Ch 8: Fixed Income Securities- Analysis

A coupon bond that pays interest semi-annually has a par value of $1,000, matures in 7 years and has a yield to maturity of 7.5%. If the annual coupon rate is 9%, what is the approximate value of the bond today?

$1,081 To adjust for semi-annual compounding, the number of years is multiplied by 2, and the YTM and coupon payment are divided by 2. N = 14 i = 3.75 PMT = $45 FV = $1,000 PV = $1,080.55

The Anderson bond is a 5% coupon bond with semiannual coupon payments that matures in 10 years. If the YTM for this bond is 4%, what is the value of the bond?

$1,081.76 FV $1,000.00 N 20 i 2.0% Pmt $25 PV $1,081.76

The Echo bond is a 6% coupon bond with semiannual coupon payments that matures in 15 years. If the YTM for this bond is 4%, what is the value of the bond?

$1,223.96 FV $1,000.00 N 30 i 2.00% Pmt $30.00 PV $1,223.96

The Gecko bond is a 10% coupon bond with semiannual coupon payments that matures in 20 years. If the YTM for this bond is 4%, what is the value of the bond?

$1,820.66 FV $1,000.00 N 40 i 2.00% Pmt $50 PV $1,820.66

The Ignite bond is a 20-year zero-coupon bond. If the YTM for this bond is 6%, what is the value of the bond? Assume semiannual compounding.

$306.56 FV $1,000.00 N 40 i 3.00% Pmt 0 PV $306.56

The Kraft bond is a 17-year zero-coupon bond. If the YTM for this bond is 3%, what is the value of the bond? Assume semiannual compounding.

$602.77 FV $1,000.00 N 34 i 1.50% Pmt $0 PV $602.77

Anderson bought a bond with a modified duration of 11.20. By approximately what percentage will the bond price change assuming interest rates increase by 90 basis points?

-10.08% -11.20 x 0.0090 x 100 = -10.08% Since the yield has increased, the price of the bond will fall by 10.08%.

Laramie bought a 20-year zero-coupon bond for $672.93. Using the formula for modified duration, approximately what percentage will the bond price change assuming interest rates increase by 120 basis points?

-23.53% YTM 2% N 40 PV -672.93 FV 1,000 I/Yr 0.9953*2= 2% PCIP= [-D/(1+Y)]*CiY -20/1+0.02*0.012

Reese purchased a 20-year bond with a 3% coupon, paid semi-annually, for $863.22. Which of the following statements is correct? 1. If Reese reinvested the coupon payments at an annual rate of return of 3%, she would have an actual YTM that was higher than expected when she bought the bond? 2. If Reese reinvested the coupon payments at an annual rate of return of 6%, she would have an actual YTM that was higher than expected when she bought the bond?

1 only The IRR (YTM) equals 4% N = 40; PV = -863.22; PMT = 15; FV = 1,000; solve for I/YR = 2.00% x 2 = 4%. Using the 4%, or rather, the 2% rate per semiannual period, yields a future value of $1,906.03 PV = 0 N = 40 I = 2 Pmt = 15 FV = 906.03 + 1,000 (par value) = 1,906.03 YTM assumes the coupon payments are reinvested at the YTM rate. The 3% return on reinvested coupons will not be higher than the expected FV. The 6% return on reinvested coupons will certainly have a higher YTM than expected.

A coupon bond that pays interest annually of $100 has a par value of $1,000, matures in 5 years, and is selling today for $894.50. What is the yield to maturity on this bond?

13% N = 5 PV = -894.50 PMT = $100 FV = $1,000 i = 12.9999

Linda just purchased a Louisiana general obligation bond with a yield of 3%. She is in the 25% federal bracket and 4% state bracket. If Linda lives in Louisiana, what is the equivalent yield on a corporate bond?

4.23% 3% / (1 - 0.29) = 4.23%

Jack is considering purchasing a 6-year bond that is selling for $1,150. The bond can be called in 3 years at 104. What is the YTC for this bond if it has a 9% coupon, paid semiannually?

4.82% PV -$1,150.00 N 12 FV $1,040.00 Pmt $45 i 3.249 3.249 x 2 =6.497

Carla is considering purchasing a 35-year bond that is selling for $500. What is the YTM for this bond if it has a 2% coupon, paid semiannually?

5.06% PV -$500.00 N 70 Pmt $10 FV $1,000.00 i 2.532% ix2 = 5.06%

James is considering purchasing an 11-year bond that is selling for $1,250. What is the current yield for this bond if it has a 6.5% coupon, paid semiannually?

5.2% $65/$1250 = 5.2%

Sam has a $3 million fixed-income portfolio that consists of Bond A, Bond B, Bond C, and Bond D. The bonds have durations of 2, 3, 8, and 10, respectively. If Sam has 20% invested in Bond A, 30% in Bond B, and 25% invested in each of the other two bonds, what is the duration for the portfolio? Assume that the correlation among the bond is 0.5.

5.80 The duration of a portfolio of bonds is the weighted duration. 0.2(2)+0.3(3)+0.25(8)+0.25(10) 0.4+0.9+2.0+2.5 = 5.8

Dirk is considering purchasing a 6-year bond that is selling for $1,150. What is the YTM for this bond if it has a 9% coupon, paid semiannually?

