Transcript
1
Example 1-1How to calculate the settlement proceed?
A bond has a par value of $50,000 and is currently offered at a quoted price of 98 5/32. What is the dollar amount that an investor must pay in order to purchase the bond?
A. $98.16
B. $49,078.15
C. $50,000.00
D. $4,907,812.50
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Answer to Example 1-1
B If the quoted price is 98 5/32 this means that the dollar
amount is 0.981563 * $50,000 = $49,078.15
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Example 1-2 Floating-Rate Coupon
The coupon of a floating-rate bond will be reset every six months and be calculated with reference to the 6-month LIBOR and a quoted margin of 150 basis points. (A basis point is 1/100 of 1%, or 0.01%).
If the current 6-month LIBOR is 4.75%, what is the relevant coupon rate for the next interest payment period?
New coupon rate = 4.75% + 1.50% = 6.25%
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Example 1-3Features of an Inverse Floater
Which of the following statements does NOT describe a characteristic of an inverse floater? A floating-rate issue:
A. Whose coupon is determined by subtracting a reference rate from some stated maximum rate.
B. Whose coupon rate will increase as market rates decrease and decrease as market rates increase.
C. That may, under certain circumstances, require the bondholder to make payments to the issuer.
D. That has an implicit cap on the maximum coupon rate and typically includes a floor on the minimum coupon rate.
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Answer to Example 1-3
C The bondholder always receives coupon payments made by
the issuer and not the opposite since that would imply a negative interest rate.
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Example 1-4Are caps & floors beneficial to investors? Which of the following statements is TRUE regarding a
floating-rate issues that have caps and floors?
A. A cap is an advantage to the bondholder while a floor is an advantage to the issuer.
B. A cap is an disadvantage to the bondholder while a floor is an disadvantage to the issuer.
C. A floor is an disadvantage to both the issuer and the bondholder while a cap is an advantage to both the issuer and the bondholder.
D. A floor is an advantage to both the issuer and the bondholder while a cap is an disadvantage to the issuer and the bondholder.
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Answer to Example 1-4
B A cap limits the upside potential of the coupon rate paid on
the floating-rate bond and is therefore a disadvantage to the bondholder.
A floor limits the downside potential of the coupon rate and is therefore a disadvantage to the bond issuer.
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Example 1-5What is a Call Provision?
Which of the following statements is TRUE with regard to a call provision?
A. A call provision is an advantage to the bondholder.
B. A call provision will benefit the issuer in times of declining interest rates.
C. A callable bond will trade at a higher price than an identical noncallable bond.
D. A nonrefundable bond provides more protection to the bondholder than a noncallable bond.
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Answer to Example 1-5
B A call provision gives the bond issuer the right to call the
bond at a pre-specified price. A bond issuer may want to call a bond if he is paying a high coupon and interest rates have decreased so that he would be able to get cheaper financing.
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Example 2-1 FV of Annuity
You plan to buy a property and are saving $100,000 at the end of each year. Your savings can earn an interest rate of 6%. How much down payment will you be able to make 5 years from now?
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Answer to Example 2-1 The amount you can save in 5 years:
= $100,000 * [(1+6%)5- 1] / 6%
= $563,709.30
Using a financial calculator:
PMT = 100,000
n = 5
i = 6
PV = 0
FV = ? = -563,709.30
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Example 2-2
Should you buy an asset that will generate income of $1,200 at the end of each year for 8 years? The price of the asset is $6,200 and the annual interest rate is 10%.
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Answer to Example 2-2
Calculate the PV of the cash inflows:
= $1,200 * [1 – 1/(1+0.1)8] / 0.1
= $6,401.91 PV(Cash Inflows) > Cost of Asset You should buy it
Using a financial calculator:PMT = 1,200
n = 8
i = 10
FV = 0
PV = ? = -6,409.91
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Example 2-3 How to Calculate the Price of a Bond?
Consider a 2-year annual-coupon bond with 6% coupon and the required yield is 7%.
What is the price of the bond?
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Answer to Example 2-3
98.192
87.3445.241 5.607
)100
71(
100
)100
71(
6
)100
7(1
6
221
P
Coupon = 6Principal = 100Coupon = 6
time = 1 time = 2
P = ?
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Example 2-4
What is the price of a zero-coupon bond that matures 15 years from now, if the maturity value is $1,000 and the required yield is 9.4%?
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Answers to Example 2-4
M = $1,000 r = 0.094 / 2 = 0.047 N = 2 * 15 = 30
$252.12
96644.3
000,1$
)047.1(
000,1$30
P
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Example 2-5 How to construct a market bid-ask spread?
