NOTES H
IX. How to Read Financial Bond Pages
Understanding of the previously discussed interest rate measures will permit you to
make sense out of the tables found in the financial sections of newspapers and
magazines that report on U.S. Treasury debt instruments and corporate bonds traded
on stock exchanges. He illustrates his discussion using the financial pages from the
January 26, 2000 issue of the Wall Street Journal.
This section reviews the main points of textbook discussion, using the financial
pages from the February 17, 1999 issue of the New York Times to illustrate and
elaborate key points. As will be seen, the form in which financial information is
reported in the New York Times is essentially the same as in the Wall Street Journal,
with only minor notational differences.
The asked price minus the bid price -- referred to as the bid-ask spread -- reflects the
profit margin of the bond dealers who handle trades in this bond. Hence, for obvious
reasons, the asked price always exceeds the bid price.
The fifth column (Chg) indicates the change in the BID price from the previous
trading day's quotation.
The sixth and final column (Yld) provides the yield to maturity on the bond using the
currently quoted ASKED price as the purchase price. The asked price is used
because the yield to maturity is most relevant for a person who intends to purchase
and hold the bond and thus earn the yield.
IMPORTANT: Both bid and ask prices are ‘clean’ prices. That is, they do not
include the accrued interest. See the following example based on quotes above.
This ant the following example are only for illustration, this will not be required in tests!
A. Treasury Bonds and Notes:
Treasury bonds (T-bonds) are coupon bonds with a maturity greater than ten years,
and Treasury notes (T-notes) are coupon bonds with a maturity of between one and
ten years. As in the Wall Street Journal, the New York Times provides a single table
reporting on T-bonds and T-notes because both have the same structure.
Below is a sample listing from the T-bonds and T-notes table appearing in the Wall
Street Journal (September 16, 2002, handout) which reports information for the
previous trading day, September 15, 2002:
Rate
11.125
3.625
Maturity
Aug 03
Aug 03 n
Bid
108:15
101:25
Ask
108:16
101:26
Chg
-3
…
Ask. Yld
1.66
1.70
Notational Note: For expositional simplicity, T-bonds and T-notes will hereafter be
lumped together and simply referred to as "bonds."
The first column (Rate) identifies a bond's annual coupon rate, i.e., the annual
coupon payment as a percentage of face value. Usually this annual coupon payment
is paid in two equal semiannual installments.
The second column (Month) of the sample listing identifies the month and year that a
bond matures. A footnote may next be provided to indicate that a bond has some
special feature. For example: the letter "n" denotes "T-note".
The third and fourth columns (Bid, Ask) provide information about a bond's bid and
asked prices, which by convention are quoted as a percentage per $100 of face value
(so that 100 = face value) with fractions in 32s. Unlike the Wall Street Journal,
which uses a colon to indicate fractional values in 32s (e.g., 102:08 = 102 8/32), the
New York Times uses a decimal point (e.g., 102.08 = 102 8/32).
More precisely, the bid price quoted for a bond is the approximate market price
offered by prospective buyers of the bond on the trading day in question, so it
indicates approximately how much you would have received if you had sold the
bond on that day. In contrast, the asked price quoted for a bond is the approximate
market price demanded by prospective sellers of the bond on the trading day in
question, so it indicates approximately how much you would have had to pay to
purchase the bond on that day.
Assume that the T-bond has COUPON RATE equal to 11.125%. Its FACE
VALUE of $100,000 will be paid on August 13th, 2003 (=MATURITY
DATE). Note that T-bonds have semi-annual coupons.
1/ What is accrued interest on September 15th, 2002?
First notice that during the remaining 332 days this bond will pay total interest
of 11.125%*$100,000=$11,125 and the principal of $100,000. There will be
two payments. In 149 days (March 13th, 2003) owner of the bond will receive
first of the two coupon payments of $5,562.50. 183 days later (August 13th,
2003) she will receive $105,556.50 of second coupon and principal.
On September 15th, it was 33 days from the last payment of coupon on August
13th. Thus, accrued interest is 33/(33+149) * $5,562.50=$1,008.60.
2/ How much would you pay on September 15th, 2002 to buy this bond?
You will have to pay both ask price and the accrued interest. Therefore you
would pay $100,000 * (108+16/32) + $1,008.60 = $109,508.60.
3/ What was this bond’s ask yield to maturity on September 15th, 2002?