5.99% PV -$1,150.00 N 12 Pmt $45 FV $1,000.00 i 2.994% ix 2 = 5.99%

Holly bought a 7-year bond, with a 3% coupon paid semi annually. It was priced to yield 3% when she bought it. What is the effective duration assuming a 100-basis point change in interest rates?

6.2775 The calculated YTM = 3% since the bond was purchased at par. FV1 $1,000.00 FV 2 $1,000.00 FV 3 $1,000.00 N1 14 N2 14 N3 14 i1 1.50% i2 2.00% i3 1.00% Pmt1 $15.00 Pmt2 $15.00 Pmt 3 $15.00 PV1 $1,000.00 PV2 $939.47 PV3 $1,065.02 Effective Duration= (P if decline)-(P if increase)/[2*(Initial P)(Decimal change in yield)] (1,065.02-939.47)/[2*1,000*0.01]= 6.2775

What is the duration of a 10-year bond with a coupon rate of 6%, paid annually, and a yield to maturity of 11%?

7.32 Dur= (1+k/k)-[(1+k)+T(C-k)]/ C[(1+k)^T -1]+k C= coupon rate k= yield to maturity T= time until maturity Dur= (1+0.11/0.11)-[(1+0.11)+10(0.06-0.11)]/ 0.06[(1+0.11)^10 -1]+0.11

Brandy is considering purchasing an 8-year bond that is selling for $700. What is the current yield for this bond if it has a 6% coupon, paid semiannually?

8.57% $60/$700 = 8.57%

Drake is considering purchasing a 15-year bond that is selling for $1,123. Which of the following is correct if this bond has a 2.5% coupon, paid semiannually? The current yield < coupon rate The current yield > YTM. The YTM < coupon rate.

All of the above For bonds selling at a premium, the relationship between the coupon rate (CR), YTM, and current yield (CY) is: CR > CY > YTM.

Parker is considering purchasing a 5-year bond that is selling for $1,079. Which of the following is correct if this bond has a 5% coupon, paid semiannually? The coupon rate > current yield. The current yield > YTM. The YTM < current yield.

All of the above For bonds selling at a premium, the relationship between the coupon rate (CR), YTM, and current yield (CY) is: CR > CY > YTM. CY=4.63%, CR = 5%, YTM=3.27%

Dr. David decides to invest $3 million in short-term fixed-income securities with an average duration of 3 years and $3 million in longer-term fixed-income securities with an average duration of 7 years. What type of strategy is Dr. David using?

Barbell Strategy

Donna is considering purchasing a bond. She is in the 30% tax bracket. Which one should she purchase if she is only concerned about YTM?

California 10-year bond, paying 4% semi-annually, priced at $1,131.99 Acme is yielding 3% State Street is yielding 3.2% CA is yielding 2.5%, which equates to a 3.57% taxable rate [2.5 / (1 - 0.30) = 3.57%]. FL is yielding 2.2, which equates to a 3.14% taxable rate [2.2 / (1 - 0.30) = 3.14%].

If interest rates ______, then the _______ of the bond will _______.

Decrease, price, increase.

Which of the following statements is correct about duration?

Effective duration can accommodate bonds with embedded options.

Based on Malkiel's theorems, bond prices move _____ to bond yields and for a given change in yield, _______ term bond price changes are greater than changes for _______ term bond prices.

Inversely; longer; shorter.

Byron decides to invest $3 million in fixed-income securities by buying $300,000 worth of bonds with 10 different maturities, ranging from 1-year, 2-years, all the way up to 10-years. What type of strategy is Byron using?

Ladder strategy.

Lisa, who lives in Georgia, is in the 30% federal tax bracket and 5% state income tax bracket. Which of the following bonds that she is considering purchasing has the highest after-tax yield:

Louisiana Municipal bond paying 2.6%.

Caroline is investing her funds for the next five years, when she will need the money for one of her goals. She is considering two high quality bonds: an 8-year bond with a duration of 5 years and a 5-year zero coupon bond. Which bonds should she use if she wants to attempt to immunize the portfolio and minimize reinvestment risk?

She should pick the 5-year bond because the bond will be fully immunized if held to maturity.

Donna is considering purchasing a 3-year bond that is selling for $1,000. Which of the following is correct if this bond has a 4% coupon, paid semiannually?

The YTM equals the coupon rate and current yield.

Deke is considering purchasing a 4-year bond that is pricing such that its YTM is 3%.Which of the following is correct if this bond has a 3.6% coupon, paid semi-annually?

The current yield is between 3% and 3.6%. For bonds selling at a premium, the relationship between the CR, YTM, and CY is: CR > CY > YTM. In this case the CY is between the YTM and CR, but it does not equal 3.3%.

Jackson owns a twenty-year zero-coupon bond priced at $551. If interest rates increase by 50 basis points, how much will the bond change?

The price will decrease between 5% and 10%. First, calculate the current YTM = 3.0%: YTM 3.0% PV -$551.00 N 40 PMT - FV $1,000 i 1.501% ix2 3.00% Calculate increase: N 40 Pmt 0 FV 1,000 i 3.5/2 PV $499.60 i*2= 9.3% Percent Change in P: [-D/(1+Y)] *change in Y [-20/(1+0.03)]*0.005= -9.7%