

D. Z-spread < OAS.

For callable bonds, the option value is greater than 0. That means that the holder of the bond receives compensation for writing the option to the issuer for the option. Hence, the Z-spread will be greater than the OAS. In other words, you require more yield on a callable bond than for an option-free bond.

Question ID: 13142

The one-year spot rate is 5 percent and the two-year spot rate is 6.5 percent. What is the one-year forward rate starting one year from now?

A. 5.00%.

B. 7.87%.

C. 8.00%.

D. 8.02%.

The forward rate is computed as follows:

One-year forward rate = 1.0652/1.05 – 1 = 8.02% Question ID: 22341

Which of the following statements regarding forward rates is FALSE?

A. Forward rates contain information regarding market participants' collective expectations regarding future interest rates.

B. Forward rates may be estimated from spot rates.

C. Forward rates do not account for the market's tolerance for risk.

D. By the aggregation of forward rates, spot rates can be estimated.

Spot interest rates are the result of market participant’s tolerance for risk and their collective view regarding the future path of interest rates. If we assume that these results are purely a

51 function of expectations, we can use spot rates to estimate the market’s consensus on forward interest rates.

Question ID: 13143

Given the 1-year annualized spot rate of 8.3 percent (4.15 semi-annually), and the 1.5-year spot rate of 8.93 percent (4.465 semi-annually), what is the implied six-month (1 period) rate one-year (2 half year periods) from now?

A. 4.5%.

B. 4.8%.

C. 4.2%.

D. 5.1%.

D [(1.04465)3/(1.0415)2]-1 Question ID: 13147

A downward sloping yield curve generally implies:

A. interest rates are expected to increase in the future.

B. interest rates are expected to decline in the future.

C. longer-term bonds are riskier than short-term bonds.

D. shorter-term bonds are less risky than longer-term bonds.

Question ID: 13146

If investors expect future rates will be higher than current rates, the yield curve should be:

A. vertical.

B. downward sweeping.

C. upward sweeping.

D. flat.

The current five-year spot rate is 7 percent and the six-year spot rate is 8 percent. What is the one-year forward rate in five years?

A. 11.30%.

B. 13.14%.

C. 14.56%.

D. 12.33%.

(1+f)(1+r5)5=(1+r6)6

(1+f)(1+0.07)5=(1+0.08)6

(1+f) = 1.5869.1.4026 f = 1.1314 - 1 = 13.14%

Question ID: 13154

Given the implied annual forward rates of: R1 = .06; 1r1 = .062; 2r1 = .063; 3r1 = .065, what is the theoretical 4-period spot rate?

A. 6.75%.

B. 6.00%.

C. 6.25%.

D. 6.50%.

C .25 R4 = [ (1.06) (1.062) (1.063) (1.065) ] - 1 = 6.25%. Question ID: 13155

The one-year spot rate is 6 percent and the one-year forward rates starting in one, two and three years respectively are 6.5 percent, 6.8 percent and 7 percent. What is the four-year spot rate?

A. 6.51%.

B. 7.00%.

53 C. 6.58%.

D. 6.57%.

The four-year spot rate is computed as follows:

Four-year spot rate = [(1 + 0.06)(1 + 0.065)(1 + 0.068)(1 + 0.07) ]1/4 –1 = 6.57% Question ID: 13156

Given the implied forward rates of: R1 = .04; 1r1 = .04300; 2r1 = .05098; 3r1 = .051005, what is the theoretical 4-period spot rate?

A. 6.67%.

B. 4.06%.

C. 4.62%.

D. 2.33%.

C [(1.04)(1.043)(1.05098)(1.051005)].25-1 Question ID: 13097

The yield to maturity is:

A. the discount rate that will set the present value of the payments equal to the bond price.

B. below the coupon rate when the bond sells at a discount, and about the coupon rate when the bond sells at a premium.

C. based on the assumption that any payments recieved are reinvested at the coupon rate.

D. none of these answers are correct.

Question ID: 13066

A 20-year, 9 percent semi-annual coupon bond selling for $914.20 offers a yield of:

A. 11.

54 B. 9%.

D. 10%.

D N = 20, PMT = 90, PV = -914.20, FV = 1000, CPT I/Y Question ID: 13088

A 20-year bond with a par value of $1,000 and an annual coupon rate of 6 percent currently trades at $850. It has a promised yield of:

A. 7.9%.

B. 6.8%.

C. 7.5%.

D. 9.6%.

N = 20, FV = 1000, PMT = 60, PV = 850

Compute I = 7.5

Question ID: 13071

A 30-year 10 percent annual coupon bond is sold at par. It can be called at the end of 10 years for $1,100. What is the bond's yield to call (YTC)?

A. 10.6%.

B. 10.2%.

C. 8.9%.

D. 10.0%.

A n=10, PMT=100, PV=1000, FV=1100, compute i=10.6. Question ID: 13058

An investor purchased a 10-year zero-coupon bond with a yield to maturity of 10 percent and a par value of $1,000. What would her rate of return be at the end of the year if she

55 sells the bond? Assume the yield to maturity on the bond is 9 percent at the time it is sold.

A. 15.00%.

B. 19.42%.

C. 16.00%.

D. 17.63%.

B Purchase price I=10, N=10, PMT=0, FV=1000, Compute PV=385.54

Selling price I=9, N=9, PMT=0, FV=1000, Compute PV=460.43

% Return=(460.43-385.54)/385.54 x 100=19.42%

Question ID: 13158

If the 6-month Treasury bill spot rate is 4.0 percent, and the 6-month forward rate 6 months from now is 6.0 percent, then the 1-year Treasury bill spot rate is:

A. 5.0%.

B. 3.0%.

C. 4.5%.

D. 5.5%.

{(1+0.04)(1+0.06)}?= (1+r1)

1.04995 = 1+r1 r1 = 5%

Question ID: 13159

If the current two-year spot rate is 6 percent while the one-year forward rate for one year is 5 percent, what is the current pot rate for one year?

A. 7%.

B. 6%.

C. 5%.

56 D. 5.5%.

2 (1+f)(1+r1) = (1+r2)

2 (1+05)(1+r1) = (1+.08)

1 2 (1+r1) = (1.06)

1+r1 = 1.1236/1.05

1+r1 = 1.0701

r1 = .07 or 7%

Question ID: 13060

A 10 percent coupon bond, annual payments, maturing in 10 years, is expected to make all coupon payments, but to pay only 50 percent of par value at maturity. What is the expected yield on this bond if the bond is purchased for $975?

A. 11.00%.

B. 10.68

C. 8.68%.

D. 6.68%.

PMT = 100, N = 10, FV = 500, PV = 975 compute I = 6.68

Question ID: 13085

A coupon bond that pays interest annually is selling at par, matures in 5 years, and has a coupon rate of 12 percent. The yield to maturity on this bond is:

A. 60.00%.

B. 12.00%.

C. 8.33%.

57 D. 6.00%.

PMT=120

PV=-1000

FV=1000

Compute I=12

Hint:the YTM equals the coupon rate when a bond is selling at par.

Question ID: 13073

To estimate the actual return of a bond when the bond's market price exceeds the bond's crossover price, use the:

A. HPY.

B. HPR.

C. YTC.

D. YTM.

1.C: Introduction to the Measurement of Interest Rate Risk Question ID: 24314

Which of the following approaches in measuring interest rate risk is most straightforward?

A. Convexity approach.

B. Duration approach.

C. Duration/convexity approach.

D. Full Valuation approach.

58 The most straightforward approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes.

Question ID: 13161

A bond pays a semi-annual coupon of 5 percent and has one year remaining to maturity. If the term structure of interest rates is flat but instantaneously shifts from 5 percent to 6 percent, how much does the bond price change?

A. -$0.96.

B. $0.00.

C. -$1.00.

D. $1.00.

The bond price change is computed as follows:

Bond price change = 2.5/(1 + 0.06/2) + 102.50/(1 + 0.06/2)2 – 100 = -0.96 Question ID: 24315

Which of the following steps is NOT used in the full valuation approach in measuring interest rate risk?

