Bond Yields Questions:
These multiple choice questions willl determine the understanding
you have on bond yields. I do not think any calculator is needed
because it is all very simple addition and multiplication. Students
who are economics majors should pay careful attention to each of the
following sections.
Some of this Bond Yield Questions have been answered for you
already. Professor Blackstock
Econ 215
How can duration and convexity assist the portfolio manager in
assessing the interest-rate risk inherent in a bond portfolio? This
can happen because the greater the duration and convexity, the
greater the interest-rate risk. Since interest-rate risk is a major
source of systematic risk, this makes the portfolio manager's job
easier.
One percentage point of a bond yield represents:100 basis points
If a bond is callable, this means:the issuer may redeem the bond
early.
Subtracting the inflation rate from the market interest rate
results in an approximate real risk-free rate of interest
For risk-free securities, the nominal interest rate is a function
of real rate of interest and expected inflation rate
Under the Fisher hypothesis, if a one point increase in the
inflation rate is anticipated nominal rates on short-term securities
would rise by one pointWhich of the following regarding the current
yield on a bond is not true?
The current yield shows the bond’s expected rate of return if
held to maturity.
In order to have a yield to maturity greater than the coupon rate,
the bond must be:
selling at a discount.
Typically, a yield to call calculation will use the end of the
deferred call period rather than remaining years on the term.
When interest rates rise, bond prices fall.
The yield to maturity consists solely of interest income if the
bond was purchased at par.
The YTM calculation assumes reinvestment of interest is at YTM
rate.
When calculating the yield-to-call on a bond, the stream of
interest payments is __________ and the par value is replaced by the
__________.shortened to the call period . . . call price.
The face value of most bonds is $1000
The Fisher hypothesis is an approximation of the risk-free
interest rate.
Bonds with deferred call features can only be retired after a
specified period following the date of issue.
The real rate of interest is almost always the opportunity cost of
foregoing consumption.
An increase in reinvestment rate risk results from a decline in
interest rates.
The yield-to-call is like the yield-to-maturity except for the
coupon rate and coupon payments.
The yield to maturity is 8 percent. If the yield increases by 50
basis points, the new yield is :
8.500 percent.
A bond is selling at a discount if the:yield-to-maturity is
greater than the coupon rate.
The __________ equates the present value of the total future
dollars expected to be available at the end of a specific time
period, given certain assumptions, to the price of the bond. >
horizon return
If bond investors do not reinvest the coupons received during the
life of the bond, then the
RCY will exceed the YTM.
Find the price of a 10 percent coupon bond with three years to
maturity if the yield to maturity is now 12 percent. Use semiannual
discounting. $950.85 Price = 50(4.917) + 1000(0.705)
The YTM for a zero-coupon bond with 10 years to maturity and
selling for $450 is
8.15 percent. = [1000/450]1/20 – 1
Reinvestment rate risk increases with a ________ coupon rate and a
________ term to maturity.
high . . . long
Which of the following statements regarding the realized compound
yield (RCY) is true?
The RYC does not assume coupons are reinvested at the YTM.
Bond Prices
Which of the following statements regarding changes in bond prices
relative to changes in market yields is true? Short-term bond prices
will increase less than long-term bond prices if market yields
decrease.
Which of the following bonds would you expect to have the greatest
price volatility? 5%, 10 year bond
Which of the following statements about the risk premium affecting
market interest rates is FALSE? The risk premium is not associated
with the issuer's own particular situation.
Bond Price Changes – understand inverse relationships
All other factors constant, the -------------- of a bond, the
shorter the duration. higher the coupon rate
DURATION
Duration can be used minimize interest rate risk.
Duration tells weighted average maturity of a bond.
For all bonds paying coupons, duration is less than maturity.
The duration of a zero coupon bond is equal to its term.
Duration is based upon present value concepts.
Which of the following statements about bond prices is FALSE? Bond
price fluctuations and bond coupons are directly related.
The term used to describe the degree to which duration changes as
the yield to maturity changes is linearity. Not True
Maturity constant, increases in interest rates ___ bond prices by
proportionately __ amounts than decreases in rates ___ bond prices.
decrease . . . smaller . . . increase
Convexity is important in bond analysis because the relationship
between bond price changes and duration is an approximation.
