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CFP NOV 2024 Prep > Investments Ch 8 > Flashcards

Investments Ch 8 Flashcards

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1
Q

VALUATION OF FIXED-INCOME SECURITIES

A

VALUATION OF FIXED-INCOME SECURITIES

  • The value of a bond is equal to the present value of the expected
    future cash flows.
  • To determine the present value of a bond, the expected cash flows
    are discounted at an appropriate discount rate.
    Cash Flows
  • The cash flows for a bond consist of periodic coupon payments and
    the par value, or maturity value, of the bond. The coupon payments
    can be made over any period but are usually paid on a semi-annual
    or annual basis.

Discount Rate
* The discount rate, or the rate at which the cash flows are
discounted, is a critical factor in determining the value of a bond

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2
Q

RESENT VALUE: EXAMPLE
Assume a three-year, $1,000 face value bond that pays an 8 percent
coupon semiannually ($40 twice each year). What is the value of the
bond if comparable bonds are yielding 10 percent?

A

RESENT VALUE: EXAMPLE
Assume a three-year, $1,000 face value bond that pays an 8 percent
coupon semiannually ($40 twice each year). What is the value of the
bond if comparable bonds are yielding 10 percent?

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3
Q

VALUATION OF FIXED INCOME SECURITIES

Fixed Rate Bonds

Floating Rate Bonds

Zero-Coupon Bonds

A

VALUATION OF FIXED INCOME SECURITIES

Fixed Rate Bonds
* Bonds that make fixed coupon payments over the life of the bond

Floating Rate Bonds
* Bonds with a coupon rate that changes every year based on
changes in a reference interest rate

Zero-Coupon Bonds
* Bond that make no coupon payments and will sell at a significant
discount from par.

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4
Q

MEASURES OF BOND RETURNS – CURRENT YIELD

Current Yield (CY)

  • The current yield of a bond is an indication of the return or income
    (cash flow) an investor will receive based on the coupon payment
    and the current price of the bond.
  • The formula for calculating the current yield is:
A

MEASURES OF BOND RETURNS – CURRENT YIELD

Current Yield (CY)

  • The current yield of a bond is an indication of the return or income
    (cash flow) an investor will receive based on the coupon payment
    and the current price of the bond.
  • The formula for calculating the current yield is:
                             Annual coupon payments  Current Yield  =   ---------------------------------------
                                   Current Price
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5
Q

CURRENT YIELD: EXAMPLE

A ten-year bond has a 10 percent coupon and is currently selling for
$850

A

CURRENT YIELD: EXAMPLE

A ten-year bond has a 10 percent coupon and is currently selling for
$850.

                         Annual coupon payments  Current Yield  = -------------------------------------- 
                                  Current Price

= $1000 x 10% $100
——————– = ———– = 1176 x 100 = 11.76 %
$ 850 $850

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6
Q

MEASURES OF BOND RETURNS – YIELD TO MATURITY (YTM)

A

MEASURES OF BOND RETURNS – YIELD TO MATURITY (YTM)

  • It is the interest rate that equates the market price of the bond to the discounted PV of the bond cash flows.
  • YTM assumptions:
    –the investor buys the bond, holds the bond until it matures
    –cash flows are reinvested at the yield to maturity`
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7
Q

YIELD TO MATURITY: EXAMPLE

A 30-year bond that pays a 9% annual coupon, paid semi-annually
and selling for $1,249.45 has a yield to maturity of 7%, calculated as
follows:

A

Yield to maturity of a bond: EXAMPLE

PV = < $ 1,249.45 > Current bond price

N = 60 = ( 30 years x 2 ) for semi annual interest

PMT = $45 = ( $90 / 2 ) semi annual cash flow PMT

FV = $1,000 maturity par value

I = 3.5 x 2 = 7 % YTM ( annual )

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8
Q

MEASURES OF BOND RETURNS – RELATIONSHIPS

A

MEASURES OF BOND RETURNS – RELATIONSHIPS

Par = Coupon Rate= Current Yield = Yield to Maturity

Discount = Coupon Rate < Current Yield < Yield to Maturity

Premium = Coupon Rate > Current Yield > Yield to Maturity

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9
Q

MEASURES OF BOND RETURNS – YTC

A

MEASURES OF BOND RETURNS – YIELD TO CALL (YTC)

Yield to call (YTC) is that rate of return that equates the present value
of the bond (purchase price) to the expected cash flows, adjusted for
the call feature.