For a particular bond, the following bid-ask spreads are quoted by three different dealers:
Bid Price Ask Price
Dealer A 97 3/32 97 7/32
Dearer B 97 2/32 97 5/32
Dealer C 97 4/32 97 7/32
Which of the following is the market bid-ask spread?A. 1/32
B. 2/32
C. 3/32
D. 4/32
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Answer to Example 2-5
Answer: A The lowest quoted ask price is Dealer B’s ask price (97 5/32),
and the highest quoted bid price is Dealer C’s bid price (97 4/32). Thus, the bid-ask spread is 1/32.
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Example 2-6 What is a fractional coupon period?
A bond analyst is evaluating a certain high-grade corporate bond that carries a maturity of May 15,2004; assume this bond is being valued (priced) for settlement on March 10, 2002. The bond’s coupon is paid annually, and is 7.5 percent. Par value is $100, and the day count convention is 30E/360. What is the fractional coupon period (i.e. the “v” value) in this situation?
A. 0.1778
B. 0.1806
C. 0.1833
D. 0.1861
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Answer to Example 2-6 Answer: B
0.1806 65/360 v
360 periodcoupon in days of no.
65 14)-1(May 14 (Apr) 30 30)-10(Mar 21
couponnext and settlementbetween days of no.
periodcoupon in days
datepayment coupon next and settlementbetween days v
v
P (March 10, 2002)
C (May 15, 2002) M+C (May 15, 2004)C (May 15, 2001) C (May 15, 2003)
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Example 2-7 How to calculate dirty price?
A bond analyst is evaluating a certain high-grade corporate bond that carries a maturity of May 15,2004; assume this bond is being valued (priced) for settlement on April 9, 2002. The bond’s coupon is paid annually, and is 7.5 percent. Par value is $100, and the day count convention is 30E/360. The bond’s “v” value is 0.100. Given a required yield of 6.50 percent, what is the dirty price of the bond?
A. 108.634
B. 102.241
C. 101.906
D. 100.000
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Answer to Example 2-7
A v = 36/360 = 0.1 (there are 22 days in April and 14 in May)
Unfortunately, there is not an easy way to do this problem with your financial calculator. One method is that you break the problem up into three present value computations as follows:
6344.108)065.01(
100
0.065)(1
7.5 Value Bond
1-30.1
3
1t1-t0.1
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Answer to Example 2-7 (cont’d) n = 0.1, i = 6.5, FV = 7.5, PMT = 0, PV = ? = -7.453 n = 1.1, i = 6.5, FV = 7.5, PMT = 0, PV = ? = -6.998 n = 2.1, i = 6.5, FV = 107.5, PMT = 0, PV = ? = -94.183 Add each cash flow for a dirty price of 108.634
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Example 2-8 How to calculate accrued interest (AI)?
Using the data in example 2-7, how much accrued interest is there in the dirty price?
A. 8.634
B. 6.750
C. 2.241
D. 1.906
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Answer to Example 2-8
B Accrual Interest = (1 – v) * coupon payment
= (1.0 – 0.1) * 7.5 = 6.75
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Example 2-9 How to calculate clean price?
Using the data in example 2-7, what is the clean price of the bond?
A. 95.156
B. 95.491
C. 101.884
D. 100.000
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Answer to Example 2-9
C Clean Price = Dirty Price – Accrued Interest
= 108.634 – 6.75 = 101.884
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Exercise 2-1How to use a financial calculator to compute the bond price?
Assume a flat term structure, where rates are 5 percent across all maturities. A 2-year bond pays an annual coupon of 6 percent. By how much will the bond price change if the term structure shifts up in a parallel manner by 1 percent?
A. -$1.859
B. -$1.00
C. $0.00
D. $5.446
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Answer to Exercise 2-1
A By using a financial calculator, the current price of the bond
(i.e., where a 6% bond is being priced to yield 5%) can be found as follows:
n = 2; FV = 100; PMT = 6, i = 5; PV = ? = -101.859
Now, since the new interest rate equals the coupon rate of the bond, the new price on the bond (i.e. a 6% bond being priced to yield 6%) will be its par value. Thus,
Bond price change = 100 – 101.859 = -1.859
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Exercise 2-2 Discount, Par & Premium
Two bonds have par values of $100. Bond A is a 5%, 15 year-bond priced to yield 8%; Bond B is a 7 ½ percent, 20 year-bond priced to yield 6 percent. Using annual compounding, the prices of these 2 bonds would be:
Bond A Bond B
A. $74.061 $84.708
B. $74.061 $117.204
C. $74.322 $117.204
D. $131.139 $131.139
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Answer to Exercise 2-2
C For Bond A, using a financial calculator;
n = 15, i = 8, FV = 100, PMT = 5, PV = ? = - 74.322 For Bond B, using a financial calculator;
n = 20, i = 6, FV = 100, PMT = 7.5, PV = ? = - 117.204 Because the coupon on Bond A is less than its required yield,
the bond will sell at a discount; conversely, because the coupon on Bond B is greater than its required yield, the bond will sell at a premium.