A. Recompute bond prices using the new required yields.

B. Compare resulting price changes.

C. Calculate the bond's convexity.

D. Estimate hypothetical changes in required yields.

The most straightforward approach method for measuring interest rate risk is the so-called full valuation approach. Essentially this boils down to the following four steps: (1) begin with the current market yield and price, (2) estimate hypothetical changes in required yields, (3) recompute bond prices using the new required yields, and (4) compare the resulting price changes.

An investor gathered the following information about two 7 percent annual-pay, option-free bonds:

 Bond R has 4 years to maturity and is priced to yield 6 percent  Bond S has 7 years to maturity and is priced to yield 6 percent  Both bonds have a par value of $1,000.

Given a 50 basis point parallel upward shift in interest rates, what is the value of the two- bond portfolio?

A. $2,044.

B. $2,086.

C. $2,030.

D. $2,138.

Given the shift in interest rates, Bond R has a new value of $1,017 (N = 4, PMT = 70, FV = 1,000, I/Y = 6.50%, CPT PV = 1,017). Bond S’s new value is $1,027 (N = 7, PMT = 70, FV = 1,000, I/Y = 6.50%, CPT PV = 1,027). After the increase in interest rates, the new value of the two-bond portfolio is $2,044 (1,017 + 1,027).

Question ID: 24326

A portfolio manager gathered the following information about three bond portfolios with identical maturities:

 Bond Portfolio G has a coupon of 4%  Bond Portfolio H has a coupon of 5%  Bond Portfolio I has a coupon of 6%  All bonds in the three portfolios are option-free

Which of the bond portfolios has the highest interest rate exposure?

A. Bond Portfolio I.

B. Bond Portfolio H.

C. Bond Portfolio G.

60 D. All three have equal interest rate exposure.

All else being equal, the lower the coupon, the greater the bond price volatility.

Question ID: 13162

An investor observes that a bond price changes 5 percent in response to a 1 percent fall in interest rates. What is the bond's effective duration?

A. +5.

B. -5.

C. -20.

D. +20.

Question ID: 24336

Which of the following bond portfolios is most difficult to apply the full valuation approach on? A bond portfolio with a:

A. small number of bonds with callable options attached.

B. large number of bonds that are option-free.

C. large number of bonds that are non-callable.

D. large number of bonds having embedded options.

The full valuation approach is difficult with a portfolio consisting of a large number of bonds because there are many tedious computations. This is especially true if the portfolio contains bonds with embedded options (i.e., putable, callable,...).

Question ID: 24409

An investor gathered the following information on 4 bond portfolios:

 Bond Portfolio F has 400 bonds, 300 of which are callable

61  Bone Portfolio G has 50 bonds, 40 of which are putable  Bond Portfolio H has 20 bonds, none of which have embedded options  Bond Portfolio I has 300 bonds, 45 of which have embedded options

Which of the portfolios is most difficult to apply the full valuation approach on?

B. Bond Portfolio F.

C. Bond Portfolio H.

D. Bond Portfolio G.

The full valuation approach is difficult with a portfolio consisting of a large number of bonds because there are many tedious computations. This is especially true if the portfolio contains bonds with embedded options (i.e., putable, callable,...). Bond Portfolio F has both the largest number of bonds and the largest number of embedded options.

Question ID: 24400

An investor gathered the following information on 4 different bond portfolios:

 Bond Portfolio F has 400 bonds, 200 of which are callable  Bond Portfolio G has 50 bonds, 40 of which are callable  Bond Portfolio H has 20 bonds, none of which have embedded options  Bond Portfolio I has 300 bonds, 75 of which have embedded options

Which of the portfolios is least difficult to apply the full valuation approach to?

B. Bond Portfolio G.

C. Bond Portfolio H.

D. Bond Portfolio F.

The full valuation approach is difficult with a portfolio consisting of a large number of bonds because there are many tedious computations. This is especially true if the portfolio contains

62 bonds with embedded options (i.e., putable, callable,...). Bond Portfolio H has both the smallest number of bonds and the fewest number of embedded options.

Question ID: 13163

Consider two bonds, A and B. Both bonds are presently selling at par. Each pays interest of $120 annually. Bond A will mature in 5 years while bond B will mature in 6 years. If the yields to maturity on the two bonds change from 12 percents to 10 percents, both bonds will:

A. increase in value, but bond A will increase more than bond B.

B. decrease in value, but bond B will decrease more than bond A.

C. increase in value, but bond B will increase more than bond A.

D. decrease in value, but bond A will decrease more than bond B.

Question ID: 13164

Which of the following bonds is likely to exhibit the greatest volatility due to interest rate changes? A bond with a:

A. low coupon and a short maturity.

B. low coupon and a long maturity.

C. high coupon and a long maturity.

D. high coupon and a short maturity.

Question ID: 13166

Holding other factors constant, the interest rate risk of a coupon bond is higher when the bond's:

A. yield to maturity is lower.

B. current yield is higher.

C. coupon rate is higher.

D. term to maturity is lower.

The convexity of a bond is affected as follows.

A. Inversley with maturity and the coupon.

B. Inversely with maturity.

C. Inversley with coupon.

D. Positively with yield.

Question ID: 13165

A 1 percent decline in yield will have the greatest effect on the price of the bond with a:

A. 10-year maturity, selling at 100.

B. 20-year maturity, selling at 100.

C. 20 -year maturity, selling at 80.

D. 10-year maturity, selling at 80.

Question ID: 13178

Can a fixed income security have a negative convexity?

A. No.

B. Need more information to answer question.

C. Yes, but only whenthe price yield curve is linear.

D. Yes.

Question ID: 17209

Which of the following bonds may have negative convexity:

A. All of these choices are correct.

64 B. Callable bonds.

C. High yield bonds.

D. Mortgage backed securities.

Question ID: 17210

At a market rate of 7 percent, a $1,000 callable par value bond is priced at $910, while a similar bond that is non-callable is priced at $960. What is the value of the embedded call option?

A. $40.

B. $50.

C. $90.

D. $30.

Question ID: 13176

How does the price-yield relationship for a callable bond compare to the same relationship for an option-free bond? The price-yield relationship is:

A. concave for low yields for the callable bond and always convex for the option-free bond.

B. the same for both bond types.

C. concave for the callable bond and convex for an option-free bond.

D. concave for an option-free bond and convex for a callable bond.

A Since the issuer of a callable bond has an incentive to call the bond when interest rates are very low in order to get cheaper financing, this puts an upper limit on the bond price for low interest rates and thus introduces the concave relationship between yields and prices. Question ID: 24379

An investor finds that for every 1 percent increase in interest rates, a bond’s price decreases by 4.21 percent compared to a 4.45 percent increase in value for every 1 percent decline in

65 interest rates. If the bond is currently trading at par value, the bond’s duration is closest to:

A. 86.60.

B. 4.33.

C. 8.66.

D. 43.30.

Duration is a measure of a bond’s sensitivity to changes in interest rates. Duration = (V- – V+)/[2V0(change in required yield)] where V- = estimated price if yield decreases by a given amount V+ = estimated price if yield increases by a given amount V0 = initial observed bond price Thus, duration = (104.45 – 95.79)/(2*100*0.01) = 4.33. Remember that the change in interest rates must be in decimal form.

Question ID: 24375

An international bond investor has gathered the following information on a 10-year, annual-pay U.S. corporate bond:

 Currently trading at par value  Annual coupon of 10%  Estimated price if rates increase 50 basis points is 96.99%  Estimated price is rates decrease 50 basis points is 103.14%

The bond’s duration is closest to:

A. 3.14.

B. 6.58.

C. 0.62.

D. 6.15.

Duration is a measure of a bond’s sensitivity to changes in interest rates. Duration = (V- – V+)/[2V0(change in required yield)] where V- = estimated price if yield decreases by a given amount V+ = estimated price if yield increases by a given amount V0 = initial observed bond price Thus, duration = (103.14-96.99)/(2*100*0.005) = 6.15. Remember that the change in interest rates must be in decimal form.