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10
Q

YIELD TO CALL (YTC): EXAMPLE

A 30-year bond ($1,000) that pays an annual coupon of 9%, paid
semiannually, is selling for $1,249.45. The YTM is 7%. The bond is
callable in 5 years at 104 (i.e., 104 percent of the par value). The yield
to call equals 4.15 percent.

A

YIELD TO CALL (YTC): EXAMPLE

A 30-year bond ($1,000) that pays an annual coupon of 9%, paid
semiannually, is selling for $1,249.45. The YTM is 7%. The bond is
callable in 5 years at 104 (i.e., 104 percent of the par value). The yield
to call equals 4.15 percent.

PV = < $ 1,249.45>

n = 10 = ( 5 years x 2 )

PMT = 45 = ( $ 90 / 2 ) semin annual payments

FV = $1040 = ( 104% call price x $1000 )

I = 2.076 x 2 = 4.152 %

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11
Q

COMPARING BOND RETURNS

A

COMPARING BOND RETURNS

  • The taxable bond market consists of U.S. Treasury bonds, U.S.
    government agency bonds, and corporate bonds.
  • The tax-exempt bond market consists of bonds issued by
    municipalities, including states, counties, cities and parishes.
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12
Q

TAX EQUIVALENT YIELD (TEY) (1 OF 2)
An investor can convert a municipal bond yield to an equivalent
taxable yield using the following formula:

A

TAX EQUIVALENT YIELD (TEY)

An investor can convert a municipal bond yield to an equivalent
taxable yield using the following formula:

                 Tax- exempt yield  TEY  =   -----------------------------------
                1- marginal tax rate
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13
Q

For an investor in the 40 percent income tax bracket, what is the TEY
of a municipal bond that is offering a five percent yield?

If comparable credit-worthy taxable corporate bonds are offering a
yield of 7.5 percent, which bond is preferred?

What is the after-tax yield on the corporate bond?

A

EXAMPLE TAX EQUIVALENT YIELD (TEY)

For an investor in the 40 percent income tax bracket, what is the TEY
of a municipal bond that is offering a five percent yield?

         Tax- exempt yield                 .05 TEY  =   ------------------------------ = -------------    = .0833  = 8.33% 
         1- marginal tax rate         1  -  .40

If comparable credit-worthy taxable corporate bonds are offering a
yield of 7.5 percent, which bond is preferred? the TAX FREE

What is the after-tax yield on the corporate bond?

after tax = taxable return x ( 1-marginal tax rate )

            =      7.50               x      (   1 -   .40 ) 
           =      4.50%
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14
Q

RISKS OF FIXED-INCOME SECURITIES

Systematic Risk Unsystematic Risk

A

RISKS OF FIXED-INCOME SECURITIES

Systematic Risk Unsystematic Risk
_____________________________________________________
Interest rate risk Default Risk ( credit risk
Reinvestment Rate risk Cal Risk
Purchasing Power risk Liquidity Risk
Exchange Risk

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15
Q

RISKS OF FIXED-INCOME SECURITIES

Interest Rate Risk

A

RISKS OF FIXED-INCOME SECURITIES

Interest Rate Risk
Interest rate risk is the risk that fluctuations in yields will adversely
impact the value of a security.

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16
Q

ADDITIONAL RISKS OF FIXED-INCOME SECURITIES

A

ADDITIONAL RISKS OF FIXED-INCOME SECURITIES

  • Credit Risk
  • Reinvestment Rate Risk
  • Purchasing Power Risk
  • Call Risk
  • Exchange Rate Risk
  • Liquidity Risk
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17
Q

TERM STRUCTURE OF INTEREST RATES

Yield Curves

A

TERM STRUCTURE OF INTEREST RATES

Yield Curves
* The Treasury yield curve reflects current market interest rates for
various bond maturities.