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Exercise 2-3 Repeat for semiannual-pay bond
Bond A is a 15-year, 10 ½ percent semiannual-pay bond that is being priced to yield 8%, while Bond B is a 15-year, 7 percent semiannual-pay bond that is also being priced to yield 8%. Given both bonds have par values of $100, the prices of these 2 bonds would be:
Bond A Bond B
A. $121.615 $91.354
B. $113.898 $94.441
C. $74.661 $94.441
D. $74.661 $117.559
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Answer to Exercise 2-3 A For Bond A, using a financial calculator;
n = 15 * 2 = 30, i = 8 / 2 = 4, FV = 100, PMT = 10.5 / 2 = 5.25;
PV = ? = - 121.615 For Bond B, using a financial calculator;
n = 30, i = 4, FV = 100, PMT = 7 / 2 = 3.5;
PV = ? = - 91.354
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Exercise 2-4 Testing your concept of Discount, Par & Premium
Given the following bonds, which is not priced correctly?
A. AB. BC. CD. D
Bond Coupon Rate Yield to Maturity Price
A 6% 6% $100.0
B 8% 6% $105.0
C 6% 8% $102.5
D 8% 9% $97.5
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Answer to Exercise 2-4
C If the coupon rate of the bond is less than the yield to
maturity, the bond must sell at a discount to par. Bond C sells for $102.5, which is premium to par.
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Review Question 1 – Return/Yield
A financial instrument currently selling for $800 promises to pay $1000 three years from now. What is the yield for this investment?
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Review Q.1 – Answer
The yield is:
= (1000/800)1/3 – 1
= 7.72%
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Review Question 2 – Yield/IRR
A financial instrument selling for $850 promises to make the following annual payments:
Years from Now Promised Annual Payments
1 100
2 1000
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Review Q.2 – Answer
The yield (y) is computed by solving the following equation:850 = 100/(1+y) + 1000/(1+y)2
y = 14.507%
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Review Question 3 – Annualizing Yield
A bank quotes you an annual deposit rate of 6% with interest paid quarterly. What is your effective annual yield?
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Review Q.3 – Answer
The effective annual yield is:
= (1 + 6%/4)4 – 1
= 6.1364%
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Example 3-1 How to calculate Current Yield?
ABC Co. 7 1/8 percent, 4-year, semiannual-pay bond trading at 102.347 percent of par (where par = $1,000). Assume that the bond is callable at 101 in two years, and putable at 100 in two years. What is the bond’s current yield?A. 6.962%
B. 7.500%
C. 7.426%
D. 7.328%
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Answer to Example 3-1
A Current yield = 7.125/102.347 = 0.06962 or 6.962%
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Example 3-2 How to calculate Yield to Maturity?
ABC Co. 7 1/8 percent, 4-year, semiannual-pay bond trading at 102.347 percent of par (where par = $100). Assume that the bond is callable at 101 in two years, and putable at 100 in two years. What is the bond’s yield to maturity?A. 3.225%
B. 6.450%
C. 6.334%
D. 5.864%
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Answer to Example 3-2
B
6.45% 2 3.225 ? i
102.347- PV 3.5625, PMT 100,FV 8, n Or,
%45.6
)2/1(
100
)2/1(
5625.3347.102
8
8
1t
YTM
YTMYTM t
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Example 3-3 Characteristics of Yield to Maturity (YTM) Which of these statements is NOT true about a bond’s yield
to maturity (YTM):
A. It is the internal rate of return of a bond
B. It is the discount rate that equates a bond’s cash flows to a bond’s price
C. It expresses yield as a percentage of par value and not the price of the bond
D. It assumes that all cash flows are reinvested at the yield to maturity
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Answer to Example 3-3
C A, B & D are all characteristics of a bond’s yield to maturity.
Internal rate of return and yield to maturity for a bond are the same.
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Example 3-4 How to calculate Yield to Call (YTC)?
