WEEK 11 - Bond Pricing and the Yield Curve

Question 1

What do we call Issuers and Holders of bonds?

Answer 1

Borrowers -> Issuers

Holders -> Creditors

Question 2

What is the Indenture?

Answer 2

Contract between the issuer and the bondholder.

Gives the coupon rate, maturity date, and par value.

Question 3

What is usually the Par Value?

Answer 3

Face or par value is typically £100 ($1000 in the US); this is the principal repaid at maturity.

Question 4

What does the Coupon Rate determine?

Answer 4

Determines interest payment.

->Interest is usually paid semiannually.

Question 5

What are the Characteristics of Callable,Convertable,Puttable and Floating Rate Bonds?

Answer 5

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

Question 6

What are the different types of bonds?

Answer 6

Straight bonds
Zero coupon bonds (pure discount bonds)
Perpetual bonds and preferred stock
Gilts
Corporate bonds
Eurobonds
Foreign bonds

Question 7

How do you calculate Bond Price?

Answer 7

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

Question 8

What is the relationship between Prices and Yields (Required Rate of Return)?

Answer 8

inverse relationship

Question 9

What happen to bonds when the maturity gets longer?

Answer 9

longer the maturity, the more sensitive the bond’s price to changes in market interest rates.

Question 10

How can we rewrite the bond price Equation (Equation 2 of bond price)

Answer 10

price = Coupon ×1/r

[1 −1/(1 + r)t]+ Par value ×1/(1 + r)t

Question 11

What is the Yield to Maturity?

Answer 11

Interest rate that makes the present value of the bond’s

payments equal to its price

Question 12

How do you calculate the Yield To Maturity?

Answer 12

PB =∑ c/(1 + r)t +ParValue/ (1 + r)t

SEE EXAMPLE IN NOTES

Question 13

How do you calculate r?

Answer 13

r = Coupon + Par−P/T/ (Par + P)/2

Question 14

What is the difference between the YTM and the Current Yield?

Answer 14

YTM
1. The YTM is the bond’s
internal rate of return.

2. YTM is the interest rate that makes the present value of a bond’s payments equal to its price.
3. 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.

2. For bonds selling at a
   premium, coupon rate > current yield>YTM.
3. For discount bonds,
   relationships are reversed.

Question 15

What is the difference between YTM V HPR?

Answer 15

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.

Question 16

What are the different rating companies and what are the categories they rate bonds in?

Answer 16

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

Question 17

How can you get info on expected future short term rates?

Answer 17

Implied from the yield curve

Question 18

What is the yield curve?

Answer 18

->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

Question 19

What are the 3 theories to explain the observed yield curve (Term Structure)?

Answer 19

1. Segmented Mkt Theory
2. Expectations Theory
3. Liquidity Premium Theory

Question 20

When it comes to Bond Pricing what do we need to consider?

Answer 20

Each bond cash flow as a stand-alone zero coupon bond when valuing coupon bonds -> Since Yield on dif maturity bonds not equal

Question 21

When faced with certainty what does an sloping yield curve imply?

Answer 21

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

Question 22

How do we calculate Forward Rates from Observed rates?

Answer 22

(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)

Question 23

What happens when we face interest rate uncertainty (Investors)?

Answer 23

Investors require a risk premium to hold a longer-term bond

This liquidity premium compensates short-term investors for the uncertainty about future prices

Question 24

What does the Segmented Market Theory claim?

Answer 24

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

Question 25

What does the Expectations Theory argue?

Answer 25

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

Question 26

What does the Liquidity Premium Theory?

Answer 26

• > 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

Question 27

How do we interpret the Term Structure?

Answer 27

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