  • The yield curve is generally upward sloping indicating that yields on
    longer-term bonds are higher than yields on shorter-term bonds.
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18
Q

YIELD CURVES

A

YIELD CURVES

Normal Yield Curve
Flat Yield Curve
Inverted Yield Curve
Humped Yield Curve

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19
Q

YIELD CURVE THEORIES

A

YIELD CURVE THEORIES
* The Pure Expectations Theory
* The Liquidity Preference Theory
* The Preferred Habitat Theory
* The Market Segmentation Theory

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20
Q

BOND PRICE VOLATILITY

A

BOND PRICE VOLATILITY

  • Bond prices move inversely to bond yields.
  • For a given change in yield, longer-term bond price changes are
    greater than changes for shorter-term bond prices.
  • A decrease in yields raises bond prices more than the same
    increase in yields lowers prices.
  • Price movements resulting from equal absolute increases and
    decreases in yield are asymmetric.
  • The higher the coupon, the smaller the percentage price fluctuation
    for a given change in yield (except for one-year securities and
    consols).
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21
Q

LONG-TERM VS . SHORT-TERM BONDS

A

LONG-TERM VS. SHORT-TERM BONDS

  • Longer-term bonds are more volatile than shorter-term bonds.
  • Lower coupon bonds are more volatile than higher coupon bonds.
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22
Q

BOND PRICE CONVERGENCE

A

BOND PRICE CONVERGENCE

  • A bond’s price is subject to the relationship between the coupon
    rate, YTM, and term for that particular bond.
  • Bonds with a coupon rate in excess of the YTM will sell at a
    premium, while bonds with a coupon rate below the YTM will sell at
    a discount.
  • All bonds, whether sold at a premium or a discount, will converge to
    par value as the remaining term approaches zero.
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23
Q

BOND PRICE VOLATILITY

A

BOND PRICE VOLATILITY

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24
Q

DURATION

A

DURATION

Duration is a time-weighted measure of a fixed income security’s cash flows in terms of payback.

Three important uses for duration include:
* Providing a measure of a bond’s volatility;
* Estimating the change in the price of a bond based on changes in
interest rates; and
* Immunizing a bond or bond portfolio against interest rate risk.

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25
Q

CALCULATING DURATION

The following formula is one method for calculating Macaulay duration:

A

CALCULATING DURATION

The following formula is one method for calculating Macaulay duration:

n = Number of periods until maturity
Cf୲ = Cash flow that occurs in period t
k = Yield to maturity
t = Time period

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26
Q

MACAULAY DURATION

Another method of calculating Macaulay duration is to use the
following closed-end formula:

A

MACAULAY DURATION

Another method of calculating Macaulay duration is to use the
following closed-end formula:

C = Coupon rate (as a decimal)
k = Yield to maturity (as a decimal)
t = Time until maturity (in periods)

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27
Q

DURATION: EXAMPLE

Calculate the duration of a 10-year bond that pays an 8% coupon
annually. The bond is price to yield 9%

A

DURATION: EXAMPLE

Calculate the duration of a 10-year bond that pays an 8% coupon
annually. The bond is price to yield 9%

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28
Q

BOND DURATION

A

BOND DURATION

  • Coupon Rate (inverse relationship)
  • Maturity (direct relationship)
  • Yield to Maturity (inverse relationship)
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29
Q

MODIFIED DURATION

A

MODIFIED DURATION

  • Modified duration is used as an estimate of the percentage
    change in the price of a bond based on its duration and the
    change in market interest rates.
  • Modified duration is a linear approximation of the price-yield
    relationship
                                            Macaulay Duration  Modified Duration =    ---------------------------------------
                                             Current YTM 
                                   1 + -------------------------------
                                            # PMT's in a year
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30
Q

PRICE CHANGE ESTIMATES

We can use Modified Duration to estimate price change.