If bond prices fall 5 percent in response to a .5 percent increase in interest rates, what is the bond's effective duration?

A. -5.

B. +10.

C. +5.

D. -10.

B Approximate percentage price change of a bond = - (duration) (delta y) = 5 = - (duration) (.5) = 10. Question ID: 13190

The price of a bond is equal to $101.76 if the term structure of interest rates is flat at 5 percent. The following bond prices are given for up and down shifts of the term structure of interest rates. Using the following information what is the approximate percentage price change of the bond using only its effective duration?

Bond price: $98.46 if term structure of interest rates is flat at 6 percent Bond price: $105.56 if term structure of interest rates is flat at 4 percent

A. 0.174%.

B. 0.0087%.

C. 1.74%.

D. 0.87%.

The effective duration is computed as follows:

Effective duration = 105.56 - = 3.49 98.46 2 x 101.76 x 0.01

Using the effective duration, the approximate percentage price change of the bond is computed as follows:

Percent price change = -3.49 x (-0.005) x 100 = 1.74%

A bond has the following characteristics:

 A duration of 18 years  Maturity of 30 years  Modified duration of 16.9 years  Current yield to maturity is 6.5 percent

If the market interest rate decrease by 0.75 percent, what will be the percentage change in the bond's price?

A. 0.750%.

B. +0.750%.

C. -12.675%.

D. +12.675%.

Approximate percentage price change of a bond = (-)(duration)(Δy)

= (-16.9)(-.75%) = +12.675%

Question ID: 13187

Par value bond XYZ has a modified duration of 5. Which of the following statements regarding the bond is TRUE? If the market yield:

A. increases by 1% the bond's price will decrease by $60.

B. increases by 1% the bond's price will increase by $50.

C. increases by 1% the bond's price will decrease by $50.

D. decreases by 1% the bond's price will decrease by $45.

Approximate percentage price change of a bond = (-)(Duration)(Δy)

(-5)(1%) = -5%

($1000)(-.05) = $50

Using only duration to estimate the price change of a straight bond, how will the price estimate of the bond compare to the true bond price for a decrease in yield? The price estimate using duration is:

A. higher than the true bond price.

B. lower than the true bond price.

C. higher than the true bond price for large interest rate declines and lower for small declines.

D. the same as the true bond price.

B The duration concept does not account for the convexity in the price-yield relationship. Therefore, bond price estimates using duration will underprice the bond for both interest rate declines and interest rate increases. Question ID: 13197

The price volatility of a bond is a function of market interest rates and the bond's:

A. coupon rate.

B. price relative to its par value.

C. all of these choices are correct.

D. remaining term to maturity.

Question ID: 13195

The concept of duration and convexity assumes:

A. an upward sweeping yield curve.

B. parallel shifts in the yield curve.

C. the price yield curve is stable.

D. variable interest rates.

Which of the following is FALSE?

A. duration to first call is longer than duration to maturity.

B. option-adjusted duration cannot exceed duration to maturity.

C. convexity of a callable bond is always lower than that of a noncallable bond may either fall or rise.

D. callabe bonds' convexity can be negative.

Question ID: 24382

When calculating duration, which of the following bonds would an investor least likely use effective duration on rather than modified duration?

A. Putable bond.

B. Callable bond.

C. Convertible bond.

D. Option-free bond.

The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.

Question ID: 24384

An investor gathered the following information on two U.S. corporate bonds:

 Bond J is callable with maturity of 5 years  Bond J has a par value of $10,000  Bond M is option-free with a maturity of 5 years  Bond M has a par value of $1,000

For each bond, which duration calculation should be applied?

A. Bond J, Effective Duration; Bond M, Modified Duration.

B. Bond J, Modified Duration; Bond M, Modified Duration.

C. Bond J, Modified Duration; Bond M, Effective Duration.

D. Bond J, Effective Duration; Bond M, Effective Duration.

The duration computation remains the same. The only difference between modified and effective duration is that effective duration is used for bonds with embedded options. Modified duration assumes that all the cash flows on the bond will not change, while effective duration considers expected cash flow changes that may occur with embedded options.

Question ID: 24393

Which of the following explains why modified duration should NOT be used for bonds with call options? Modified duration assumes that the cash flows on the bond will:

A. be affected by a convertible bond.

B. not change.

C. be affected by a putable bond.

D. change with the bond's embedded options.

Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.

Question ID: 24391

Why should effective duration, rather than modified duration, be used when bonds contain embedded options?

A. Effective duration considers expected changes in cash flows.

B. Neither duration method should be used when embedded options are present.

C. Either could be used if the bond has embedded options.

71 D. Modified duration considers expected changes in cash flows.

Modified duration assumes that the cash flows on the bond will not change (i.e., that we are dealing with non-callable bonds). This greatly differs from effective duration, which considers expected changes in cash flows that may occur for bonds with embedded options.

Question ID: 13206

Effective duration is a better measure of price sensitivity to yield changes because it accounts for:

A. cash flow changes when yields change.

B. all of these choices are correct.

C. the availability of options embedded in the bond.

D. nonparallel yield curve shift.

Question ID: 24416

For which of the following situations is modified duration NOT a good approximation of price changes for non-callable bonds?

A. Modified duration can be used effectively for all interest rate changes.

B. Large change in interest rates.

C. Small change in interest rates.

D. No change in interest rates.

Modified duration is a good approximation of price changes for an option-free bond only for relatively small changes in interest rates. As rate changes grow larger, the curvature of the bond price/yield relationship becomes more prevalent. This implies that a linear estimate of price changes will contain errors. Modified duration is a linear estimate. That is, it assumes that the price change due to fluctuations in interest rates will be the same regardless of whether rates go up or down.

All of the following are limitations to Macaulay and modified duration EXCEPT:

A. duration assumes the yield curve is upward sloping.

B. duration assumes the yield curve will shift in a parallel fashion.

C. duration calculations assume bonds are non-callable.

D. duration estimates are only good for small changes in yields.

Question ID: 13211

A 5 percent semi-annual coupon bond has a Macaulay duration of 5.67 and a yield to maturity of 5.88 percent. What is it's modified duration?

A. 5.78.

B. 5.51.

C. 5.35.

D. 5.67.

The modified duration of the bond is computed as follows:

Modified duration = 5.67/(1 + 0.0588/2) = 5.51 Question ID: 13213

Which of the following statements is FALSE concerning the duration of a bond?

A. lower yields(YTMs) lead to a longer duration.

B. lower coupons result in a longer duration.

C. a longer duration means higher volatility.

D. shorter maturity means longer duration.

Question ID: 13216

73 In bond investment, duration refers to:

A. the half-life of a zero coupon bond.

B. a weighted average maturity of a portfolio of corporate bonds.

C. the point in the life of a bond when its yield-to-maturity exactly equals its expected yield.

D. a weighted average of the maturities of the cash flows from a bond's coupon and principal payments.

Question ID: 13214

Which of the following causes a decrease in duration?

A. an increase in coupon rate.

B. an increase in yield-to-maturity.

C. all of these choices are correct.

D. a decrease in time to maturity.

Question ID: 13215

Which of the following bonds would have a duration equal to their years to maturity?

A. Floating rate bonds.

B. Zero-coupon bonds.

C. Perpetuity bonds.

D. Par bonds.

Question ID: 24424

74 An investor gathered the following information on a U.S. corporate bond:

 Current price of $9,340  Par value of $10,000  Estimated price of $9,504 if yield decreases by 25 basis points  Estimated price of $9,181 if yield increases by 25 basis points

The bond’s convexity is closest to:

A. 42.8.

B. 85.6.

C. 4.3.

D. 5.0.

The approximate measure of convexity is as follows, Convexity = (V- + V+ - 2V0)/(2V0 * (change in required yield)2] where V- = estimated price if yield decreases by a given amount V+ = estimated price if yield increases by a given amount V0 = initial observed bond price Thus, convexity = [9,504 + 9,181 – (2*9,340)]/[2*9,340*(0.0025)2]=42.8. Remember that the change in interest rates must be in decimal form.