ABC Co. 7 1/8 percent, 4-year, semiannual-pay bond trading at 102.347 percent of par (where par = $100). Assume that the bond is callable at 101 in two years, and putable at 100 in two years. What is the bond’s yield to call?A. 3.167%
B. 5.664%
C. 6.334%
D. 5.864%
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Answer to Example 3-4 C
6.334% 2 x 3.167 ? i
102.347- PV 3.5625, PMT 101,FV 4, n Or,
%334.6YTC
)2/YTM1(
101
)2/YTC1(
5625.3347.102
4
4
1tt
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Example 3-5 How to calculate Yield to Put (YTP)?
ABC Co. 7 1/8 percent, 4-year, semiannual-pay bond trading at 102.347 percent of par (where par = $100). Assume that the bond is callable at 101 in two years, and putable at 100 in two years. What is the bond’s yield to put?A. 2.932%
B. 6.450%
C. 4.225%
D. 5.864%
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Answer to Example 3-5 D
5.864% 2 x 2.932 ? i
102.347- PV 3.5625, PMT 100,FV 4, n Or,
%864.5YTP
)2/YTP1(
100
)2/YTP1(
5625.3347.102
4
4
1tt
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Example 3-6 What is a Bond Equivalent Yield?
You observe a bond with an annual coupon that is being priced to yield 6.350%. What is this issue’s bond equivalent yield?A. 3.175%
B. 3.126%
C. 6.252%
D. 6.172%
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Answer to Example 3-6
C Bond Equivalent Yield
= ([1+EAY]0.5 -1) * 2 = ([1.0635]0.5 -1) * 2 = 6.252%
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Example 3-7 A Compounding and Decompounding Exercise You determine that the cash flow yield of GNMA Pool
3856 is 0.382 percent per month. What is the bond equivalent yield?A. 9.582%
B. 9.363%
C. 4.682%
D. 4.628%
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Answer to Example 3-7 D Bond Equivalent Yield
= [(1+ Monthly CFY)6 -1] * 2
= [(1.00382)6 -1] * 2 = 4.628% Or: Equivalent Annual Yield
= (1+ Monthly CFY)12 -1
= (1.00382)12 -1 = 4.682% Bond Equivalent Yield
= ([1+EAY]0.5 -1) * 2
= ([1.04682]0.5 -1) * 2 = 4.628%
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Example 3-8 How to calculate Discount Margin?
Nestle’s 4-year floating rate bond is currently trading at 97.65. The coupon, paid annually, is LIBOR + 125 basis point. LIBOR is currently 6.375 percent. What is the discount margin?A. 71 basis points
B. 196 basis points
C. 125 basis points
D. 334 basis points
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Answer to Example 3-8
B Expected coupon = (100 * (0.06375 + 0.0125)) = 7.625
points basis 196or 1.96 6.375 - 8.34 Margin Discount
8.34% i
97.65- PV 7.625, PMT 100, FV 4, n Or,
%34.8
)1(
100
)(1
7.625 97.65
4
4
1tt
YTM
YTMYTM
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Example 3-9 Concept of Interest on Interest (Reinvestment Income) You observe an 8.5 percent semiannual bond with 5 years to
maturity trading 97.051. The yield to maturity of the bond is 9.25 percent. How much is the interest-on-interest income (in dollars) if the reinvestment rate of all the coupon interests is 9.25 percent over the 5 years?A. $88.24
B. $511.24
C. $100.30
D. $525.30
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Answer to Example 3-9
C N = 10, PMT = 4.25, PV = 0, I = 4.625
=> FV = ? = 52.53
However, the 52.53 include 42.5 in coupon payments. Therefore, you need to earn:
52.53 – 42.5 = 10.03 in interest on interest income
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Example 3-10 Concept of Interest on Interest (Reinvestment Income) You observe an 8.5 percent semiannual bond with 5 years to
maturity trading 97.051. The yield to maturity of the bond is 9.25 percent. How much interest-on-interest income (in dollars) will you need to earn in order to have a realized return of 9.25 percent on your investment over 5 years?A. $88.24
B. $511.24
C. $100.30
D. $525.30
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Answer to Example 3-10
C Realizing YTM implies that the reinvestment rate for all the
coupons is equal to YTM, that is, 9.25%. N = 10, PMT = 4.25, PV = 0, I = 4.625
=> FV = ? = 52.53
However, the 52.53 include 42.5 in coupon payments. Therefore, you need to earn:
52.53 – 42.5 = 10.03 in interest on interest income
63
Question 3-11 Total Return Suppose that an investor with a five-year investment horizon
is considering purchasing a seven-year 9% coupon bond
selling at par. The investor expects that he can reinvest the
coupon payments at an annual interest rate of 9.4% and that
at the end of the investment horizon two-year bonds will be
selling to offer a yield to maturity of 11.2%. What is the total
return for this bond?