A

PRICE CHANGE ESTIMATES

We can use Modified Duration to estimate price change.

change P - D
————- = —————— x change YTM
P 1 + YTM

Change P / P = percentage change in the price of the a bond
D = Macaulay Duration of the bond
YTM = Yield to maturity for the bond
change YTM = Change in the YTM as a decimal

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31
Q

MODIFIED DURATION EXAMPLE
The duration for a 10-year bond that pays a 10 percent coupon,
annually, and is yielding 10 percent is 6.76 years. How much will the
price of the bond change in value if interest rates decrease by 1
percent or 100 basis points to 9 percent?

A

MODIFIED DURATION EXAMPLE

The duration for a 10-year bond that pays a 10 percent coupon,
annually, and is yielding 10 percent is 6.76 years. How much will the
price of the bond change in value if interest rates decrease by 1
percent or 100 basis points to 9 percent?

change P - D
————- = —————— x change YTM
P 1 + YTM

change P - 6.76
———— = ———————– x ( .09 - .10)
p 1 + .10

change P
————- = .06145 = 6.145 %
p

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32
Q

EFFECTIVE DURATION

A

EFFECTIVE DURATION

  • Direct measure of the sensitivity of a bond to changes in interest
    rates.
  • Accommodates for changing cash flows.
                                 (price if Yield declines )  - (price if Yield Increases) Effective Duration = ----------- -----------------------------------------------------------
                                  ( 2)  ( initial Price )  ( Decimal change in yield )
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33
Q

PORTFOLIO DURATION

A

PORTFOLIO DURATION

The duration of a portfolio of bonds is equal to the weighted average of the durations of bonds included in the portfolio

Portfolio Duration = W1D1 + W2D2 + ,,,,,Wn Dn

Wn = the percentage of the bond portfolio that the market value for bond n represents

Dn = the duration for Bond n

n = number of bonds in the portfolio

34
Q

PORTFOLIO DURATION: EXAMPLE
Max owns the following bonds:

A

PORTFOLIO DURATION: EXAMPLE

Max owns the following bonds:
Duration
A $1,000 3.0
B $2,000 4.5
C $3,000 5.0

total $6,000

The duration of the portfolio is 4.5 years:

                                   1                   2                  3 Portfolio Duration = ------- (3.0) + ---- ( 4.5)  + -- --- ( 5.0)    = 4.50 
                                    6                  6                  6
35
Q

PROBLEMS WITH DURATION

  • Duration Pricing Error
  • Yield Curve Risk
A

PROBLEMS WITH DURATION

  • Duration Pricing Error
  • Yield Curve Risk
36
Q

DURATION PRICING ERROR

A

DURATION PRICING ERROR

37
Q

EFFECTS ON INTEREST RATES

The effect of interest rates on bond prices and reinvested coupon
payments is illustrated in the following exhibit:

A

EFFECTS ON INTEREST RATES

The effect of interest rates on bond prices and reinvested coupon
payments is illustrated in the following exhibit:

Interest Rate Move Value of bond Value of Reinvested Coupon
Payments (move is direct to
interest rate )
—————————————————————————————————-
UP Down UP
Down UP Down

38
Q

IMMUNIZATION

A

IMMUNIZATION

  • Immunization is the concept of minimizing the impact of changes in
    interest rates on the value of the investment.
  • The goal of immunization is to protect the bond portfolio from
    interest rate fluctuations and reinvestment rate risk.
  • A bond portfolio is defined as being initially immunized at the point of duration.
39
Q

IMMUNIZATION: EXAMPLE

Kyle purchases a 10-year bond with a coupon rate of 8 percent, paid
annually. The yield on the bond equals 10% and the duration of the
bond matches Kyle’s time horizon of approximately seven years. Kyle
is concerned that fluctuations in interest rates may adversely affect the amount of cash that he expects to receive in seven years.
Kyle is expected to have the same value at the end of 7 years,
regardless of the possible initial changes in interest rates

A

IMMUNIZATION: EXAMPLE

Kyle purchases a 10-year bond with a coupon rate of 8 percent, paid
annually. The yield on the bond equals 10% and the duration of the
bond matches Kyle’s time horizon of approximately seven years. Kyle
is concerned that fluctuations in interest rates may adversely affect the amount of cash that he expects to receive in seven years.
Kyle is expected to have the same value at the end of 7 years,
regardless of the possible initial changes in interest rates

