How are bond prices typically expressed?
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As a percentage of face value.
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How are bond prices typically expressed?
As a percentage of face value.
What was the interest rate on long-term Treasury bonds in the summer of 2016?
1.4%.
What are stripped bonds?
Bonds that make a single payment at a specific time.
What does duration represent in bond valuation?
The weighted average of the times to each of the cash payments.
What is modified duration?
Duration divided by one plus the yield to maturity.
How does modified duration relate to bond price changes?
It measures the percentage change in bond price for a 1 percentage-point change in yield.
What is the total cash payment received at maturity for the OAT?
€106.00 (final interest payment plus principal).
What is the yield to maturity assumed in the bond price calculations?
4%.
What is the yield to maturity of a bond priced at 144.99% with a coupon payment of 6.00%?
The yield to maturity is 0.3%.
What should you enter for the frequency of coupon payments in the PRICE and YLD functions?
1 for annual payments or 2 for semiannual.
What is the measure used to predict a bond's price exposure to interest rate fluctuations?
Duration or Macaulay duration.
Which bond would benefit more from a fall in yields, the 3s or the 9s?
The 3s would benefit more due to their longer effective life.
What factor does the expectations theory leave out that is crucial for investors?
Risk.
What occurs when the yield is higher than the bond's coupon rate?
The bond sells at a discount to face value.
Which type of bond is more sensitive to interest rate fluctuations?
Long-term bonds are more sensitive to interest rate fluctuations than short-term bonds.
What was the long-term interest rate in December 2017?
More than 2.5%.
How are Treasury bonds, notes, and bills traded?
They are traded by a network of bond dealers, not on the stock exchange.
What are three reasons an investor might hold one-year Treasuries despite low returns?
What does the DURATION function in Excel calculate?
The duration of a bond.
What does the Expectations Theory of the Term Structure state?
Investment in a series of short-maturity bonds must offer the same expected return as a single long-maturity bond.
What happens to bond prices when the yield to maturity is equal to the bond's coupon rate?
The bond sells for exactly its face value.
What significant change occurred in interest rates after 1979?
Interest rates climbed sharply due to Paul Volcker's tight money policy.
What was the short-term interest rate in December 2017?
About 1.8%.
What is the duration of the 9% seven-year bonds calculated in the example?
5.69 years.
What is the modified duration of a seven-year 9% bond with a yield of 4%?
5.47.
What is the face value of the bond mentioned?
$1,000.
What is the forward rate of interest?
The extra return for lending for one more year, which reflects future interest rate expectations.
What does a 1% change in yield to maturity result in for the bond’s price?
A 6.15% change.
What is the semiannual yield for the 8.00% bond if bought at the asked price?
0.947%.
What is the present value of the cash flow for year 1 at a 4% yield?
$86.54.
What components make up the present value of a bond?
The present value of the annuity of coupon payments and the present value of the final payment of principal.
Why is modified duration a good predictor of interest rate changes only for small moves?
Because the plot of price against yield is not a straight line.
What is a potential cost that Ms. Kraft might incur when borrowing?
The bank would need to charge more than 7% on the loan to cover its costs.
What was the capital gain for an investor who bought the bond at the issue price?
$416.70.
What is the asked price for the 8.00% bond of 2021?
123.41% of face value.
What is the present value of $1,000 at a 7% interest rate for two years?
$873.
Why might long-duration bonds be more volatile than short-duration bonds?
A sharp increase in interest rates can significantly decrease the price of long-term bonds.
What is a potential strategy for reducing exposure to inflation risk for long-term investors?
Investing in short-term securities and rolling over the investment.
How sensitive are long-term bonds to changes in interest rates compared to short-term bonds?
The price of long-term bonds is more sensitive to changes in interest rates than that of short-term bonds.
What does a 1% change in interest rates predict for bond price changes, according to the text?
A 5.47% change in bond price.
What is the risk associated with investing in 20-year strips for retirement savings?
Uncertainty about future inflation and its impact on purchasing power.
How is the yield to maturity reported in terms of annual rate?
As R%, where R is the semiannual rate multiplied by 2.
What does the law of one price state regarding cash payments?
The same commodity must sell at the same price in a well-functioning market.
Why does the discount factor decline as futurity increases?
The longer you have to wait for your money, the less its present value.
What is the face value of the OAT bond mentioned?