Setup Text:

Janice Brown, is a fixed income portfolio manager for a large investment house. On January 1, 2000, Brown is considering purchasing one of the 10-year AAA corporate bonds shown in Table 1. Prices are quoted as a percentage of par. Brown needs to reduce her cash position in her portfolio by purchasing some fixed income securities. She would like to analyze the behavior of some instruments under various interest rate scenarios that she deems likely.

Brown notes that the yield curve is currently flat at 5%. Unless otherwise stated, Brown assumes that yield curve shifts occur in an instantaneous and parallel manner.

Table 1 AAA Corporate Bond C Description Coupon (SA) Price Callable Call Price ABC due Jan. 1, 2009 6.00% 107.1767 Noncallable Not applicable XYZ due Jan. 1, 2009 6.20% 107.1767 Currently 109.00 Callable

75 Brown has noticed that for ABC there are also two other bond issues outstanding: a floating rate (FRN) and an inverse floating rate bond (IF). Their characteristics are shown in Table 2.

Table 2 Bond Characteristics for Floating Rate and Inverse Floating Rate Bond Description Coupon (SA) Type Callable Fabozzi Convexity ABC due Jan. 1, 2009 LIBOR Floating Rate Noncallable 0.475907198 ABC due Jan. 1, 2009 12% -LIBOR Inverse FloatingNoncallable 111.1977205 Rate

The price value of a basis point (PVBP) for the ABC Fixed rate bond shown in Table 1 is 748.6068. The ABC FRN has a PVBP of 0.4878.

Question ID: 20751

Brown wonders how the interest rate sensitivity of the coupon-paying ABC bond in Table 1 differs from the interest rate sensitivity of an otherwise equivalent zero-coupon bond. Which of the following is CORRECT? The interest rate sensitivity of the coupon-paying ABC bond is:

A. higher.

B. lower.

C. higher or lower.

D. the same.

B Since there is only one payoff at maturity for the zero-coupon bond and no interim cash flows, its price will be maximally affected by changing interest rates. The interest rate sensitivity of a bond is measured by its duration. A zero-coupon bond's duration is equal to its time to maturity. Question ID: 20751

Brown is now considering the effects of convexity in isolation. Of all the bonds in Tables 1 and 2 Brown wonders which would be the most likely to have the best convexity properties with respect to investing. Which of the following bonds has the most desirable convexity properties?

A. IF.

B. XYZ bond.

C. Fixed coupon ABC bond.

76 D. FRN.

A The IF will have the highest convexity of all the bonds. The higher the convexity the better for the investor. Question ID: 20751

Brown now begins analyzing the FRN in Table 2. Specifically, she would like to price the FRN immediately following a coupon payment. Which of the following is the closest to Brown's answer?

A. 107.18.

B. 100.00.

C. 98.55.

D. 97.56.

B At a coupon reset date, the floating rate bond is always equal to its par value since the coupon yield is the same as the discount rate used to price the bond. So the two rates cancel each other. Question ID: 13230

Suppose the price of a bond is equal to $101.76 if the term structure of interest rates is flat at 5 percent. The following bond prices are given for up and down shifts of the term structure of interest rates. Using the following information what is the effective convexity of the bond?

Bond price: $98.46 if term structure of interest rates is flat at 6 percent Bond price: $105.56 if term structure of interest rates is flat at 4 percent

A. 614.19.

B. 6.14.

C. 0.12.

D. 24.57.

The effective convexity is computed as follows:

Effective convexity = 105.56 + 98.46 - 2 x 101.76 = 2 x 101.76 x 0.012 24.57

An investor gathered the following information on a non-callable U.S. corporate bond:

 Current price of $1,090  Par value of $1,000  Annual coupon of 11%  Estimated price of $1,209 if yield decreases by 150 basis points  Estimated price of $987 if yield increases by 150 basis points

The bond’s convexity is closest to:

A. 44.

B. 16.

C. 33.

The approximate measure of convexity is as follows, Convexity = (V- + V+ - 2V0)/(2V0 * (change in required yield)2] where V- = estimated price if yield decreases by a given amount V+ = estimated price if yield increases by a given amount V0 = initial observed bond price Thus, convexity = [1,209 + 987 – (2*1,090)]/[2*1090*(0.015)2]= 32.6. Remember that the change in interest rates must be in decimal form.

Question ID: 24436

An investor gathered the following information about an option-free U.S. corporate bond:

 Par Value of $10 million  Convexity of 45  Duration of 7

If interest rates increase 2 percent (200 basis points), the bond’s percentage price change is closest to:

A. -1.4%.

78 B. -14.0%.

C. -12.2%.

D. -15.8%.

Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration * (change in yields)] plus [convexity * (change in yields)2] = (-7)(0.02) + (45)(0.02) 2 = -12.2%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

Question ID: 13236

Assume that a straight bond has a duration of 1.89 and a convexity of 15.99. If interest rates decline by 1 percent what is the total estimated percentage price change of the bond?

A. 1.56%.

B. 1.89%.

C. 15.99%.

D. 2.05%.

The total percentage price change estimate is computed as follows:

Total estimated price change = -1.89 x (-0.01) x 100 + 15.99 x (-0.01)2 x 100 = 2.05% Question ID: 24428

A bond’s duration is 4.5 and its convexity is 43.6. If interest rates rise 100 basis points, the bond’s percentage price change is closest to:

A. -3.91%.

B. -4.94%.

C. -4.50%.

D. -4.06%.

79 Recall that the percentage change in prices = Duration effect + Convexity effect = [-duration * (change in yields)] plus [convexity * (change in yields)2] = (-4.5)(0.01) + (43.6)(0.01) 2 = -4.06%. Remember that you must use the decimal representation of the change in interest rates when computing the duration and convexity adjustments.

Question ID: 24443

Macaulay’s duration can be converted into modified duration by:

A. subtracting Macaulay's duration by [1+yield/2].

B. multiplying Macaulay's duration by [1+yield/2].

C. dividing Macaulay's duration by [(1+yield)*2].

D. dividing Macaulay's duration by [1+yield/2].

The only reason that we have modified duration is that the original Macaulay’s duration had a flaw in it and needed to be modified by dividing by [1+yield/2].

Question ID: 24440

Which of the following best describes the difference between modified convexity and effective convexity?

A. There is no such thing as modified convexity.

B. Effective convexity should never be used on putable bonds.

C. Effective convexity should never be used on callable bonds.

D. There is no such thing as effective convexity.

There is no such thing as modified convexity. Effective convexity is the same as standard convexity, except that it considers expected cash flows that may occur for bonds with embedded options. The only reason that we have the term modified duration is that the original Macaulay’s duration had a flaw in it and needed to be modified by dividing by [1+yield/2].

Question ID: 24446

One major difference between standard convexity and effective convexity is:

80 A. effective convexity reflects any change in estimated cash flows due to embedded bond options.

B. standard convexity reflects any change in estimated cash flows due to embedded options.

C. effective convexity is Macaulay's duration divided by [1+yield/2].

D. effective convexity is Macaulay's duration multiplied by [1+yield/2].

The calculation of effective convexity requires an adjustment in the estimated bond values to reflect any change in estimated cash flows due to the presence of embedded options. Note that this is the same process used to calculate effective duration.

Question ID: 24453

Which of the following statements regarding interest rate risk is FALSE?

A. A bond's maturity will impact its interest rate risk.

B. Expected yield volatility plays a role in a bond's expected interest rate risk.

C. Duration provides a complete measure of a bond's interest rate risk.

D. A bond's coupon rate will impact its interest rate risk.

Duration alone does not provide a complete measure of a bond’s interest rate risk: expected yield volatility is also an important determinant of a bond’s expected interest rate risk. Thus, duration tells only part of a bond’s interest rate risk measure.

Question ID: 24451

Which of the following statements regarding interest rate risk for bonds is FALSE?

