Chap 3 Flashcards
How many years do notes mature in?
10 years or less
How long do treasury bills take to mature?
A year or less
Treasury bonds, notes, and bills are traded in the
fixed income market
What bond price do you use when calculating the yield? Clean or dirty?
Clean price also known as flat price
How do you present value a bond?
Present value of all coupons (FV x r x 6/12) plus the present value of (redemption value + final coupon)
The interest rate on 10-year U.S. Treasury bonds was highest in…
1977-1984
What is special about bonds with long maturity dates?
Bonds with long maturities end up with short maturities when they approach the final payment date.
Thus you will encounter 30-year bonds trading 20 years later at the same prices as new 10-year notes (assuming equal coupons).
Are long term or short term bonds more sensitive to a change in interest rate?
The price of long-term bonds is more sensitive
How does interest affect price?
They are inversely related. The higher interest rate results in a lower price.
How do you know if a bond is selling at a premium or discount?
Premium: cpn rate > yield
Discount: yield > cpn rate
Bond investors hope for interest rates…
to fall so the value of their investment increases
What is the equation for rate of return?
(coupon income + price change)
_____________________________
investment
Does a change in interest affect near or distant cash flows more?
the value of distant cash flows
What does duration (Maculay duration) measure?
weighted average of the times to each of the cash payments
the lower the coupon, the higher the average time to each cash flow
-because a higher proportion of the cash flows occurs at maturity, when the face value is paid of
duration also predicts the exposure of each bond’s price to fluctuations in interest rates
-ex: if interest rates drop 1%, will there be a greater price increase in a 3% cpn bond or a 9% if they have the same maturity time? (3%)
When interest rates change, will the price of a higher or lower cpn bond be more affected?
Lower cpn bond
How is duration calculated?
- chart with (years to maturity) on the left most column
- cpn payment
- then the pv of cpn payment
- then the fraction of the pv of cpn over total pv
- then the year T times this fraction
Why do investors track duration?
because it measures how bond prices change when interest rates change
What is modified duration?
volatility = duration/ (1+ yield)
Say the duration is 5.47%, what does this mean?
This means that a 1% change in the yield to maturity should change the bond price by 5.47%.
What is the term structure of interest rates?
The relationship between short- and long-term interest rates
What does a downward sloping term structure mean?
long-term interest rates were lower than short-term rates
Is modified duration a good predictor for large changes in interest rates?
No, modified duration is a good predictor of the effect of interest rate changes only for small moves in interest rates
What if you calculate macaulay duration assuming annual cpn’s and then you want it for semi annual?
To calculate modified duration with semiannual coupons you need to divide Macaulay duration by the semiannual yield to maturity.
What is a spot rate? When do we use r1 vs r2 etc.?
r1 is a one year spot rate. We would use this when we need the pv of a single cash flow 1 year from now
r2 is the two year spot rate we would use if we needed to discount back 1$ that is paid at the end of 2 years
if you had an investment that paid $1 at the end of year 1 and again at the end of year 2, you would use r1 for the first and r2 on the second
Do short- and long-term interest rates always move in parallel?
NOOOO
Can we calculate yield to maturity without knowing price? What about if you know spot rates?
You cant calculate yield without knowing price. Spot rates come first, then bond prices are found, then yield to maturity is found.
What is the law of one price? What does it have to do with spot rates?
it states that the same commodity must sell at the same price in a well- functioning market
all safe cash payments delivered on the same date must be discounted at the same spot rate
When the law of one price is applied, are YTM rates and bond maturity positively or inversely related? Why?
yield to maturity increases as bond maturity increases, there is a positive relationship. investors will demand a higher rate of return on a longer investment (assuming equal risk)
The yields increase with maturity because the term structure of spot rates is upward-sloping (see graph in tb)
How do yield rates and spot rates connect?
Yields to maturity are complex averages of spot rates
Can a dollar today be worth less than a dollar tomorrow?
NO
Is there such thing as arbitrage in well functioning markets?
NO
Why would you hold onto a one year investment with a low rate of return?
- You believe that short-term interest rates will be higher in the future.
- You worry about the greater exposure of long-term bonds to changes in interest rates.
- You worry about the risk of higher future inflation.
When would the term structure of interest be upward sloping?
when future interest rates are expected to rise; short-term interest rates to rise
How is the yield rate an “average” of spot rates?
A two-year yield rate will incorporate both today’s one-year rate (r1) and the consensus forecast of next year’s one-year rate (r2)
What does the expectations theory state?
It states that in equilibrium investment in a series of short-maturity bonds must offer the same expected return as an investment in a single long-maturity bond. Only if that is the case would investors be prepared to hold both short- and long-maturity bonds.
When would we have declining term structure?
investors expect short-term rates to fall
What does the expectations theory leave out?
RISK
What is the forward rate of interest? Can it be negative?
The extra return for lending for one more year, it can never be negative
Does a higher volatility create extra risk?
Volatility of long-term bonds does create extra risk for investors who do not have such long-term obligations
These investors will be prepared to hold long bonds only if they offer the compensation of a higher return.
How can you reduce exposure to inflation risk?
You can reduce exposure to inflation risk by investing short-term and rolling over the investment (reinvesting?)
You do not know future short-term interest rates, but you do know that future interest rates will adapt to inflation. If inflation takes off, you will probably be able to roll over your investment at higher interest rates.
When inflation is uncertain, would term structure be upward or downward sloping?
steeply upward sloping
What is the formula for converting between real and nominal rates/ cash flows?
(1+r) = (1+nominal r)
__________________
(1 + inflation)
if cash flows, replace rates and do (1 + inflation)^t
OR r real = r nominal − inflation rate
When were indexed bonds started in the states and what are they called?
1997, called TIPS. The cash flows increase with inflation, and decrease with deflation. Purchasing power will remain constant at interest rate.
were almost unknown prior to this time, but not completely unknown
If the yield on TIPS is less than nominal yield on normal Treasury bonds, and inflation is grater then the difference between the two, do investors holding tips earn higher or lower rate of return?
What if the inflation rate is less than the difference between real and nominal?
a) Investors will earn a higher return by holding long-term TIPS
b) The investor would have been better off with nominal bonds
What 2 things do the real interest rate depend on?
1) willingness to save (the supply of capital)
2) opportunities for productive investment by governments and businesses (the demand for capital)
If investment opportunities rise what happens to interest? What about if they fall?
If investing rises, thee rate has to rise to induce individuals to save the additional amount that firms want to invest
If investment opportunities decrease, there will be a fall in the real interest rate.
Investment grade bonds vs junk bonds?
Investment grade:
Moodys: Aaa, Aa, A, Baa
Standards: AAA, AA, A , BBB
Junk Bonds:
Moodys: Ba, B, Caa, Ca C
Standards: BB , B , CCC, CC, C
Why are yields on corporate bonds higher than government bonds?
Because of default risk, higher risk = higher yield
Corporate bonds are also less liquid the treasuries
Explain the 4 different kinds of debt (Sovereign, Foreign , Own Currency, Eurozone)
Debts relating to government that can cause defaults
Sovereign is government debt
Foreign = foreign government borrows dollars
Own currency = less liklihood of default, can just print more money
Eurozone = the 19 countries in the eurozone do not even have the option of printing money to service their domestic debts
Occasionally, defaults have been a case of “won’t pay” rather than “can’t pay.” True or false?
True