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Solution to Question 3-11
Step 1: Coupon interest + interest on interest
PMT = 45, i = 4.7, n = 10, PV = 0, FV = ?; FV = -558.14
Step 2: The projected sale price = the present value of the coupon payments + present value of maturity value
PMT = 45, i = 5.6, n = 4, FV = 1,000, PV = ?; PV = -961.53
Step 3: Total future dollars = $558.14 + $961.53 = $1,519.67
Step 4: Total return = 2* [($1,519.67 / $1000)0.1 -1] = 8.54%
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Example 4-1 What is the duration of a zero-coupon bond?
Assuming a flat term structure of interest rates at 5 percent, what is the duration of an option-free zero-coupon bond with 5 years remaining to maturity?
A. 3.76
B. 4.35
C. 5.00
D. 6.34
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Answer to Example 4-1
C The duration of a zero coupon bond is always equal to its term
to maturity.
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Example 4-2 What is the duration of a floating rate debt?
What is the duration of a floating rate bond that has six years remaining to maturity and has semi-annual coupon payments? Assume a flat term structure of 6 percent. Which of the following is closest to the correct duration?
A. 0.285
B. 0.500
C. 4.800
D. 12.000
68
Answer to Example 4-2
B The duration of a floating rate bond is equal to the time until
the next coupon payment takes place. As the coupon rate changes semi-annually, the duration on
this bond will be half a year, or 0.5. In effect, a floating rate bond has the same duration as a pure
discount (zero coupon) bond with time to maturity equal to the time to the next coupon payment of the floating rate bond.
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Example 4-3 How to apply the concept of duration?
Which of the following five-year bonds has the highest interest rate risk?
A. A floating rate bond
B. A zero-coupon bond
C. A callable 5% coupon bond
D. An option-free 5% coupon bond
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Answer to Example 4-3
B The zero-coupon bond will have the longest duration of any
of the 4 bonds and will be subject to the greatest amount of price risk/interest rate risk.
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Example 4-4 How to apply modified duration to estimate percentage change in bond price?
Suppose that you determine that the modified duration of a bond is 7.87. Estimate the percentage change in price due to duration given yields decrease by 110 basis points.
A. -8.657%
B. -7.155%
C. +7.155%
D. +8.657%
72
Answer to Example 4-4
D Estimated percentage change in price = -7.87 * (-1.10%) =
8.657%
73
Example 4-5 How to calculate the convexity of a bond?
Consider a 14 percent semiannual-pay coupon with 6 years to maturity. The bond is currently trading at par. Use a 25 basis-point change in yield to compute the convexity value. Assume the bond is option-free.A. 1.04
B. 2.08
C. 10.4
D. 20.8
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Answer to Example 4-5
D
Since the bond is trading at Par, the yield to maturity now is 14.00%
To calculate the convexity, we can shift the interest rate down by 25 basis points, i.e. at 13.75% to calculate P- and shift the
interest rate up by 25 basis points, i.e. at 14.25% to calculate P+.
To calculate P-: PMT=14/2=7, n =6*2=12, i = 13.75/2=6.875,
FV=100, PV=?=100.999
To calculate P+: PMT=14/2=7, n =6*2=12, i = 14.25/2
=7.125, FV=100, PV=?=99.014
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Answer to Example 4-5 (cont’d)
8.2025)(100)(0.00
200 - 99.014 100.999
)y(P
P2PPConvexity
2
20
0
76
Example 4-6 How to apply convexity to estimate percentage change in bond price?
Suppose that you’ve found that the convexity of a bond to be 57.3. Estimate the convexity effect if yield increases by 110 basis points.A. -1.673%
B. -0.347%
C. +0.347%
D. +1.673%
77
Answer to Example 4-6
C Convexity Effect = ½ * Convexity * (y)2
= ½ * 57.3 * (0.011)2
= 0.00347 or 0.347%
78
Example 4-7 How to estimate percentage change in bond price?
Assume you are looking at a bond that has a modified duration of 10.5 and a convexity of 97.3. Using both of these measures, find the estimated percentage change in price for this bond, if the yield increases by 200 basis points.
A. -22.95%
B. -19.05%
C. -17.11%
D. -24.89%
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Answer to Example 4-7
B Total estimated price change
= (duration effect + convexity effect)
= [-duration * (y)] + [½ * convexity * (y)2]
= [-10.5 * ] + [½ * 97.3 * ()2]
= -21.0% + 1.946% = -19.05%
80
Example 4-8Why convexity is good for bond investors?