A. Duration alone provides only part of a bond's interest rate risk.

B. A bond's maturity determines part of its interest rate risk.

C. Expected yield volatility plays no role in a bond's expected interest rate risk.

D. A bond's coupon rate determines part its interest rate risk.

81 Duration alone does not provide a complete measure of a bond’s interest rate risk: expected yield volatility is also an important determinant of a bond’s expected interest rate risk. Thus, duration tells only part of a bond’s interest rate risk measure.

Question ID: 24455

Which of the following statements regarding interest rate risk is TRUE?

A. A bond's maturity determines all of its interest rate risk.

B. Duration alone provides only part of a bond's interest rate risk.

C. A bond's coupon rate determines all its interest rate risk.

D. Expected yield volatility plays no role in a bond's expected interest rate risk.

Duration alone does not provide a complete measure of a bond’s interest rate risk: expected yield volatility is also an important determinant of a bond’s expected interest rate risk. Thus, duration tells only part of a bond’s interest rate risk measure.

Question ID: 13200

For a given yield and maturity, a bond with a lower coupon rate also has a convexity that is:

A. more variable.

B. less variable.

C. lower.

D. greater.

Question ID: 13217

Which of the following bond portfolio strategies would an analyst recommend if he believes that the market interest rate is about to fall? Sell the:

A. shorter duration bonds and buy those with longer duration

B. longer duration bonds and buy those with shorter duration.

C. longest duration bonds and buy those with even longer duration.

D. shortest duration bonds and buy those with even shorter duration.

Question ID: 17207

Negative convexity is most likely to be observed in:

A. callable bonds.

B. treasury bonds.

C. municipal bonds.

D. zero coupon bonds.

Question ID: 13177

How does the price-yield relationship for a putable bond compare to the same relationship for an option-free bond? The price-yield relationship is:

A. concave for an option-free bond and convex for a putable bond.

B. more convex at some yields for the putable bond than for the option-free bond.

C. the same for both bond types.

D. more convex for a putable bond than for an option-free bond.

B Since the holder of a putable has an incentive to exercise his put option if yields are high and the bond price is depressed, this puts a lower limit on the price of the bond when interest rates are high. The lower limit introduces a higher convexity of the putable bond compared to an option-free bond when yields are high. Question ID: 13191

James Walters, CFA, is an active fixed income portfolio manager. He manages a portfolio of fixed income securities worth$7,500,000 for an institutional client. Walters expects a widening yield spread between intermediate and long term securities. He would like to capitalize on his expectations and considers several transactions in a number of different securities. On 01/31/98, Walters expects the yield of the 2-Year Treasury Note to decrease by 10 basis points and the yield of the 30-Year Treasury Bond to increase by 11 basis points. The characteristics of these two fixed income securities are shown in Table 1. Prices

83 are quoted as a percentage of par value and the Price Value of a Basis Point is per $1 million par amount. Table 1 Security Characteristics - 2-Year T-Note 30-Year T- Bond Maturity 01/31/00 11/15/27 Bid-Ask Spread (basis points) 5.0 5.0 Coupon 5.375% 6.125% Bid Price 99.7236 104.6086 Ask Price 99.7736 104.6586 Yield to Maturity 5.51% 5.80% Price Value of a Basis Point 186.6484 1461.1733

He also has the three year term structure of interest rates. This is shown in Table 2.

Table 2 Term Structure of Interest Rates Year Spot Rate 0.50 5.5227% 1.00 5.5537% 1.50 5.5444% 2.00 5.5205% 2.50 5.5114% 3.00 5.5156%

Walters thinks of several different trading strategies that would allow him to take advantage of his expectations. He would like to evaluate each strategy to determine which offers the best risk-return tradeoff.

James wants to translate the estimated price change into a change in value of a position in a particular security. What is the best estimate of the change in value of a $100,000 principal position in Treasury Notes if yields change by -10 basis points?

A. $18.66.

B. $0.19.

C. $186.65.

D. $1,866.48.

84 The change in value is computed as follows:

Change in ValueT-Note = Price Value of a Basis Point/10 x (-Yield Change)

So we have

Price ChangeT-Bond = 186.6484/10 x ( -10 bp) = $186.65

Question ID: 13208

A 6 percent, 5-year government bond is priced to yield 7 percent. The Macaulay duration for this bond is 2.07. The bond's modified duration is:

A. 2.17.

B. 2.00.

C. 1.93.

D. 1.83.

Modified duration = 2.07/1+.07

= 2.07/1.07 = 1.93

Setup Text:

Janice Brown, is a fixed income portfolio manager for a large investment house. On January 1, 2000, Brown is considering purchasing one of the 10-year AAA corporate bonds shown in Table 1. Prices are quoted as a percentage of par. Brown needs to reduce her cash position in her portfolio by purchasing some fixed income securities. She would like to analyze the behavior of some instruments under various interest rate scenarios that she deems likely.

Brown notes that the yield curve is currently flat at 5%. Unless otherwise stated, Brown assumes that yield curve shifts occur in an instantaneous and parallel manner.

Table 1 AAA Corporate Bond C Description Coupon (SA) Price Callable Call Price ABC due Jan. 1, 2009 6.00% 107.1767 Noncallable Not applicable XYZ due Jan. 1, 2009 6.20% 107.1767 Currently 109.00 Callable

85 Brown has noticed that for ABC there are also two other bond issues outstanding: a floating rate (FRN) and an inverse floating rate bond (IF). Their characteristics are shown in Table 2.

Table 2 Bond Characteristics for Floating Rate and Inverse Floating Rate Bond Description Coupon (SA) Type Callable Fabozzi Convexity ABC due Jan. 1, 2009 LIBOR Floating Rate Noncallable 0.475907198 ABC due Jan. 1, 2009 12% -LIBOR Inverse FloatingNoncallable 111.1977205 Rate

The price value of a basis point (PVBP) for the ABC Fixed rate bond shown in Table 1 is 748.6068. The ABC FRN has a PVBP of 0.4878.

Question ID: 13192

Brown would like to estimate the new price of the ABC bond in Table 1 if interest rates shift up by 100 basis points. Using the given information only, which of the following is the closest to the new price of the ABC bond?

A. 101.83

B. 100.10.

C. 100.00.

D. 99.69.

D The new bond price is computed as follows:

New Bond Price = Original Bond Price - [Original Bond Price x Modified Duration x (yield shift in basis points x 0.0001)]

So we have

New Bond Price =107.1767 - 107.1767 x 6.9848 x (100 bp x 0.0001) = 99.69

Question ID: 13192

Brown would now like to consider the affect that convexity will have on her estimated price of the ABC bond when interest rates increase by 100 bps. Which of the following is a possible price of the ABC bond when convexity is considered?

A. 104.99.

86 B. 107.18.

C. 100.01.

D. 99.69.

C This is the only value that makes sense because it is more that just the duration estimated price with an adjustment that is less in magnitude than the price change from the duration.

The exact price estimate is computed as follows (even though convexity was not given in the problem):

New Bond Price = Original Bond Price - [Original Bond Price x Modified Duration x (yield shift in basis points x 0.0001)] + [0.5 x Fabozzi Convexity x Original Bond Price x (yield shift in basis points x 0.0001)2]

So we have

New Bond Price = 107.1767 - 107.1767 x 6.9848 x (100 bp x 0.0001) + 0.5 x 59.5438 x 107.1767 x (100 bp x 0.0001)2 = 100.01

Question ID: 13192

Continuing her analysis of the FRN in Table 2 Brown wants to carry out the same analysis for the FRN as for the corresponding fixed rate bond in Table 1. She has to compute the duration of the bond. What is the Macaulay duration of the FRN immediately following a coupon payment?