40
Q

BOND CONVEXITY

A

BOND CONVEXITY

  • Convexity is a measure of the curvature of the price of a bond along
    a spectrum of yields.
  • It can be used to provide a more precise measure of expected
    changes in the price of a bond than using duration alone.
41
Q
A

CONVEXITY FORMULA
P0 = Price of bond as of today, before any change in Y
P + = Price of bond based on an increase in interest rates equal to Y
P - = Price of bond based on a decrease in interest rates equal to Y
Y = yield to maturity
The impact of convexity on the price of the bond can be estimated with the following formula:

Convexity % Δ in price =

42
Q

BOND DURATION AND CONVEXITY

A

BOND DURATION AND CONVEXITY

relationship Between Coupon Rate, YTM, and Maturity
________________________________________________________________
Bond Feature Duration Convexity
________________________________________________________________
Coupon rate Inverse Inverse
Yield to maturity Inverse Inverse
Maturity Direct Direct

43
Q

BOND PORTFOLIO MANAGEMENT STRATEGIES

There are two broad categories of bond portfolio management
strategies.

A

BOND PORTFOLIO MANAGEMENT STRATEGIES

There are two broad categories of bond portfolio management
strategies.

  • Passive Strategies
  • Active Strategies
44
Q

BOND SWAPPING

A

BOND SWAPPING

Bond Swapping: Sell one bond and replace it with another.

  • Substitution Swap
  • Intermarket Spread Swap
  • Rate Anticipation Swap
  • Pure Yield Pickup Swap
  • Tax Swaps
45
Q

Addison 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?

A

-10.08%.
Rationale

The estimated percentage change in the value of the bond
= - D x change in yield
or duration x change in yield

90 basis points = .0090

-11.20 x 0.0090 = -10.08%

46
Q

Shanice 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?

A
47
Q

Reuben 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 semi-annually?

The coupon rate > current yield.
The current yield > YTM.
The YTM < current yield.
All of the above.

A

All of the above.

Rationale

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

BONDS AT PREMIUM = CR > CY > YTM.

CY=4.63%,
CR = 5%,
YTM=3.27%

48
Q

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.

A

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.

Rationale

Bond prices move inversely with bond yields. For a given change in yield, longer-term bond price changes are greater than changes for shorter-term bond prices.

49
Q

Jackie 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 semi-annually?

A

4.82%.

Rationale

PV -$1,150.00 current price
N 6 3 yrs x 2 = 6 semi annual periods
Pmt $45 $1000 x 9% = $ 90/yr = $45 /semi annual
FV $1,040.00 $1000 par plus 102 call price
i 2.412% x 2 = 4.82%

50
Q

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?

A
  • 23.53 %
  1. Solve for TTM
    N 40 = ( 20 x 2 )
    I solve for .9952 x 2 = 1.99 or 2.00%
    PV -672.93
    PMT 0
    FV 1000
    < D >
  2. % change in Price = —————- ( change in YTM)
    ( 1 + YTM )
         - 20  =    --------------------( .012 )  = 23.53 % 
    1 + .02
51
Q

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

A

$1,081.76.
Rationale

FV $1,000.00
N 20
i 2.0%
Pmt $25.00
PV $1,081.76

52
Q

Tyrell just purchased a Louisiana general obligation bond with a yield of 3%. He is in the 24% federal bracket and 4% state bracket. If Tyrell lives in Louisiana, what is the equivalent yield on a corporate bond?(Assume he is not subject to the federal 3.8% Net Investment Income Tax.)

A

4.17%.
Rationale

Corporate bonds are subject to federal and state income tax.
Treasury bonds are subject to federal income tax only.
Municipal bonds are not subject to federal income tax, but are subject to state income tax if they are not issued by the taxpayer’s state of residence. The tax equivalent yield is equal to the tax-exempt yield ÷ (1 - tax bracket). Note that when calculating the after-tax yield, the tax bracket used is the taxes paid, but when calculating a tax equivalent yield the tax bracket is the taxes saved.

3% ÷ (1-0.28) = 4.17%

53
Q

Armand 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 semi-annually?