An analyst has determined that if market yield rises by 100 basis points, a certain high-grade corporate bond will have a convexity effect of 1.75%; further, she found that the total estimated percentage change in price for this bonds should be -13.35%. Given this information, it follows that the bond’s percentage change in price due to duration as:A. -15.10%
B. -11.60%
C. +15.10%
D. +16.85%
81
Answer to Example 4-8
A Total percentage change in price = Duration effect +
Convexity effect.
Thus
-13.35% = Duration effect + 1.75%
=> Duration effect = -13.35% - 1.75% = -15.10%
(Note the duration effect must be negative because yields are rising)
82
Example 4-9 What drives bond price changes?
The total price volatility of a typical option-free bond can be found as follows:
A. Add the bond’s convexity effect to its duration effect.
B. Add the bond’s negative convexity effects to its modified duration.
C. Subtract the bond’s negative convexity from its positive convexity.
D. Subtract the bond’s modified duration from its effective duration, then add any positive convexity.
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Answer to Example 4-9
A Total percentage change in price = Duration effect +
Convexity effect.
84
Example 5-1 Bond Terminology
Which of the following applies to an on-the-run Treasury issue? An on-the-run issue is:
A. The most recently issued Treasury security
B. The most widely held type of Treasury security
C. A bond that is alive rather than having matured already
D. A short term agency issue that is almost as secure as a Treasury bond.
85
Answer to Example 5-1
A The on-the-run Treasury issue is the most recently issued
Treasury security of a certain type as opposed to an off-the run issue that has been issued earlier.
86
Example 5-2 Concept of Absolute Yield Spread Assume the following yields for different bonds issued by
a corporation.
- One-year rate: 5.50%
- Two-year rate: 6.00%
- Three-year rate: 7.00% If the on-the-run three-year U.S. Treasury is yielding 5
percent, then what is the absolute yield spread on the three-year corporate issue?A. 0.40
B. 1.40
C. 100bps
D. 200bps
87
Answer to Example 5-2
D Absolute yield spread = yield on the 3-year corporate issue –
yield on the on-the-run 3-year Treasury issue
= 7.00% - 5.00% = 2.00% or 200 bps.
88
Example 5-3 Concept of Relative Spread
Assume the following corporate yield curve:
- One-year rate: 5.50%
- Two-year rate: 6.00%
- Three-year rate: 7.00%
If an on-the-run three-year U.S. Treasury is yielding 6 percent, the three-year relative yield spread is:A. 16.67%
B. 40.00%
C. 14.28%
D. 100bps
89
Answer to Example 5-3 A The yield on the corporate is 7% so the relative yield is
(7% - 6%)/6% which is 1/6 or 16.67% of the 3-year Treasury-yield.
90
Example 5-4 Flight to Quality
If a U.S. investor is forecasting that the yield spread between U.S. Treasury bonds and U.S. corporate bonds is going to widen, then which of the following is most likely to be true?
A. The economy is going to expand
B. The economy is going to contract
C. No change in the economy
D. The U.S. dollar will weaken
91
Answer to Example 5-4
B Flight to quality
92
Example 5-5 Yield curve trading strategy Assume that the following hypothetical Treasury securities
(settlement date: 30-Oct-02) are trading actively.
Assume that an investor believes that all yield curves are going to flatten. Under this scenario and using these bonds, which of the following trades is correct?
A. Intramarket trade that buys bond A and short sells bond B.B. Intermarket trade that short sells bond A and buys bond B.C. Intramarket trade that short sells bond A and buys bond B.D. Intermarket trade that buys bond A and short sells bond B.
Coupon Maturity Price
Bond A 8% 15-Sep-03 100.35
Bond B 9.75% 15-Aug-20 100
93
Answer to Example 5-5
C If you expect the yield curve to flatten then short term interest
rates have to increase relative to long term interest rates (but not necessarily in absolute terms). Therefore, short-term bonds will underperform and long-term bonds will outperform – this strategy is consistent with your beliefs.
This is an intramarket trade.
94
Example 5-6 Yield curve trading strategy Assume that the following hypothetical Treasury securities
(settlement date: 30-Oct-02) are trading actively.
Assume that an investor believes that all yield curves are going to steepen. Under this scenario and using these bonds, which of the following trades is correct?