A. 6.98.

B. 7.16.

C. 0.49.

D. 0.50.

D Macaulay duration of a floating rate bond is equal to the time until the next coupon reset date. Question ID: 13229

Convexity is more important when rates are:

A. high.

B. stable.

87 C. depends on whether the note is selling at a premium or a discount.

D. low.

2: Discounted Cash Flow Applications Question ID: 23703

A Treasury bill has 40 days to maturity, a par value of $10,000, and is currently selling for $9,900. Its effective annual yield is closest to:

A. 1.01%.

B. 9.60%.

C. 1.00%.

D. 9.00%.

The effective annual yield (EAY) is an annualized number based on a 365-day year that accounts for compound interest. EAY=(1+holding period yield)365/t-1. The holding period yield formula is (price received at maturity – initial price + interest payments)/(initial price) = (10,000-9,900+0)/(9,900) = 1.01%. EAY = (1.0101)365/40 – 1 = 9.60%.

Question ID: 23701

A Treasury bill has 40 days to maturity, a par value of $10,000, and was just purchased by an investor for $9,900. Its holding period yield is closest to:

A. 1.00%.

B. 1.01%.

C. 9.37%.

D. 9.00%.

The holding period yield is the return that the investor will earn if the bill is held until it matures. The holding period yield formula is (price received at maturity – initial price + interest

88 payments)/(initial price) = (10,000-9,900+0)/(9,900) = 1.01%. Recall that when buying a T-bill, investors pay the face value less the discount and receive the face value at maturity.

Question ID: 19390

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the bank discount yield?

A. 5.41%.

B. 5.14%.

C. 2.04%.

D. 4.18%.

The bank discount yield takes the dollar discount from par and expresses it as a fraction of the bond’s face value. It is based on a 360-day year.

(2,000/100,000) x (360/140) = 0.0514, or 5.14%.

Question ID: 19391

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the holding period yield?

A. 4.08%.

B. 2.04%.

C. 5.25%.

D. 5.14%.

The holding period yield is the return the investor will earn if the T-bill is held to maturity. HPY = (100,000 – 98,000)/98,000 = 0.0204, or 2.04%.

Question ID: 23700

A Treasury bill with a face value of $1,000,000 and 45 days until maturity is selling for $987,000. The Treasury bill’s bank discount yield is closest to:

A. 10.40%.

89 B. 5.20%.

C. 10.54%.

D. 7.90%.

The bank discount yield is computed by the following formula, r=(dollar discount/face value)*(360/number of days until maturity)= [(1,000,000-987,000)/(1,000,000)]*(360/45)= 10.40%.

Question ID: 23706

A Treasury bill has 90 days until its maturity and a holding period yield of 3.17 percent. Its effective annual yield is closest to:

A. 12.68%.

B. 3.17%.

C. 13.49%.

D. 13.30%.

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY=(1+HPY)365/t-1 = (1.0317) 365/90-1 = 13.49%.

Question ID: 23708

An investor has just purchased a Treasury bill for $99,400. If the security matures in 40 days and has a holding period yield of 0.604 percent, what is its money market yield?

A. 5.569%.

B. 5.512%.

C. 5.650%.

D. 5.436%.

90 The money market yield is the annualized yield on the basis of a 360-day year and does not take into account the effect of compounding. The money market yield = (holding period yield) (360/number of days until maturity) = (0.604%)(360/40) = 5.436%.

Question ID: 19395

The holding period yield for a T-Bill maturing in 110 days is 1.90 percent. What are the equivalent annual yield (EAY) and the money market yield (MMY)?

A. EAY MMY 6.90% 6.80%

B. EAY MMY 6.44% 6.22%

C. EAY MMY 5.25% 5.59%

D. EAY MMY 5.80% 5.41%

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. (1+0.0190)365/110 -1 = 1.06444 – 1 = 6.44%. Using the HPY to compute the money market yield = HPY x (360/t) = 0.0190 x (360/110) = 0.06218 = 6.22%.

Question ID: 19394

The equivalent annual yield (EAY) for a T-bill maturing in 150 days is 5.04 percent. What are the holding period yield (HPY) and money market yield (MMY) respectively?

A. HPY MMY 5.25% 2.04%

B. HPY MMY 2.04% 4.90%

C. HPY MMY 1.90% 3.80%

D. HPY MMY 2.80% 5.41%

91 The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. Deannualizing to find the HPY = (1+0.0504)150/365 = 1.2041 – 1 = 2.04%. Using the HPY to compute the money market yield = HPY x (360/t) = 0.0204 x (360/150) = 0.04896 = 4.90%.

Question ID: 23705

A Treasury bill, with 80 days until maturity, has an effective annual yield of 8.00 percent. Its holding period yield is closest to:

A. 8.00%.

B. 1.75%.

C. 1.72%.

D. 1.70%.

The effective annual yield (EAY) is equal to the annualized holding period yield (HPY) based on a 365-day year. EAY=(1+HPY)365/t-1. HPY=(EAY+1)t/365 –1 = (1.08)80/365 –1 = 1.70%.

Question ID: 23709

A 10-year zero-coupon bond has a face value of $10,000 and a yield to maturity of 7.50 percent. The current value of the bond is closest to:

A. $10,000.

B. $4,852.

C. $6,920.

D. $4,789.

The value of a zero coupon bond is (face value)/(1+ yield to maturity/2)N, where N is the number of semiannual compounding periods to maturity. Price = (10,000)/(1.0375)20 = $4,788.92. Or, N=20, I/Y = 3.75%, PMT = 0, FV= 10,000, CPT PV = 4,788.92. Zero coupon bonds are typically based on semiannual periods.

Question ID: 19396

A zero-coupon bond with 4 years to maturity has a yield to maturity (YTM) of 6.0 percent.

92 What is the intrinsic value of the bond?

A. $789.41.

B. $744.09.

C. $660.00.

D. $886.42.

Remember semi-annual compounding means 8 semi-annual periods. P = Par Value(1 + (YTM/2))-N = $1000 (1.03)-8 = $1000 x 0.78941 = $789.41.

Question ID: 23712

If a 3-year zero-coupon bond ($10,000 face value) has a yield-to-maturity of 8.90 percent, the value of the bond is closest to:

A. $7,743.

B. $7,679.

C. $7,701.

D. $10,000.

The value of a zero coupon bond is (face value)/(1+ yield to maturity/2)N, where N is the number of semiannual compounding periods to maturity. Price = (10,000)/(1.0445)6 = $7,701. Or, N=3*2=6, I/Y = 8.9/2=4.45, PMT = 0, FV= 10,000, CPT PV = $7,701. Zero coupon bonds are typically based on semiannual periods.

Question ID: 23710

If a 5-year zero-coupon bond has a price of $750 and a par value of $1,000, its yield to maturity is closest to:

A. 5.84%.

B. 11.67%.

C. 5.92%.

D. 2.92%.

The price of a zero coupon bond is equal to (face value)/(1+ yield to maturity/2)N, where N is the number of semiannual compounding periods to maturity. Yield to maturity = [(Face Value/Price)1/N –1]*2 = [(1,000/750)1/10 – 1]*2= 5.84.

Or, N=10, PV = -750, PMT = 0, FV= 1,000, CPT I/Y = 2.9186 *2 = 5.84%. Zero coupon bonds are typically based on semiannual periods. Question ID: 19398

A graph of zero-coupon bond rates versus the term to maturity is called the:

A. spot yield curve.

B. forward yield curve.

C. future yield curve.

D. current yield curve.

The yield to maturity on a zero-coupon represents the present yield for that time horizon and is called the spot interest rate. The graph of spot rates versus term to maturity is called the spot yield curve.

Question ID: 23719

Which of the following statements regarding zero-coupon bonds and spot interest rates is TRUE?

A. If the yield to maturity on a 2-year zero coupon bond is 6%, then the 2-year spot rate is 3%.

B. Spot interest rates will never vary across the term structure.

C. All zero-coupon bonds have at least two coupon payments.

D. Price appreciation creates all of the zero-coupon bond's return.

Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a

94 single cash flow to be received in the future. If the yield to maturity on a 2-year zero is 6%, we can say that the 2-year spot rate is 6%.

Question ID: 23717

Which of the following statements regarding zero-coupon bonds is TRUE?

