### Bond Yield and Bond Prices 17 Blackstock Econ 215

#### 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.

### 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.

 Stocks

۞ = 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

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%