A. Intramarket trade that short sells bond A and short buys bond B.
B. Intermarket trade that buys bond A and short sells bond B.
C. Intramarket trade that buys bond A and short sells bond B.
D. Intermarket trade that short sells bond A and buys bond B.
Coupon Maturity Price
Bond A 8% 15-Sep-03 100.35
Bond B 9.75% 15-Aug-20 100
95
Answer to Example 5-6
C If you expect the yield curve to steepen then short term
interest rates have to decrease relative to long term interest rates (but not necessarily in absolute terms). Therefore, this strategy is consistent with your beliefs.
96
Example 5-7 – Concept of Equivalent Taxable Yield Assume an investor is in the 31% marginal tax bracket. She
is considering the purchase of either a 7½ percent corporate bond that is selling at par, or a 5¼ percent municipal bond that is also selling at par. Given the two bonds are comparable in all respects but tax features, and based on the equivalent taxable yields, the investor should buy the:
A. Corporate bond, as it has the higher yield (7.50%)
B. Municipal bond, since the equivalent taxable yield on it is 10.87%
C. Municipal bond, as it has a higher equivalent taxable yield (7.61%)
D. Corporate bond, since the equivalent taxable yield on the muni is 5.17%
97
Answers to Example 5-7
C
%61.70.31 -1
5.25% yield taxableEquivalent
rate tax Marginal- 1
ldexempt yie-Tax yield taxableEquivalent
98
Example 5-8 Taxability of Interest
Assume that the following hypothetical Treasury securities are trading actively.
Which of the following is most likely to be true?A. Bond A is a tax-exempt issueB. Bond A is a corporate issue with an embedded call option.C. Bond B is a callable bondD. Bond B is an off-the-run U.S. Treasury
Coupon Maturity Price
Bond A 6% 15-Aug-20 100.35
U.S. Treasury Bond B 9.75% 15-Aug-20 100
99
Answer to Example 5-8
A The reduction in coupon is mostly likely a reflection of the
fact that the coupon income is not taxable.
100
Example 5-9 – Concept of Liquidity Premium
Which of the following statements concerning the liquidity of a bond is true? Higher liquidity:
A. Positively affects the price of a bond
B. Negatively affects the price of a bond
C. Increases a bond’s interest rate sensitivity
D. Decreases a bond’s interest rate sensitivity
101
Answer to Example 5-9 A Since more liquid bonds have lower transaction costs
associated with them and tend to trade more frequently, investors prefer liquidity and are therefore willing to pay premium prices for more liquid bonds.
102
Example 5-10 Concept of Implied Forward Rate
The 4-year spot rate is 9.45 percent, and the 3-year spot rate
is 9.85 percent. What is the 1-year forward rate 3 years from
today?
A. 0.400%
B. 9.850%
C. 8.256%
D. 11.059%
103
Answer to Example 5-10
C (1.0945)4 = (1.0985)3 * (1+1f3)
%256.8 1)0985.1(
)0945.1(31 3
4
f
104
Example 5-11 A coupon bond is a combination of zero-coupon bonds
Suppose a bond analyst determines that the 2-year spot rate is 7.55 percent. The analyst also finds that he can trade 2-year zero-coupon bonds at a YTM of 7.65 percent. If there are correctly priced 1-year zeros and corresponding 2-year coupon bonds available, how would he take advantage of this arbitrage opportunity?
A. Sell 2-year zeros, sell 1-year zeros, and buy 2-year coupon bonds.
B. Sell 2-year zeros, buy 1-year zeros, and buy 2-year coupon bonds.
C. Buy 2-year zeros, buy 1-year zeros, and sell 2-year coupon bonds.
D. Buy 2-year zeros, sell 1-year zeros, and sell 2-year coupon bonds.
105
Answer to Example 5-11
C The YTM on the 2-year zero is too high => its price too low. You want to buy some arbitrary quantity of 2-year zeros. He completes the arbitrage by buying enough of the 1-year
zeros so that he can aggregate these into 2-year coupon bonds and sell the coupon bonds
106
Example 5-12 Simple Bootstrapping
A 1-year Australian government T-bill has an annually compounded YTM of 5.5 percent. A 2-year Australian government 6.75 percent annual coupon bond is trading at par. What is the 2-year spot rate?
A. 6.973%
B. 6.793%
C. 6.750%
D. 5.500%
107
Answer to Example 5-12
B
%793.61602.93
75.106
)1(
75.106
)055.1(
75.6100
2
1
2
22
t
Z
Z
108
Example 5-13 Arbitrage-Free Valuation
A 3-year Eurobond with a par value of $100 is priced at $105. The bond has an interest rate of 10% and makes payments annually. The 1-year spot rate is 4%, the 2-year spot rate is 6%, and the 3-year spot rate is 7%. Using the arbitrage free method for finding the fair price, would you purchase this bond?