A. Zero-coupon bonds have substantial amount of coupon reinvestment risk.

B. An investor who holds a zero-coupon bond until maturity will receive an annuity of coupon payments.

C. An investor who holds a zero-coupon bond until maturity will receive a return equal to the bond's effective annual yield.

D. An investor who holds a zero-coupon bond until maturity will receive an annuity of coupon payments plus recovery of principal at maturity.

Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. An investor who holds a zero-coupon bond until maturity will receive a return equal to the bond’s effective annual yield.

Question ID: 23721

Which of the following statements regarding zero-coupon bonds and spot interest rates is FALSE?

A. Spot interest rates will never vary across the term structure.

B. Zero-coupon bonds have no coupons.

C. A graph of spot rates versus term to maturity is called the spot yield curve.

D. Price appreciation creates all of the zero-coupon bond's return.

Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a single cash flow to be received in the future. A graph of spot rates versus term to maturity is called the spot yield curve.

Which of the following statements regarding spot rates and zero-coupon bonds is FALSE?

A. The graph of current corporate bond yields is called the spot yield curve.

B. An investor who holds a zero coupon bond to maturity will receive a realized return equal to the bond’s equivalent annual yield.

C. With zero coupon bonds, investors have no reinvestment risk.

D. The yield to maturity on a zero coupon bond is called the spot interest rate.

The graph of yields on zero-coupon bonds (spot rates) is called the spot yield curve. Note that the return on zero-coupon bonds is based entirely on price appreciation. An investor in a default-free zero-coupon bond will not have to worry about reinvesting coupons to realize the yield to maturity – the holder will receive a realized return equal to the bond’s effective annual yield.

Question ID: 23729

Which of the following statements regarding zero-coupon bonds and spot interest rates is TRUE?

A. Zero-coupon bonds have at least two coupon payments.

B. Price appreciation creates only some of the zero-coupon bond's return.

C. A coupon bond can be viewed as a collection of zero-coupon bonds.

D. Spot interest rates will never vary across time.

Zero-coupon bonds are quite special. Because zero-coupon bonds have no coupons (all of the bond’s return comes from price appreciation), investors have no uncertainty about the rate at which coupons will be invested. Spot rates are defined as interest rates used to discount a single cash flow to be received in the future. Any bond 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.

Question ID: 23731

Can spot interest rates be used to value a mortgage-backed security?

96 A. Yes, as long as interest rates are not expected to increase in the future.

B. It depends on the slope of the term structure.

C. No.

D. Yes.

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 prepayments.

Question ID: 23730

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

A. Yes.

B. Yes, however spot interest rates cannot be used to value a putable bond.

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

D. No.

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.

Question ID: 19400

A three-year bond with an 8 percent coupon has a yield to maturity of 9 percent. Current spot rates are as follows:

1-Year: 6.5%

97 2-Year: 7.0%

3-Year: 9.2%

Using the arbitrage-free valuation approach, should the bond be purchased at $980.00? (assume annual, rather than semi-annual interest payments).

A. Yes, the bond is undervalued by approximately $15.42.

B. No, the bond is overvalued by approximately $18.60.

C. No, the bond is overvalued by approximately $5.60.

D. Yes, the bond is undervalued by approximately $24.50.

The arbitrage-free valuation approach values each cash flow, each cash flow is discounted at the appropriate spot rate to find the present value. Discount each annual payment:

Year 1 PV = 80/1.065 = $75.12

Year 2 PV = 80/(1.07)2 = $69.88.

Year 3 PV = 1080/(1.092)3 = $829.38

Arbitrage-free value of the bond = (75.12 + 69.88 + 829.38) = $974.38. The bond is overvalued by approximately $5.60.

Question ID: 23743

An investor gathered the following information on three zero-coupon bonds:

· 1-year, $600 par, zero-coupon bond valued at $571 · 2-year, $600 par, zero-coupon bond valued at $544 · 3-year, $10,600 par, zero-coupon bond valued at $8,901

Given the above information, how much should an investor pay for a $10,000 par, 3-year, 6 percent, annual-pay coupon bond?

A. $10,016.

B. $10,600.

C. Cannot be determined by the information provided.

98 D. $10,000.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the three zero-coupon bonds. Hence, the value of the 3-year annual-pay bond should be $10,016 (571 + 544 + 8,901).

Question ID: 19401

Current spot rates are as follows:

1-Year: 6.5%

2-Year: 7.0%

3-Year: 9.2%

Which of the following is TRUE?

A. The yield to maturity for 3-year annual pay coupon bond can be found by taking the geometric average of the 3 spot rates.

B. The yield to maturity for 3-year annual pay coupon bond can be found by taking the arithmetic average of the 3 spot rates.

C. For a 3-year annual pay coupon bond, all cash flows can be discounted at 9.2% to find the bond’s arbitrage-free value.

D. For a 3-year annual pay coupon bond, the first coupon can be discounted at 6.5%, the second coupon can be discounted at 7.0%, and the third coupon plus maturity value can be discounted at 9.2% to find the bond’s arbitrage- free value.

Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year’s payment. Note that the yield to maturity is the bond’s internal rate of return that equates all cash flows to the bond’s price. Current spot rates have nothing to do with the bond’s yield to maturity.

Question ID: 23744

99 An investor gathered the following information on two zero-coupon bonds:

· 1-year, $800 par, zero-coupon bond valued at $762 · 2-year, $10,800 par, zero-coupon bond valued at $9,796

Given the above information, how much should an investor pay for a $10,000 par, 2-year, 8 percent, annual-pay coupon bond?

A. $10,000.

B. $11,600.

C. $10,558.

D. $9,796.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The value of the coupon bond should simply be the summation of the present values of the two zero-coupon bonds. Hence, the value of the 2-year annual-pay bond should be $10,558 ($762 + $9,796).

Question ID: 23733

· 1-year, $200 par, zero-coupon bond valued at $190 · 2-year, $200 par, zero-coupon bond valued at $178 · 3-year, $10,200 par, zero-coupon bond valued at $8,811

Which of the following best substitutes for the combination of the three zero-coupon bonds?

A. 3-year, $20,000 pay, 2% coupon, annual-pay bond.

B. 3-year, $10,000 par, 2% coupon, annual-pay bond.

C. 3-year, $10,000 pay, 4% coupon, semiannual-pay bond.

D. 6-year, $10,000 par, 2% coupon, annual-pay bond.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The cash flows from the three listed zero-coupons will be identical to the cash flows received by an investor with a 3-year, par value of $10,000, 2% annual-pay coupon bond.

An investor has determined the following information for a 5-year U.S. corporate semiannual bond:

· Par value is $10,000 · Coupon Rate is 14 percent · Current Price is $9,400 · Yield to Maturity of Comparable Credit Quality is 16 percent

Using the required yield-to-maturity approach to find the bond’s fair value, should the investor buy the bond?

A. No, the bond is overvalued by $55.

B. Yes, the bond is undervalued by $71.

C. Yes, the bond is undervalued by $55.

D. No, the bond is overvalued by $71.

When pricing a bond using the required yield to maturity (YTM) method, investors use information about the YTMs at which comparable bonds (i.e., similar credit quality) are trading. The required yield-to-maturity approach discounts all cash flows at the yield to maturity. In this case, the required yield is 16%. The bond’s fair value can be computed as:

PMT=700 (10,000 * 0.14/2), I/Y=8 (16/2), FV=1,000, N=10, CPT PV=9,329. Hence, the bond is currently overvalued by $71 (9,329 – 9,400). Question ID: 19402

A three-year bond with a 10 percent annual coupon has cash flows of $100 at Year 1, $100 at Year 2, and pays the final coupon and the principal for a cash flow of $1100 at year 3. The spot rate for Year 1 is 5 percent, the spot rate for year 2 is 6 percent, and the spot rate for Year 3 is 6.5 percent. What is the arbitrage-free value of the bond?