Ask yield to maturity i, satisfies: Present Value of future payments = Purchasing
price. That is, purchasing price of $109,508.60 equals to present value of
5,562.50
105,562.50
------------ + -------------1+i*(149/365)
1+i*(332/365)
This is true only for i=0.0166=1.66%.
Note: The treasury note with coupon rate 3.625 has a maturity date August 29th.
It also pays interest twice a year (in 165 and 348 days). Thus, its price is
$101,980.85 ($101,812.50 of clean price + $168.35 of accrued interest), its ask
yield to maturity is 1.7%.
Note on Treasury Zero Coupon Issues: Coupon stripping is the act of removing the
individual coupon payments from a coupon bond and treating each payment as a
separate zero coupon bond. The remaining face-only bond is then also in effect a
15
zero coupon bond. For example, a 20-year bond with a face value of $100,000 and
an annual coupon payment of $10,000 could be stripped into 21 separate zerocoupon instruments: namely, 20 "interest strips" consisting of the 20 annual coupon
payments of $10,000, each due on the specified annual coupon payment date; and
one "principal strip" consisting of an instrument having a face value of $100,000 due
in 20 years.
Merrill
Lynch
began the market
10
10
0
0
0
0
for
stripped
securities
in
10
10
0
0
0
1982. The U.S.
Treasury
10
10
0
0
introduced
stripping of its
10
100
10
100
coupon
bond
issues
in
February 1985, referring to the resulting zero-coupon securities as STRIPs (Separate
Trading of Registered Interest and Principal of Securities). U.S. Treasury strips are
mentioned in the explanatory notes for the Wall Street Journal bonds.
B. Treasury bills:
Treasury bills (T-bills) are discount bonds with a maturity of one year or less. Since
a coupon rate is zero, they are identified solely by their maturity date.
Below is a sample listing from the T-bills table appearing in the WSJ (September
16, 2002) which reports information for the previous trading day, September 15,
2002:
Date
Jan
9 03
Jan 16 03
Days to Mat.
114
121
Bid
1.65
1.66
Ask
1.64
1.65
Chg
0.01
0.01
Yield
1.67
1.68
The first column (Date) gives the month, day, and year of the maturity date.
The third column (Bid) gives the discount yield in percentage terms using as the
purchase price Pd the BID price, i.e., the price offered by prospective buyers. The
third column (Ask) gives the discount yield in percentage terms using as the
purchase price Pd the ASKED price, i.e., the price demanded by prospective sellers.
Recall that the discount yield varies inversely with the purchase price Pd. It follows
that, for T-bill issues, the bid discount yield reported in the Bid column is always
greater than the asked discount yield reported in the Ask column, indicating that the
bid price is less than the asked price.
The fourth column (Chg) reports the change in the asked discount yield from the
previous trading day measured in terms of basis points, which are hundredths of a
percentage point (e.g., -0.04 means the asked discount yield has fallen in percentage
terms by 4 basis points).
The fifth and final column (Yield) provides the yield to maturity using the current
ASKED price as the current value.
Can you verify that the presented yields to maturity is computed correctly?
Assume that F=$100. In case of the first T-bill, idb=1.64% and
there are 114 days to maturity. Thus from equation (6) we can
find price of the bill Pd:
$100 - Pd
360
1.64% = --------- * ------ -> Pd = $99.48
$100
114
Yield to maturity equals to i, where
$100
Pd= ----------------1 + i*(114/365)
thus,
$100 - Pd
365
i = --------- * -----Pd
114
= 0.0167 = 1.67%.
C. Corporate Bonds Traded on Exchanges:
A majority of bonds, and all municipal or tax-exempt bonds, are not listed on
exchanges; rather, they are traded over-the-counter. However, the New York Stock
Exchange (NYSE), and to a much less extent the American Stock Exchange
(AMEX), do list various coupon bonds issued by corporations with strong credit
ratings.
Below is a sample listing from the NYSE corporate bond table appearing in the New
York Times (February 17, 1999, page C17) which reports information for the
previous trading day, February 16, 1999:
Company
ATT
ARetire
Coupon
Rate
5 1/8
5 3/4
Mat.
01
02
Cur.Yld.
5.1
cv
Vol.
60
25
Price
99 7/8
89 1/2
Chg.
+
1/8
1 1/2
The first column (Company) shows the issuing company, the second column gives
the original coupon rate, and the third column gives the last two digits of the
maturity year. The fourth column reports the annual current yield (Cur. Yld.). In
some cases, a footnote may instead be inserted to call attention to a special feature of
the bond; for example, the letters "cv" in the above table denote "convertible into
stock under special conditions".