€100.
What was the yield of the 4.375% bond after the financial crisis?
The yield fell to 2.5%.
How do bond prices react to changes in interest rates?
Bond prices move in opposite directions to interest rates; when interest rates rise, bond prices fall, and vice versa.
What is the initial investment amount for Ms. Kraft's one-year Treasury strip?
$833.
What is the yield to maturity?
The yield to maturity is the discount rate that explains the bond price.
What will the Treasury strip pay off next year?
$1,000.
How can a bond be valued?
As a package of an annuity (the coupon payments) and a single final payment (the repayment of principal).
What is the present value of the 6.00% OAT bond?
€144.99.
What was the peak interest rate on 10-year government bonds within two years after 1979?
15.8%.
What happens if everyone expects future one-year rates to exceed 9%?
Investors would prefer to invest in one-year bonds and reinvest at the higher rate.
What does the term 'arbitrage' refer to in financial markets?
The opportunity to make a risk-free profit by exploiting price differences.
What is the general procedure for calculating the yield to maturity?
Trial and error, or using a spreadsheet program or a specially programmed calculator.
What is the method for calculating accrued interest?
It varies from one type of bond to another.
How do you calculate the present value (PV) of cash flows using spot rates?
PV = 1 / (1 + r1) + 1 / (1 + r2)^2.
What is the calculated duration of a bond priced at $1,300.10?
5.69 years.
What is the purpose of the MDURATION function in Excel?
To calculate the modified duration (or volatility) of a bond.
What is the relationship between the timing of cash payments and bond price sensitivity?
Bonds with cash flows occurring later (at maturity) are more sensitive to interest rate changes.
How much profit does Ms. Kraft make by borrowing 830?
$43.
What is the relationship between coupon payments and duration calculations?
Duration calculations recognize that coupon payments are semiannual.
What is the term structure of interest rates?
The relationship between short- and long-term interest rates.
What happens to long-term interest rates in a downward-sloping term structure?
Long-term interest rates are lower than short-term rates.
What must be true for the prices of securities X and Y in a capital market equilibrium?
They must be in a specific relationship to avoid potential arbitrage profits.
What does the term structure of interest rates represent?
The series of spot rates r1, r2, ..., rt.
How are spot rates related to bond prices?
Spot rates are used to discount cash flows, which determine bond prices.
What is the annual interest payment (coupon) for the 6.00% OAT?
€6.00.
How do changes in interest rates affect the value of near-term vs. distant cash flows?
A change in interest rates has a modest impact on near-term cash flows but a much greater impact on distant cash flows.
Why do investors track duration?
Because it measures how bond prices change when interest rates change.
What is the formula for calculating duration?
Duration = (1 × PV(C1) + 2 × PV(C2) + ... + T × PV(CT)) / PV.
What is the present value of cash flows if investors demand a return of 0.947% every six months?
$1,234.10.
What happens to the price of a bond when there is a 1% fall in yield?
The price of the bond increases.
What does an upward-sloping term structure indicate?
Investors expect short-term interest rates to rise.
What is the key lesson regarding the value of a dollar received at different times?
A dollar tomorrow cannot be worth less than a dollar the day after tomorrow.
Why might investors demand higher returns for holding long-term bonds?
Due to the extra risk and volatility associated with long-duration bonds.
What happens to the term structure when inflation is particularly uncertain?
It often becomes steeply upward-sloping.
What are Treasury bonds, notes, and bills?
They are U.S. government securities traded in the fixed-income market, with varying maturities.
What is the face value of U.S. Treasury bonds?
$1,000.
What do financial managers often refer to instead of spot interest rates?
Yields to maturity.
What happens to the duration of 3% bonds compared to the initial bond?
Duration increases to 6.40 years.
How is the weight for each cash payment in duration calculated?
By dividing the present value of the cash flow received at that time by the total present value of the bond.
Which function in Excel calculates the yield to maturity of a bond given its price?
YLD.
What was the average return difference between long-term U.S. Treasury bonds and short-term Treasury bills from 1900 to 2017?
1.5 percentage points higher for long-term bonds.
What is the modified duration for the 3% bond mentioned in the text?
6.15%.
How much does each bond cost at the asked price?
$1,234.10.
What are the cash payments for the 9% bond in the example?
1,090 in the final year.