A

5.2%.

Rationale

                         annual coupon  Current Yield = ------------------------
                            current price

The current yield is the annual coupon divided by the current price.
$65÷$1,250 = 5.2%

54
Q

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

A

1,820.66.

Rationale

FV $1,000.00
N 40
i 2.00%
PMT $50.00
PV $1,820.66

55
Q

Valerie is considering purchasing a bond. She is in the 30% tax bracket. Which one should she purchase if she is aiming to maximize her after-tax yield?

A

California 10-year bond, paying 4% semi-annually, priced at $1,131.99

Rationale

SOLVE FOR YTM FOR EACH BOND WITH CALC:

YTM is calculated using the current price as PV (enter as a negative number), $1,000 as the FV, the semi-annual coupon amount as PMT, and the number of years to maturity x 2 (for semi-annual) as N, then solving for i.

This will calculate the semi-annual yield. Multiply by 2 to get the annual YTM.

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%].

56
Q

Yasmine 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 semi-annually?

A

The YTM equals the coupon rate and current yield.

Rationale

Bond priced at par will have a YTM equal to the current yield and coupon rate.

57
Q

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?

A

Ladder strategy.

Rationale

The ladder strategy is accomplished with staggered maturities, in this case, over 10 years.

58
Q

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

A

$1,223.96..

Rationale

FV $1,000.00 par value at maturity
N 30 15 yr x 2 = 30 semi annual periods
i 2.00% The YTM is stated at 4% , so / 2= 2 %
Pmt $30.00 $1000 x 6% = $60/yr = $30/ semi annual
PV $1,223.96 «&laquo_space; the current value of the bond

59
Q

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 semi-annually?

A

5.99%.

Rationale

PV -$1,150.00 current price of bond
N 12 6 yrs x 2 = 12 periods
Pmt $45 $1000 x 9% = $90/yr = $45/semi annual
FV $1000.00 Par value at matuirty
i 2.994% x 2 = 5.99%

60
Q

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

A

1+ .11 ( 1 + .11 ) + 10 ( .06-.11)
———- - ————————————————— = 7.32
.11 .06 [ ( 1+ .11) 10 - 1 ] + .11

61
Q

Elton 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 Elton using?

A

Barbell strategy.

Rationale

This is a classic barbell strategy with a large portion of the portfolio invested at a shorter duration and the rest of the portfolio invested at a longer duration.

62
Q

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.

A

602.77.

Rationale

FV $1,000.00 maturity value
N 34 17 yrs x 2 = 34 semi annual periods
i 1.50% YTM = 3% / 2 = 1.5% sem,i annual interest
Pmt $0 none, pays at maturity
PV $602.77 «&laquo_space; current value of bond

63
Q

Tonya 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 8-year bond because the duration is closest to her time horizon.

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

She should pick the 8-year bond because the duration is closest to her time horizon.

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

A

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

Rationale

Tonya wants to immunize her portfolio, which means that the duration of the portfolio should equal the time horizon of five years. The zero-coupon bond provides the easiest way to immunize the portfolio, not only initially, but until maturity.

64
Q

Reese purchased a 20-year bond with a 3% coupon, paid semi-annually, for $863.22. Which of the following statements is correct?

A. 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.

B 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.

C Both a and b.

D Neither a nor b.

A

B 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.

Rationale

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 semi-annual 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

If Reese is able to reinvest at a rate of 6%, a rate higher than the YTM, she will realize a higher return. This is because the FV of her returns at 6% will be higher:
PV = 0
N = 40
PMT = 15
i = 3
FV = 1,131.02 + 1,000 (par value) = 2,131.02

65
Q

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?

A

The current yield is between 3% and 3.6%.

Rationale

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%.

66
Q

Winston 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 semi-annually?

A

8.57%.

Rationale

The current yield = annual coupon divided by the current price.

$60 / $700 = 8.57%

67
Q

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.

A

$306.56.

Rationale

FV $1,000.00
N 40
i 3.00%
Pmt $0.00
PV $306.56 ««< price of bond

68
Q

Which of the following statements is correct about duration?

The duration of a bond increases as the coupon rate increases.