The remaining three columns report the number of bonds traded for the day
measured in $1000 face value (Vol.), the bond's closing price for the day expressed
as a percentage of face value with 100 equaling face value (Price), and the difference
between the current trading day's closing price and the previous trading day's closing
price (Chg).
X. Interest Rates vs. Return Rates
Given any asset A held over any given time period T, the return to A over the
holding period T is, by definition:
the sum of all payments (rents, coupon payments, dividends, etc.) generated
by A during period T, assumed paid out at the end of the period,
16
PLUS the capital gain (+) or loss (-) in the market value of A
over period T, measured as the market value of A at the
end of period T minus the market value of A at the
beginning of period T.
NOTES I
P (1 )
C
C
C
C + FV
C
C + FV
Y ie ld to M a tu rity P V = P (1 )
P (1 )
P (2 )
C + P (2 )
C
R a te o f
R e tu rn
The return rate on asset A over the holding period T is then defined to be the return
on A over period T divided by the market value of A at the beginning of period T.
More precisely, suppose that an asset A is held over a time period that starts at some
time t and ends at time t+1. Let the market value of A at time t be denoted by P(t)
and the market value of A at time t+1 be denoted by P(t+1). Finally, let V(t,t+1)
denote the sum of all payments accruing to the holder of asset A from t to t+1,
assumed to be paid out at time t+1.
Then, by definition, the return rate on asset A from t to t+1 is given by the following
formula:
(24)
Return Rate on
Asset A From
time t to t+1
=
V(t,t+1) + P(t+1) - P(t)
--------------------------P(t)
=
V(t,t+1)
--------P(t)
= payments
received as
percentage
of P(t)
+
+
P(t+1) - P(t)
------------P(t)
Capital Gain (if +)
or Loss (if -) as
percentage of P(t)
the return rate defined by formula (24) and the interest rate on the bond defined by
yield to maturity, current yield, or discount yield?
The return rate on a bond is not necessarily equal to the interest rate on that
bond, whether defined by yield to maturity, the current yield, or the discount yield.
The reason for this is that the return rate calculated for a particular holding period
takes into account any capital gains or losses that occur during this holding period, in
addition to payments received during the holding period. In contrast, the current
yield ignores capital gains and losses altogether, and the yield to maturity and the
discount yield only take into account the overall anticipated capital gain or loss that
is incurred when the bond is held to maturity (as measured by the difference between
the final face value payment and the initial purchase price).
EXAMPLE A: COUPON BONDS
Suppose you purchase a coupon bond at time t at a price P(t) with coupon payment C
and face value F, you receive a coupon payment C at time t+1, and you also sell the
coupon bond in a secondary market at a price P(t+1) at time t+1. By definition, the
current yield that you receive on this coupon bond during the holding period from t
to t+1 is given by
(25)
ic(t) = C/ P(t)
Also, the percentage capital gain or loss you incur on the coupon bond during the
holding period from t to t+1, denoted by g(t,t+1), is given by
P(t+1) - P(t)
(26)
g(t,t+1)
=
----------------.
P(t)
It then follows from definition (9) that the return rate on the coupon bond from t to
t+1 can be expressed as
C + P(t+1) - P(t)
(27) --------------------=
ic(t) + g(t,t+1) .
P(t)
Clearly the return rate (24) coincides with the current yield ic(t) if
(28)
P(t)
=
P(t+1) .
Condition (28) implies that there are no capital gains or losses on the coupon bond
during the holding period from t to t+1, i.e., g(t,t+1) = 0. Conversely, if condition
(28) fails to hold, then the return rate (27) does not coincide with the current yield
ic(t). Thus, condition (28) is both necessary and sufficient for the return rate (27)
from t to t+1 to equal the current yield ic(t). That is:
Return Rate
From t To t+1
=
ic(t)
if and only if
<-------------->
P(t) = P(t+1)
Now suppose, instead, that Time Period from t to t+1 = Bond Maturity Period:
Return Rate = i(t)
From t To t+1
if and only if
<-------------->
Period From t to t+1
= Maturity Period
Formula (24) holds for any asset A, whether physical or financial. In particular, it
holds for bonds. The question then arises: For bonds, what is the connection between
17
EXAMPLE B: DISCOUNT BOND
For a discount bond with a purchase price Pd and a face value F, the return rate (9)
over any holding period t to t+1 reduces to
P(t+1) - Pd
(29)
----------.