Convexity is largest for bonds with _________ coupons, ________
maturities, and ________ yields to maturity. low . . . long . . . low
Why is the yield to call a more appropriate measure to use for
callable bonds with high coupons rather than the yield to maturity?
High coupon bonds face a greater chance of being called than low
coupon bonds so investors will more likely to receive the yield to
call than the yield to maturity.
Which of the following bond relationships is NOT inverse? Duration
and maturity
Coupon and duration, Interest rate changes and bond prices,
Duration and yield to maturity are INVERSE relationships
A current yield = coupon______
current market price
= 100/850 = 11.76 percent
B = 2 pmts per year, 1000 FV, -850 PV, 20 N, 50 pmt, solve for
interest rate = 12.69 percent
Two 10 percent coupon bonds are selling at par. Bond A has a 15
year maturity and Bond B has a 25 year maturity. If the appropriate
required rate of return for these two bonds drops to 8 percent,
calculate the percentage change in the price of each bond, using a
financial calculator. Assume interest is paid semi-annually.
With regard to duration, choose the INCORRECT statement. Yield to
maturity is directly related to duration.
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Stocks | |
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=
TRUE
X
= FALSE
۞X
Treasury bonds are typically used a proxy for the short-term
riskless rate.
X
The real risk-free rate of interest is the rate that must be
offered to persuade individuals to invest rather than save.
X
If the current yield is above the coupon rate, the bond is
selling at a premium.
X
If two bonds have the same coupon rate and the same term, they
will have the same intrinsic value.
X
The horizon return is the bond return to be earned based on
assumptions about reinvestment rates.
۞
Bond Prices
In bond valuation, the appropriate discount rate is the required
yield.
۞
The higher the discount rate used in bond valuation, the lower the
bond’s intrinsic value.
۞
Bond Price Changes
Duration measures the weighted average maturity of a noncallable
bond’s cash flows on a present value basis is True
Duration expands with time to maturity at an increasing rate is
Not True
Bond Yields
What is the reinvestment rate assumption in regard to the yield to
maturity?
That all receipts of coupon payments are reinvested at the yield
to maturity.
Bond Price Changes
What weakness of modified duration does convexity correct?
Modified duration predictions are linear approximations. Convexity
corrects the answer for the curvature of the price function.
Why does the coupon rate affect the volatility of bond price? The
higher the coupon rate and payment, other things the same, the more
of the bond’s value comes from the coupon payments and the less
from the maturity value. The coupon payments are received sooner than
the maturity value, and, therefore, are affected less by compounding.
For each of the following variables, state whether duration has a
direct or inverse relationship: term to maturity, size of coupon
payment, yield to maturity.
Term to maturity – direct; size of coupon payment - inverse;
yield to maturity – inverse.
Calculate the duration of a bond with a 7 percent coupon and a
3-year maturity currently priced at $1,000. Interest is paid
annually.
Year Cashflow Present Value PV of CF PV/ Price Year X PV/Price
$70 .9346 $65.42 .065 .065
$70 .8734 $61.14 .061 .122
$1070 .8163 $873.44 .873 2.619
$1000 2.806 years
How does value of a bond change as it nears its maturity? Bond
prices will change so that the bond will be worth its face value on
the maturity date.
The next section tests the students general understanding of the
entire chapter. I hope you enjoy this blog entry and find it helpful.
3 reasons that duration is important in bond analysis and
management {
i It measures effective lives of alternative bonds.
ii It is used in bond management strategies.
iii It measures bond price sensitivity to interest rate changes.
.
The following are mathmatical problems. I reccommend using your
iPhone or calculator or computer determine the following answers:
A 10-year, $1000 corporate bond with a 10 percent coupon rate
(interest is paid semi-annually) is currently selling for $850:
(a) Calculate its current yield.
(b) Calculate its yield to maturity (using a financial calculator)
Bond A = original price = $1,000; new price = 1000 FV, 8 interest
rate, 50 pmt, 30 N, solve for PV = $1,172.92
Percentage change in price = 1172.92 - 1000
1000 = .1179 = 11.79%
Bond B = original price = $1,000; new price = 1000 FV, 8 interest
rate, 50 pmt, 50 N, solve for PV = $1,214.82
Percentage change = 1214.82 - 1000
1000 = .2148 = 21.48%