L12 - BP

Question 1

What are bonds?

Answer 1

• Bonds are debt. Issuers are borrowers and holders are creditors.
• The indenture is the contract between the issuer and the bondholder.
• The indenture gives the coupon rate, maturity date, and par value.
• Face or par value is typically £100 ($1000 in the US); this is the principal repaid at maturity.
• The coupon rate determines the interest payment.
• Interest is usually paid semiannually.
• The coupon rate can be zero.
• Interest payments are called “coupon payments”.

Question 2

Different types of bonds?

Answer 2

• Callable bonds can be repurchased before the maturity date.
• Convertible bonds can be exchanged for shares of the firm’s common stock.
• Puttable bonds give the bondholder the option to retire or extend the bond.
• Floating rate bonds have an adjustable coupon rate
• Of many types:
  
  • Straight bonds
  • Zero coupon bonds (pure discount bonds)
  • Perpetual bonds and preferred stock (dividend payments like coupons –> not always guarantee but have priority when dividends are paid)
  • Gilts
  • Corporate bonds
  • Eurobonds –> an international bond issued in Europe or elsewhere outside the country in whose currency its value is stated (usually the US or Japan).
  • Foreign bonds –> A foreign bond is a bond issued in a domestic market by a foreign entity in the domestic market’s currency as a means of raising capital.

Question 3

What is the original formula for pricing a bond?

Answer 3

Question 4

What is the formula for calculating the price of a bond by hand?

Answer 4

Question 5

What is yield to maturity?

Answer 5

• Yield to Maturity –> average interest rate you expect a bond to earn from buying it now and holding it till maturity
• Bond equivalent yield = same as APR on the bond interest rate

Question 6

What is the approximation formula for yield to maturity?

Answer 6

Question 7

YTM vs Current Yield?

Answer 7

• Current yield = annual coupon/ price of the bond (P)
  
  • whereas coupon rate = Annual coupon / Par value
• If a bond is trading a discount
  
  • Price < par value
• When bond is selling at par –> YTM = Coupon rate (based on approx, formula)

Question 8

YTM vs HPR?

Answer 8

Question 9

How does default risk relate to bond pricing?

Answer 9

• more risk, require a higher return (yield)
• spread widen during 2008 financial crisis
  
  • indication we are heading towards a recession

Question 10

Overview of Term Structure?

Answer 10

• Information on expected future short term rates can be implied from the yield curve
• The yield curve is a graph that displays the relationship between yield and maturity
  
  • Term Structure –> structure of interest rates for discounting different cashflows of varying lengths
• Three major theories are proposed to explain the observed yield curve

Question 11

Different types of yield curves?

Answer 11

1. Flat
2. Rising
3. Inverted
4. Hump Shapred

Yield curve that reflects the YTM of zero-coupon bonds it is called a pure yield curve

• If it reflects the YTM of coupon bonds it is called an on-the-run yield curve (usually those that have just been released and are close to par value)

Question 12

How do we value coupon bonds using zero-coupon bonds?

Answer 12

• Calculate yield curve under certainty (certainty of future interest rates)
  
  • Basically a geometric average of the two short term interest rates
• Yields on different maturity bonds are not all equal.
• Need to consider each bond cash flow as a stand-alone zero-coupon bond when valuing coupon bonds.
  
  • What happens if a coupon bonds price is not equal to the sum of its zero coupons at PV?
    
    • If it is less, one could buy a coupon bond, strip it down into its zero-coupon components and sell them off in the market

Question 13

What is the Short rate vs Spot Rate?

Answer 13

• Spot rate: the rate offered today on zero-coupon bonds of different maturities.
  • In the previous example, the one-year spot rate is 5% and the two year spot rate is 6%.
  • Spot rate is the geometric average of the short rates
• Short rate: the rate for given time interval (one year) offered at different points in time.
  • In the previous example, the first-year short rate is 5% (same as the spot!) and the second-year short rate is 7.01%.

Question 14

What is the forward rate?

Answer 14

• We assumed no uncertainty previously and that all future rates were known at time zero
  
  • In reality, we don’t have perfect knowledge of time n short rates at time zero
• A forward rate is an interest rate applicable to a financial transaction that will take place in the future –> these are the market consensus about the future rates (may not actually be this)

Question 15

How does the interest rates change under uncertainty?

Answer 15

• What can we say when future interest rates are not known today?
• Suppose that today’s rate is 5% and the expected short rate for the following year is E(r2) = 6% then:
  
  • The rate of return on the 2-year bond is risky for if next year’s interest rate turns out to be above expectations, the price will lower and vice versa
    
    • This is because a 2-year bond is priced of the expected short rates zero-coupon bonds
• Investors require a risk premium to hold a longer-term bond
• This liquidity premium compensates short-term investors for the uncertainty about future prices –> as majority of investors are short-term investors
  
  • f₂ > E(r₂)
    
    • f₂ = E(r₂) + liquidity premium

Question 16

What is Segmented Market Theory?

Answer 16

• Segmented market theory has its origin in the observation that many investors and issuers of debt seem to have a strong preference for debt of a certain maturity.
• For instance insurance companies are more interested to invest in long-term bonds even when short-term rates are considerably higher than long-term rates. Same for the companies planning to invest in manufacturing plants or warehouses, they will be more interested in issuing long-term debt.
• Market segmentation theory argues that investors are sufficiently risk averse that they operate only in their desired maturity spectrum
• . No yield differential will induce them to change maturities.

Question 17

What is Expectations Theory?

Answer 17

• yield curve inverted –> future short term interest rates are declining (investors expect the interest rate to fall in the near future)
  
  • e.g. heading towards recession so interest rates will be cut
• yield curve rising –> expectations that future short term interest rates are rising
  
  • e.g. rising inflation

Question 18

What is Liquidity Premium Theory?

Answer 18

• 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

Why is it the hard to infer anything about the short term interest rate form the yield curve? (expand on this)

• Looking at the graphs, the yield curve is meant to be derived from the expected future short term rate plus a liquidity premium
• Yet as you can see the yield curves don’t seem to follow this pattern

Question 19

How can we interpret the Term Structure theories?

Answer 19

• 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
  • Liquidity premium