Why is the yield to maturity less than the coupon payment for a bond sold at a premium?
Because the bond is purchased at a price higher than its face value, leading to a capital loss.
What is the implication of a declining term structure?
Investors expect short-term rates to fall.
What happens to arbitrage opportunities in well-functioning markets?
They are eliminated almost instantaneously by investors.
What is the semiannual rate of return if the yield to maturity is reported as 1.893%?
0.00947.
What does the law of one price state regarding risk-free dollars?
Investors place the same value on a risk-free dollar regardless of whether it is provided by bond A, B, or C.
What is the significance of the discount factors in bond valuation?
They are used to calculate the present value of future cash flows from bonds.
What does the average time to cash payments indicate about a bond's duration?
The average time to cash payments can be less than the bond's maturity, affecting its sensitivity to interest rate changes.
What is the function used to find the price of a bond given its yield to maturity in Excel?
PRICE.
What does the expectations theory imply about borrowing short-term when short-term rates are lower than long-term rates?
It implies that such strategies won't work because investors expect interest rates to rise.
What was the rate of return for the investor after seven months?
45.5%.
What is the opportunity cost of capital used to discount the cash flows?
0.3%.
What does a 1% change in yield to maturity indicate for the bond price?
It should change the bond price by 5.47%.
How should yield and coupon values be entered in Excel functions?
As decimal values (e.g., 3% as .03).
What occurs when the yield is lower than the bond's coupon rate?
The bond sells at a premium.
What formula can be used to value the coupon payments of a bond?
The annuity formula.
How do long maturities of bonds change as they approach the final payment date?
They end up with short maturities.
What is the significance of the quoted yield for U.S. bonds?
It is usually quoted as twice the semiannual yields.
What is the purpose of discounting cash flows at spot rates?
To calculate the present value of future cash flows.
How is the price of a bond determined?
By adding the present values of each of its cash flows.
How can the term structure of interest rates be measured?
Using the prices of stripped bonds.
What is the formula for calculating the derivative of bond price with respect to yield?
dPV/dy = - modified duration.
How is modified duration calculated for bonds with semiannual coupons?
By dividing Macaulay duration by the semiannual yield to maturity.
What is the significance of the 'basis' entry in the PRICE and YLD functions?
It is suggested to leave this blank.
What was the yield to maturity for the U.S. Treasury bonds sold on May 15, 2008?
4.60%.
How do you calculate the present value of a loan that pays $1 at the end of one year?
PV = 1 / (1 + r1), where r1 is the one-year spot rate.
What was observed about U.S. short-term and long-term rates between September 1992 and April 2000?
Short-term rates rose sharply while long-term rates declined.
What is the relationship between yields to maturity and spot rates?
Yields to maturity are complex averages of spot rates.
What is a potential anomaly in discount factors when different spot rates exist?
A dollar received the day after tomorrow may not necessarily be worth less than a dollar received tomorrow.
What is the difference between the flat price and the dirty price of a bond?
The dirty price includes accrued interest, while the flat price does not.
What is the total cash payment for the 8.00% bond in May 2021?
$1,040.
At what price were the 4.375% U.S. Treasury bonds issued?
96.38%.
How often are coupon payments made on U.S. Treasury bonds?
Semiannually.
What happens to yield to maturity as bond maturity increases?
The yield to maturity increases.
What does a higher interest rate for longer lending periods indicate?
Investors require a higher interest rate for lending for longer periods.
What is the current yield on an investment if the coupon payment is €6.00 and the bond price is €144.99?
The current yield is 4.14%.
What is the formula for calculating the present value of bond cash flows?
PV = Σ (Cash Flow / (1 + r)^n).
What is the formula for calculating the present value of a loan that pays $1 at the end of two years?
PV = 1 / (1 + r2)^2, where r2 is the two-year spot rate.
What happens to the value of a bond priced below its face value?
It sells at a discount, and investors look forward to a capital gain.
How does the maturity of a bond affect its yield to maturity?
Different maturities can lead to different yields due to varying cash flow structures.
What is the yield to maturity (YTM) in the context of bond valuation?
The single discount rate that equates the present value of future cash flows to the bond price.
What is the relationship between coupon payments and bond pricing?
Bonds with the same coupon but different maturities will have different present values and yields.
What are the cash payments from a bond until maturity?
Regular interest payments and the face value at maturity.
