15 Bonds and Interest Rates

Question 1

Bonds

Answer 1

• Contract between lender (buyer) and issuer (borrower)
• Stipulates rights of the buyer and requirements of the issuer

Question 2

YTM

Answer 2

Bond’s internal rate of return
- Equates PV of a bond’s payments to its price
- Assumes that all bond coupons can be reinvested at the YTM (reinvestment rate risk)

Question 3

Current yield

Answer 3

• Bond’s annual coupon payment divided by the bond price

Question 4

If coupon … YTM:

Answer 4

=: bond trades at face value
>: at a premium to face
<: at a discount to face

Question 5

Bond price formula

Answer 5

P = ΣC/(1+r)ᵗ + ParValue/(1+r)ᵗ

C = coupon payments
t = periods to maturity
r = semi-annual/annual ytm

Question 6

Bond value formula

Answer 6

BondV = C[(1-1/(1+r)ᵗ)/r] + F/(1+r)ᵗ

BondV = PV(Annuity) + PV(lump sum)

Question 7

Measuring default risk

Answer 7

Rating companies
- Moody’s Investor Service, Standard & Poor’s, Fitch

Rating categories
- Highest AAA or Aaa
- Investment grade bonds: BBB/Baa and above
- Speculative grade bonds: Below BBB or Bbb

Question 8

Bond price sensitivity

Answer 8

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

+ the smaller the coupon, the greater the sensitivity

Question 9

Measuring interest rate risk - Duration

Answer 9

Duration:
- Measures the effective maturity of a bond
- Calcs the weighted average of the times until each payment is received
- Sets these weights proportional to PV of payment

Duration=Maturity for zero coupon bonds
Duration<Maturity for coupon bonds

Question 10

Duration

Answer 10

D = Σt*wₜ

where

wₜ = (CFₜ/(1+ytm)ᵗ)/P

Question 11

Modified duration

Answer 11

D* = D/(1+y)

Question 12

What does Duration tell us?

Answer 12

ΔP/P = -D*Δy

Question 13

Portfolio Duration

Answer 13

Weighted average of the durations of the bonds in portfolio

Question 14

Term structure of interest rates - Expectations Hypothesis Theory

Answer 14

• Observed long-term rate is a function of today’s short-term rate and expected future short-term rates
• fₙ = E(rₙ) and liquidity premiums are 0

Question 15

Term structure of interest rates - Yield curve under certainty

Answer 15

Invest for 2 years, either:
- buy and hold a 2yr zero
- rollover a series of 1yr bonds

Equilibrium requires that both strategies provide the same return

Question 16

Term structure of interest rates - Liquidity Preference Theory

Answer 16

• Long-term bonds are riskier: fₙ > E(rₙ)
• This excess is the liq premium
• Yield curve has an upward bias built into the long-term rates bc of liq premium

Question 17

Yield curve

Answer 17

Reasonable predictor of the business cycle
- LT rates tend to rise in anticipation of economic expansion
- Inverted YC may indicate that intrates are expected to fall and signal a recession

Question 18

Where would inverted YCs not predict a recession:

Answer 18

Credit Default Swaps (CDS)

• Acts like an insurance policy on the default risk of a corporate bond or loan
• Buyer pays annual premiums
• Issuer agrees to buy bond in a default or pay the difference between par and market values to the CDS buyer

=> Institutional bondholders used CDS to enhance creditworthiness of their loan portfolios, to manufacture AAA debt
=> Can also be used to speculate that bond prices will fall (tf there can be more CDS outstanding than there are bonds to insure)