Pd
Recalling definition for the discount yield idb, it is seen that the return rate will
generally differ from idb except in the degenerate case Pd = P(t+1) = F when both
are zero.
…In summary, then, only under special conditions will the return rate
for a bond over a given holding period coincide with the yield to maturity, the
current yield, or the discount yield.
XI. Real vs. Nominal Interest Rates
The interest rate measures examined to date have all been "nominal" in the sense that
they have not been adjusted for expected changes in prices. What actually concerns a
"rational" saver considering the purchase of a debt instrument is not the nominal
payment stream he or she expects to earn in future periods but rather the command
over purchasing power that this nominal payment stream is expected to entail. This
purchasing power depends on the behavior of prices.
Let infe(t) denote the expected inflation rate at time t, and let i(t) denote the
(nominal) interest rate for some debt instrument at time t. Then the real interest rate
associated with i(t) is defined by the following "Fisher equation:"
any holding period from t to t+1 is defined to be the (nominal) return rate (9) minus
the expected inflation rate infe(t).
TABLE – One-Year Returns on Bonds When Interest Rates Rise from 10% to 20%
(1)
Years to
maturity
when bond
is purchased
(2)
Initial
current
yield
(%)
(3)
Initial
price
10
10
10
10
10
10
10
infinite
30
20
10
5
2
1
($)
(4)
Price
next
year
($)
(5)
Rate of
capital
gain
(%)
(6)
Rate of
Return
(2+5)
(%)
1000
1000
1000
1000
1000
1000
1000
500
503
516
597
741
917
1000
-50.0
-49.7
-48.4
-40.3
-25.9
-8.3
-0.0
-40.0
-39.7
-38.4
-30.3
-15.9
1.7
+10.0
XII. Interest Rate Risk
As previously seen, at any time t, the yield to maturity i(t) for a bond with a maturity
date greater than t moves inversely with its current acquisition price P(t) -- that is, if
10%
10%
$ 1,000
$ 1,000
(30) ir(t) = i(t) - infe(t) .
$ 100 + $1,000
That is,
the real interest rate is the nominal interest rate minus the expected inflation rate.
Note: As explained by Mishkin, the real interest rate defined by (16) is more
precisely called the ex ante real interest rate because it adjusts for expected changes
in the price level. If the expected inflation rate in (16) is replaced by the actual
inflation rate, one obtains the ex post real interest rate.
Real interest rates provide a more accurate measure of the true costs of borrowing
and the true gains from lending than nominal interest rates, and hence provide a
better indicator of the incentives to borrow and lend. In particular, for any given
nominal interest rate i on a debt instrument D, the incentive to borrow (issue D) will
be higher if the real interest rate associated with i is lower (i.e., the expected inflation
rate is higher). This is so since a higher expected inflation rate means the borrower
(issuer of D) can expect to pay off his future nominal debt obligations using cheaper
dollars than he borrowed. For this same reason, the incentive to lend (purchase D)
will be lower if the real interest rate associated with i is lower.
A similar distinction is made between the (nominal) return rate defined by (9), which
has not been adjusted for expected changes in prices, and the "real return rate" which
is subject to such adjustment. More precisely, the real return rate on any asset A over
P(2)
$ 100 + P(2)
20%
?
20%
?
10%
$ 1,000
10%
?
P(2)
$ P(1)
1,000
P(2)
$ 100 + P(2)
$ 100 + $ 1,000
$100
$ 100 + $ 1,000
20%
$ 100 + P(2)
?
$100
$100
$ 100 + $ 1
20%
one goes up, the other goes down.
A fall in the price of an already held bond signals a capital loss to the holder.
Consequently, the net effect of an increase in the yield to maturity for an already
held bond can be a decrease in the return rate to its holder.
18
NOTES J
The uncertainty regarding return rate that bond holders face due to
possible changes in yield to maturity is called interest rate risk.
Table illustrates interest rate risk for bonds of different maturities, each with a
coupon payment of $10 and a face value of $1000. This illustration is worth
reviewing with some care.
First note that, for each bond in the Table, the initial yield to maturity i(1) for year 1
("this year") is equal to the initial current yield ic(1) = 10 percent for year 1 because
the initial price of the bond is set at its face value of $1000. However, by assumption,
the yield to maturity i(2) for year 2 ("next year") increases to 20 percent.