A. $1,094.87.

B. $962.38.

C. $975.84.

D. $1050.62.

101 Spot interest rates can be used to price coupon bonds by taking each individual cash flow and discounting it at the appropriate spot rate for that year’s payment. To find the arbitrage-free value:

Bond value = [$100/(1.05)] + [$100/(1.06)2] + [$1100/(1.065)3]

= $95.24 + $89.00 + $910.63 = $1094.87

Question ID: 23747

A 2-year option-free bond (par value of $10,000) has an annual coupon of 15 percent. An investor determines that the spot rate of year 1 is 16 percent and the year 2 spot rate is 17 percent. Using the arbitrage-free valuation approach, the bond price is closest to:

A. $11,122.

B. $9,694.

C. $8,401.

D. $10,000.

We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Price = [1,500/(1.16)] + [11,500/(1.17)2] = $9,694. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:

N=1, I/Y=16.0, PMT=0, FV=1,500, CPT PV=1,293 N=2, I/Y=17.0, PMT=0, FV=11,500, CPT PV=8,401

Price = 1,293 + 8,401 = $9,694. Question ID: 23746

A 3-year option-free bond (par value of $1,000) has an annual coupon of 9 percent. An investor determines that the spot rate of year 1 is 6 percent, the year 2 spot rate is 12 percent, and the year 3 spot rate is 13 percent. Using the arbitrage-free valuation approach, the bond price is closest to:

A. $1080.

B. $912.

C. $968.

D. $1,000.

We can calculate the price of the bond by discounting each of the annual payments by the appropriate spot rate and finding the sum of the present values. Price = [90/(1.06)] + [90/ (1.12)2] + [1090/(1.13)3] = 912. Or, in keeping with the notion that each cash flow is a separate bond, sum the following transactions on your financial calculator:

N=1, I/Y=6.0, PMT=0, FV=90, CPT PV=84.91 N=2, I/Y=12.0, PMT=0, FV=90, CPT PV=71.75 N=3, I/Y=13.0, PMT=0, FV=1090, CPT PV=755.42

Price = 84.91 + 71.75 + 755.42 = $912.08. Question ID: 23735

For a 6-year semiannual bond ($1,000 face value) with an 8 percent coupon rate and current price of $925, its yield to maturity is closest to:

A. 9.68%.

B. 4.84%.

C. 5.50%.

D. 11.00%.

Use your financial calculator to answer yield to maturity questions. N= 6*2= 12, PMT= 1,000 * (0.08/2) = 40, FV=1,000, PV=-925, CPT I/Y=4.84%. Remember to double this value to get 4.84%*2=9.68%.

Question ID: 23753

An investor finds the following information about a semiannual bond:

· Par value of $10,000 · Current Price of $11,080 · Coupon Rate is 12% · 10 Years to Maturity

The bond’s yield to maturity is closest to:

A. 12.00%.

B. 10.67%.

103 C. 10.25%.

D. 5.12%.

Use your financial calculator to answer yield to maturity questions. N= 10*2= 20, PMT= 10,000 * (0.12/2) = 600, FV=10,000, PV=-11,080, CPT I/Y=5.12%. Remember to double this value to get 5.12%*2=10.25%.

Question ID: 23754

An investor finds the following information about a semiannual bond:

· Par value of $1,000 · Current Price of $875 · Coupon Rate is 6% · 4 Years to Maturity

A. 6.00%.

B. 9.86%.

C. 4.93%.

D. 8.19%.

Use your financial calculator to answer yield to maturity questions. N= 4*2= 8, PMT= 1,000 * (0.06/2) = 30, FV=1,000, PV=-875, CPT I/Y=4.93%. Remember to double this value to get 4.93%*2=9.86%.

Question ID: 23688

An investor finds the following information about a semiannual-pay coupon bond:

· Par value of $1,000 · Current Price of $975 · Coupon Rate is 10% · 8 Years to Maturity

104 A. 10.00%.

B. 5.23%.

C. 12.79%.

D. 10.47%.

Use your financial calculator to answer yield to maturity questions. N= 8*2= 16, PMT= 1,000 * (0.10/2) = 50, FV=1,000, PV=-975, CPT I/Y=5.2345%. Remember to double this value to get the annualized yield to maturity (5.2345%*2=10.47%).

Question ID: 19404

A semi-annual pay coupon bond with an 8 percent coupon and 15 years remaining until maturity is currently selling for $1,196. What is the bond’s yield to maturity?

A. 9.7%.

B. 5.5%.

C. 6.0%.

D. 4.8%.

This problem can be solved most easily using your financial calculator. Using semiannual payments, PMT = 80/2 = $40, N = 15x2 = 30; FV = $1,000; PV = -$1,196. Solve for I = 3%. Semiannual compounding means that YTM = 3%x2 = 6.0%.

Question ID: 19405

A semi-annual pay coupon bond with a 6 percent coupon and 10 years remaining until maturity is currently selling for $975. What is the bond’s yield to maturity?

A. 5.55%.

B. 8.58%.

C. 6.34%

D. 9.70%.

105 This problem can be solved most easily using your financial calculator. Using semiannual payments, PMT = 60/2 = $30, N = 10x2 = 20; FV = $1,000; PV = -$975. Solve for I = 3.17%. Semiannual compounding means that YTM = 3.17%x2 = 6.34%. Note that the bond is selling for a discount, so the yield must be greater than the coupon rate of 6%.

Question ID: 19403

Given a required yield to maturity of 6 percent, what is the intrinsic value of a semi-annual pay coupon bond with an 8 percent coupon and 15 years remaining until maturity?

A. $987

B. $1,202.

C. $1,095.

D. $1,196.

This problem can be solved most easily using your financial calculator. Using semiannual payments, I = 6/2 = 3%, PMT = 80/2 = $40, N = 15x2 = 30; FV = $1,000. Solve for PV = $1,196.

Question ID: 19392

A T-bill with a face value of $100,000 and 140 days until maturity is selling for $98,000. What is the equivalent annual yield (EAY)?

A. 4.08%.

B. 2.04%.

C. 5.14%.

D. 5.41%.

The EAY takes the holding period yield and annualizes it based on a 365-day year accounting for compounding. HPY = (100,000 – 98,000)/98,000 =0.0204. EAY = (1+HPY)365/t – 1 = (1.0204)365/140 – 1 = 0.05406 = 5.41%.

Question ID: 23685

106 · 1-year maturity, $900 par value, valued at $857 · 2-year maturity, $900 par value, valued at $816 · 3-year maturity, $10,900 par value, valued at $9,416

Which of the following best substitutes for the combination of the three zero-coupons bonds?

A. 3-year maturity, $20,000 pay, 9% coupon, annual-pay bond.

B. 6-year maturity, $10,000 par, 9% coupon, annual-pay bond.

C. 3-year maturity, $10,000 par, 9% coupon, semiannual-pay bond.

D. 3-year maturity, $10,000 par, 9% coupon, annual-pay bond.

A coupon bond can be viewed simply as a portfolio of zero-coupon bonds. The cash flows from the three listed zero-coupons will be identical to the cash flows received by an investor with a 3-year, par value of $10,000, 9% annual-pay coupon bond.

Question ID: 19397

A zero-coupon bond with three years to maturity is priced at $890.00. What is the bond’s yield to maturity (YTM)?

A. 3.92%.

B. 6.00%.

C. 4.82%.

D. 3.00%.

YTM= 2[(M/P)1/N -1 = 2[(1000/890)1/6 – 1] = 2[1.0196 – 1] = 0.0392 = 3.92%.

Question ID: 23683

A 10-year zero-coupon bond has a face value of $100,000 and a yield to maturity of 8.50 percent. The current value of the bond is closest to:

A. $65,955.

107 B. $100,000.

C. $43,500.

D. $44,230.

The value of a zero coupon bond is (face value)/(1+ yield to maturity/2)N, where N is the number of semiannual compounding periods to maturity. Price = (100,000)/(1.0425)20 = $43,498.95. Or, N=20, I/Y = 4.25%, PMT = 0, FV= 100,000, CPT PV = 43,498.95. Zero coupon bonds are typically based on semiannual periods.