WEEK 11 - Bond Pricing and the Yield Curve Flashcards
What do we call Issuers and Holders of bonds?
Borrowers -> Issuers
Holders -> Creditors
What is the Indenture?
Contract between the issuer and the bondholder.
Gives the coupon rate, maturity date, and par value.
What is usually the Par Value?
Face or par value is typically £100 ($1000 in the US); this is the principal repaid at maturity.
What does the Coupon Rate determine?
Determines interest payment.
->Interest is usually paid semiannually.
What are the Characteristics of Callable,Convertable,Puttable and Floating Rate Bonds?
Callable -> can be repurchased before the maturity date
Convertible -> can be exchanged for shares of the firm’s common stock
Puttable -> give the bondholder the option to retire or extend the bond.
Floating -> have an adjustable coupon rate
What are the different types of bonds?
Straight bonds Zero coupon bonds (pure discount bonds) Perpetual bonds and preferred stock Gilts Corporate bonds Eurobonds Foreign bonds
How do you calculate Bond Price?
PB =∑ c/(1 + r)t +ParValue/ (1 + r)T
Where: c is the annual coupon payment r semi-annual discount rate or the semi-annual yield to maturity. T number of periods to maturity
SEE EXAMPLE IN NOTES
What is the relationship between Prices and Yields (Required Rate of Return)?
inverse relationship
What happen to bonds when the maturity gets longer?
longer the maturity, the more sensitive the bond’s price to changes in market interest rates.
How can we rewrite the bond price Equation (Equation 2 of bond price)
price = Coupon ×1/r
[1 −1/(1 + r)t]+ Par value ×1/(1 + r)t
What is the Yield to Maturity?
Interest rate that makes the present value of the bond’s
payments equal to its price
How do you calculate the Yield To Maturity?
PB =∑ c/(1 + r)t +ParValue/ (1 + r)t
SEE EXAMPLE IN NOTES
How do you calculate r?
r = Coupon + Par−P/T/ (Par + P)/2
What is the difference between the YTM and the Current Yield?
YTM
1. The YTM is the bond’s
internal rate of return.
- YTM is the interest rate that makes the present value of a bond’s payments equal to its price.
- YTM assumes that all
bond coupons can be
reinvested at the YTM
rate.
Current Yield
1. The current yield is the
bond’s annual coupon payment divided by the bond price.
- For bonds selling at a
premium, coupon rate > current yield>YTM. - For discount bonds,
relationships are reversed.
What is the difference between YTM V HPR?
YTM 1. YTM is the average return if the bond is held to maturity. 2. YTM depends on coupon rate, maturity, and par value. 3. All of these are readily observable.
HPR 1. HPR is the rate of return over a particular investment period. 2. HPR depends on the bond’s price at the end of the holding period, an unknown future value. 3. HPR can only be forecasted.
What are the different rating companies and what are the categories they rate bonds in?
Rating companies: Moody’s Investor Service, Standard&
Poor’s, Fitch
Rating Categories:
- > Highest rating is AAA or Aaa
- > Investment grade bonds are rated BBB or Baa and above
- > Speculative grade/junk bonds have ratings below BBB or Baa
How can you get info on expected future short term rates?
Implied from the yield curve
What is the yield curve?
->The yield curve is a graph that displays the relationship
between yield and maturity
(LOOK AT THE SLIDES IN LECTURES TO SEE YIELD CURVES) -> Flat, Rising, Inverted and Hump Shaped Yield Curve
What are the 3 theories to explain the observed yield curve (Term Structure)?
- Segmented Mkt Theory
- Expectations Theory
- Liquidity Premium Theory
When it comes to Bond Pricing what do we need to consider?
Each bond cash flow as a stand-alone zero coupon bond when valuing coupon bonds -> Since Yield on dif maturity bonds not equal
When faced with certainty what does an sloping yield curve imply?
An upward sloping yield curve is evidence that short-term rates are going to be higher next year
-> next year’s short rate is greater than this year’s short rate, the average of the two rates is higher than today’s rate
How do we calculate Forward Rates from Observed rates?
(1 + fn) = (1 + yn)n / (1 + yn−1)n−1
Where:
fn = one-year forward rate for period n, and yn = yield
for a security with a maturity of n.
(1 + yn)n = (1 + yn−1)n−1 (1 + fn)
What happens when we face interest rate uncertainty (Investors)?
Investors require a risk premium to hold a longer-term bond
This liquidity premium compensates short-term investors for the uncertainty about future prices
What does the Segmented Market Theory claim?
Investors are
sufficiently risk averse that they operate only in their desired maturity spectrum.
No yield differential will induce them to change maturities
i.e. Insurance more likely to buy long term bonds even if short term rate higher returns
What does the Expectations Theory argue?
Observed long-term rate is a function of today’s short-term rate and expected future short-term rates
Long-term and short-term securities are perfect substitutes
Forward rates that are calculated from the yield on long-term securities are market consensus expected future short-term
rates
What does the Liquidity Premium Theory?
- > Long-term bonds are more risky Investors will demand a premium for the risk associated with long-term bonds
- > The yield curve has an upward bias built into the long-term rates because of the risk premium
Forward rates contain a liquidity premium and are not equal to expected future short-term rates
How do we interpret the Term Structure?
The yield curve rises as one moves to longer maturities
A longer maturity results in the inclusion of a new forward rate that is higher than the average of the previously observed
rates. This could be because:
- >Markets are segmented
- > Higher expectations for forward rates or
- > Liquidity premium