The coupon bond listed in the Table with a 1-year maturity has a price P(2) in year 2
that is fixed (by contract) at the bond's face value, $10000. For all other listed
coupon bonds, however, their maturities exceed one year. Consequently, when i(2)
increases, their price P(2) in year 2 decreases to some value smaller than their
original price P(1) = $1000 in year 1 and hence smaller than the bond's face value of
$1000. For example, for the coupon bond with a 30-year maturity, P(2) = $503.
The return rate from year 1 to year 2 for each of the coupon bonds in Table 2 is
given by the sum of the current yield ic(1) = C/P(1) for year 1 and the capital loss
g(1,2) = [P(2)-P(1)]/P(1) from year 1 to year 2.
Consequently, except for the bond with a one-year maturity, these return rates are
smaller than they would have been without the increase in the yield to maturity in
year 2. Indeed, for the coupon bond with a 30-year maturity, the capital loss g(1,2) is
so large (-49.7 percent) that it overwhelms the 10 percent initial current yield ic(1) =
10 percent, resulting in a negative return rate of -39.6 percent from year t=1 to t=2.
More precisely, examining the return rates in column (6) of the Table as the maturity
is decreased from 30 years to 1 year, it is seen that the coupon bonds with longer
maturities experience a greater decline in their return rates when the yield to maturity
i(2) increases. This is due to the fact that this increase in i(2) results in a smaller
decline in the price P(2) for coupon bonds with smaller maturities and hence a
smaller capital loss. [To see why, consider the formula Pb = PV(i) from which the
yield to maturity i is determined.] Indeed, for coupon bonds with a one-year
maturity, P(2) remains fixed at the face value $1000.
(30)
Increase in yield to maturity
from year 1 to year 2
/|\
|
i(1)=ic(1)
i(2)
|--------------|-----------/\/\/\--|
Year
1
2
N
P(1)
P(2)
Maturity Date
|
(N > 2)
\|/
Capital loss
from t=1 to t=2
An important implication of this illustration is that the return
rates of bonds with longer-term maturities respond more
dramatically to changes in the yield to maturity than bonds with
shorter-term maturities. That is, longer-term bonds are more
subject to interest rate risk.
This is one reason why investment in longer-term bonds is considered more risky
than investment in shorter-term bonds.
XIII. More Basic Concepts and Key Issues
Current yield
Discount yield
(Nominal) return rate
Real interest rate
Real return rate
•
•
•
•
•
•
•
•
•
Consol bond (perpentuity)
Capital gain or loss
Interest rate risk
Expected inflation rate
Calculating the current yield for a consol bond
For a coupon bond, how does its maturity affect the relationship between its
current yield and its yield to maturity? What is the relationship between its
current yield, its coupon rate, its purchase price, and its face value? What is the
relationship between its current yield, its yield to maturity, its purchase price,
and its face value? What is the relationship between its current yield and its
purchase price, given any fixed level for its coupon payment?
For a discount bond, all else remaining the same, why do its discount yield and
its yield to maturity always move together?
How to read financial bond pages for information on Treasury bonds and notes,
Treasury bills, and corporate bonds traded on stock exchanges.
Why is the return rate on a bond not necessarily equal to its interest rate?
How does the maturity of a bond affect its interest rate risk? Why do bonds
with long maturities expose bond holders to greater interest rate risk than bonds
with shorter maturities?
What is the relationship between real and nominal interest rates?
Why do real interest rates provide a more accurate measure of the true costs of
borrowing and the true gains from lending than nominal interest rates?
Why do real return rates provide a more accurate measure of the true gains or
losses from holding an asset than nominal return rates?
19
XIV. Practice Questions
Answers for questions below:
Q1.
A.
B.
C.
D.
Q2.
A.
B.
C.
D.
E.
1D
2A
3B
4 22% 5 20%
6D
7B
8C
9C
10 C
11D
12D
Which of the following statements is/are true in general for FIXED PAYMENT
loans?
At maturity the borrower makes one fixed payment, equal to face value.
The borrower makes only one fixed payment, at maturity, and this payment
combines interest and principal repayment.
The borrower makes the same fixed payment in every payment period until
maturity, where the payments consist entirely of principal repayments.
The borrower makes the same fixed payment in every payment period until
maturity, where the payments consist of both interest and principal.
Which of the following statements is/are true in general for COUPON
BONDS?
The issuer makes a fixed coupon payment in every payment period during
the life of the bond, plus a face value payment at maturity.