Modified duration measures the change in the value of a bond equally as well when interest rates increase as when interest rates decrease.

Duration can exceed the maturity for a bond, if the bond has a call feature.

Effective duration can accommodate bonds with embedded options.

A

Effective duration can accommodate bonds with embedded options.

Rationale

Option a is incorrect as duration and coupon payments are inversely related.

Option b is incorrect as the pricing error will be different for increases and decreases in interest rates.
Option c is incorrect as duration cannot exceed the maturity of the bond.

69
Q

Shanice 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?

A

6.2775.

Rationale

The calculated YTM = 3% since the bond was purchased at par.

FV $1,000.00 $1,000.00 $1,000.00
N 14 14 14
i 1.50% 2.00% 1.00%
Pmt $15.00 $15.00 $15.00
PV $1,000.00 $939.47 $1,065.02

70
Q

Renee, who lives in Georgia, is in the 32% 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 (assume she is not subject to the federal 3.8% Net Investment Income Tax)?

A

Louisiana Municipal bond paying 2.6%.

Rationale

SOLVE FOR THE AFTER TAX RAT OF EACH :

Corporate bonds are subject to federal and state income tax.
Treasury bonds are subject to federal income tax only.
Municipal bonds are not subject to federal income tax, but are subject to state income tax if they are not issued by the taxpayer’s state of residence. The after-tax yield is equal to the taxable yield x (1 - tax bracket). Note that when calculating the after-tax yield, the tax bracket used is the taxes paid, but when calculating a tax equivalent yield the tax bracket is the taxes saved.
Treasury = 3.3% x (1 - 0.32) = 2.244%
Corporate = 3.7% x (1 - 0.37) = 2.331%
LA Bond = 2.6% x (1 - 0.05) = 2.47%
CA Bond = 2.4% x (1 - 0.05) = 2.28

71
Q

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?

A

13.00%.

Rationale

N = 5
PV = (894.50)
PMT = $100
FV = $1,000
i = 12.9999

72
Q

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 less than 5%.
The price will increase less than 5%.
The price will decrease between 5% and 10%.
The price will decrease more than 10%.

A

The price will decrease between 5% and 10%.

Rationale

When interest rates increase, bond prices decrease.
Fist, calculate the current YTM = 3.0%

PV -$551.00
N 40
PMT -
FV $1,000.00
i 1.501%
x 2 3.00%

By increasing the YTM from 3% to 3.5%, the value of the bond will decrease to about $499.60, (N=40; PMT = 0; FV = 1,000; i = 3.5 ÷ 2; solve for PV) a drop of 9.3%.

73
Q

Zola 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 semi-annually?

A

5.06%.

Rationale

PV -$500.00
N 70
PMT $10
FV $1,000.00
i 2.532% x 2 = 5.06%

74
Q

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 bonds is 0.5.

A

5.80.

Rationale

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

75
Q

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?

A

1,081.

Rationale

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

76
Q

If the bond market undergoes a large change in yield (for example, more than 100 basis points), then a bond’s duration will

A

understate the price appreciation when rates fall and overstate the price decline when rates increase.

77
Q

The practical application of bond portfolio immunization to investors is that immunization

allows aggressive traders to eliminate the price effects caused by interest rate changes.

allows investors to derive a specified rate of return from bond investments for a given investment horizon.

eliminates the possibility of losing money due to a company defaulting on its bond payments.

allows investors to passively manage their bond portfolio once it is initially immunized.
A

allows investors to derive a specified rate of return from bond investments for a given investment horizon.

78
Q

If the bond market undergoes a large change in yield (for example, more than 100 basis points), then a bond’s duration will

understate both the price appreciation when rates fall and the price decline when rates increase.

overstate both the price appreciation when rates fall and the price decline when rates increase.

overstate the price appreciation when rates fall and understate the price decline when rates increase.

understate the price appreciation when rates fall and overstate the price decline when rates increase.
A

Solution: The correct answer is D.

understate the price appreciation when rates fall and overstate the price decline when rates increase.

79
Q
A
80
Q
A

CFP NOV 2024 Prep (80 decks)

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