A. No, the bond is overvalued by $3.3
B. No, the bond is overvalued by $1.53
C. Yes, the bond is undervalued by $3.3
D. Yes, the bond is undervalued by $1.53
109
Answer to Example 5-13
C Using the arbitrage free method, the fair value of the bond can
be computed by:10/(1.04) + 10/(1.06)2 + 110/(1.07)3 = $108.308Or, add the following financial calculator computations:n =1, PMT = 0, FV=10, I = 4, PV=?= 9.616n =2, PMT = 0, FV=10, I = 6, PV=?= 8.900n =3, PMT = 0, FV=110, I = 7, PV=?= 89.793Based on the current selling price of $105, the bond is undervalued by (108.308 – 105) = 3.308
110
Example 5-14 – Another tool to perform treasure hunting
A 3-year U.S. corporate bond with a par value of $100 is priced at $107.5. The bond has an interest rate of 8% and makes payments semiannually. 3-year bonds with comparable credit quality have a yield to maturity of 6%. Using the required yield to maturity approach to finding the bond’s fair value, would you purchase this bond?
A. No, the bond is overvalued by $2.1
B. No, the bond is overvalued by $4.3
C. Yes, the bond is undervalued by $2.1
D. Yes, the bond is undervalued by $4.3
111
Answer to Example 5-14
A The required yield to maturity approach discount all cash
flows at the yield to maturity. In this case, the required yield to maturity is 6%. The bond’s fair value can be computed as:
PMT = 4, I = 3, FV = 100, n = 6, PV=?= 105.417
Based on the current selling price of 107.5, the bond is overvalued by (107.5 – 105.4) = 2.1
112
Example 5-15 How to estimate the price of a corporate bond? A corporate bond and a government bond have equivalent
characteristics. They both have a coupon rate of 6 percent, pay coupon annually, and have two years remaining to maturity. Assuming a flat government term structure of 7 percent, which of the following is a possible price (as a percentage of par) of the corporate bond?
A. 97.76
B. 98.19
C. 98.78
D. 101.35
113
Answer to Example 5-15 A Since the corporate bond involves credit risk and the
government bond doesn’t, the corporate bond must have a higher yield and, therefore, carry a lower price than the government bond, whose price can be computed as follows:n = 2, FV = 100, PMT = 6, i = 7; PV = ? = 98.19.Thus, since the corporate bond price has to be less than the government, there can only be one possible answer: a quote of 97.76.
114
Example 6-1
Assume that $14.5 billion of five-year T-notes are auctioned off. The amount of non-competitive bids is $2.5 billion, and the amount of competitive bids is $31.5 billion. Suppose that of the competitive bids, $11.5 billion are higher than the high yield and the rest are at the high yield. For the competitive bidders at the stop yield, what proportion of their bids will they receive?
A. 38.10%
B. 46.03%
C. 60.00%
D. 72.50%
115
Answer to Example 6-1
C This value is computed as follows:
Non-competitive bids are first subtracted from the total auction value. Therefore, amount available for competitive bids = $14.5b - $2.5b = $12 billion.
Amount of total competitive bids at high yield or lower = 31.5b - $11.5b = $20 billion.
Proportion of competitive bids at stop yield filled = $12b/$20b = 60%.
116
Example 6-2 Which of the following is a difference between an on-
the-run issue and an off-the-run issue? An on-the-run issue:
A. Will always carry a higher coupon
B. Is the most recently issued security of that type
C. Has a shorter maturity than an off-the-run issue
D. Is publicly traded whereas an off-the-run issue is not
117
Answer to Example 6-2
B On-the-run issues are the most recently issued securities.
118
Example 6-3
A Treasury security is quoted at 99-17 and has a par value of $100,000. Which of the following is its quoted dollar price?
A. $99,150.00
B. $99,531.25
C. $100,000
D. $995,312.50
119
Answer to Example 6-3
B This value is computed as follows: dollar price = 97 17/32 x
$100,000 = $97,531.25
120
Example 6-4
A T-note (principal) strip has six months remaining to maturity. How is its price likely to compare to a six-month T-bill that has just been issued? The T-note price will be:
A. Lower
B. Higher
C. The same
D. Set at the coupon rate
121
Answer to Example 6-4
A The T-note principal strip has exactly the same cash flow as
the T-bill. Therefore, the prices of the two securities should be (about)
equal. However, market imperfections, such as illiquidity, may lead
to differences.
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