The issuer makes a fixed coupon payment in every payment period during
the life of the bond, where the present value of these cumulated payments
equals the face value of the bond.
Treasury bills are examples of coupon bonds.
Only A and C of the above
Only B and C of the above
Q3.
The COUPON RATE on a coupon bond with a purchase price of $2500, a
$3000 face value, annual coupon payments of $125, and a 4-year maturity is
A. the coupon payment $125 divided by the purchase price $2500.
B. the coupon payment $125 divided by the face value $3000.
C. the average coupon payment per year, which here is $125.
D. total coupon payments ($500) divided by the purchase price $2500.
Q4. Assume the following simple loan contract:
Principal=50, Interest payment = 22, Maturity is 2 years (maturity date is 2
years from today). What is the SIMPLE (annual) INTEREST RATE?
Q5. In the example from question Q4, what is the yield to maturity i?
A. 10% B. 11% C. 20% D.22%
Q6.
Letting "*" denote multiplication, if the annual interest rate is 5 percent, then
the PRESENT VALUE of a payment stream ($50,$0,$0,$70) with $50 to be
received at the end of the FIRST year, $0 to be received at the end of the
SECOND and THIRD years, and $70 to be received at the end of the
FOURTH year is given by
A. $50/(1.05) + $70/(1.20)
B. $50*(1.05) + $70*(1.05)4
C. [$50 + $70]/(1.20)
D. $50/(1.05) + $70/(1.05)4
Q7. The (ANNUAL) YIELD TO MATURITY i on a coupon bond with a purchase
price $650, a face value $750, a 2-year coupon payment stream ($50,$50), and
a 2-year maturity is calculated as follows:
i equals the annual interest rate that, when used to calculate the present
value of the income stream _____, results in a present value equal to ____.
A. ($50,$50), $650. B. ($50,$800), $650. C. ($50,$50), $750. D. ($50,$800), $750.
Q8. Which of the following $6000 face-value securities has the HIGHEST yield to
maturity? A coupon bond with a coupon rate of __ percent that sells for ____.
A. 5 ; $6,000 B. 10 ; $6,000 C. 15 ; $6,000 D. 15 ; $6,200
Q9. The current yield on a coupon bond with a $7000 face value, a 5 percent
coupon rate, an 8 year maturity, and a current purchase price of $3500 is
A. 5 %
B. 8 %
C. 10 %
D. 16 %
E. 20 %
Q10. Which of the following statements is/are FALSE for the current yield ic of a
coupon bond with coupon payment C, face value F, and maturity N.
A. For a consol bond, the ic equals the yield to maturity.
B. For fixed C and F, the ic is a better approximation for the yield to maturity the
greater is the bond's time to maturity N.
C. For fixed C, F, and N, the ic is a better approximation for the yield to maturity
the more the bond's purchase price exceeds the face value F.
D. all of the above are false statements
E. only A and B are false statements
Q11. Consider a coupon bond that has an annual coupon payment C=$100, a face
value F=$3,000, and a maturity date January 1, 2008. Suppose you BUY this
bond on January 1, 2003 for Pb=$2500 and you SELL it on January 1, 2004
for $2000. Which of the following statements is/are TRUE for this bond:
A. Your (annual) current yield on this bond from 1/1/2003 to 1/1/2004 is equal to
C=$100 divided by the purchase price Pb=$2500.
B. Your return rate on this bond from 1/1/2003 to 1/1/2004 can be expressed
as the sum of the current yield and the rate of your capital gain or loss.
C. Your return rate on this bond from 1/1/2003 to 1/1/2004 is LESS than the
current yield on the bond.
D. All of the above are true.
E. Only A and B are true.
Q12 Suppose a consol bond pays $1 at 11:59 P.M. on December 31 of each year.
Suppose you purchased the consol bond for $100 at midnight on December
31, 2000, and you sold it for $109 at midnight on December 31, 2001.
Suppose the inflation rate during 2001 was 3 percent. Then your NOMINAL
return rate on the consol bond for 2001 was _______ and your REAL return
rate on the consol bond for 2001 was _________.
A. 1 %; -2 %
B. 1 %; 4 % C. 9 %; 6 % D. 10 %; 7 %t E. 10 %; 13 %
20
NOTES K
Summary of major interest rates on the market
Government securities
Municipal Issues
(notice that some are tax free and so their
yield is adjusted by 31% tax bracket)
Private Bonds
9