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CFAI Flashcards > Fixed Income > Flashcards

Fixed Income Flashcards

1
Q

Conversation Ratio

A

Bond face value / bond conversion price

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2
Q

Measurement of credit risk

A

Difference between yield to maturity on a corporate bond and a government bond with the same maturity

This is known as the credit spread and as G-spread

Considers both default probability and expected loss given default

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3
Q

Expected exposure to default loss

A

Projected amount of money the investor could lose if default occurs before factoring in possible recovery - i.e. PV of bond

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4
Q

Recovery rate

A

Percentage of the loss recovered from a bond in default

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5
Q

Loss given default (LGD)

A

Amount of loss if a default occurs

Notional principle x (1 - recovery rate)

(1 - recovery rate) = also known as loss severity

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6
Q

RIsk-neutral Probability of default (a.k.a. Hazard rate)

A

Probability that a bond issuer will not meet its contractual obligations on schedule

Risk-neutral probability of default should be used to value corporate bonds (i.e. using risk-free interest rate)

P(bond) = [Par value + coupon * prob of survival] + (value recovered given default * risk-neutral prob of default) / 1+ RFR

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7
Q

Difference between using actual vs. risk-neutral default probabilities

A

Actual default probabilities do not include the default risk premium associated with uncertainty over the timing of possible default loss

The observed spread of the yield on a risk-free bond includes liquidity and tax considerations in addition to credit risk

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8
Q

Credit valuation adjustment

A

Value of the credit risk in present value terms. Allows us to calculate the fair value of the bond

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9
Q

8-Steps to Calculate FV of a bond adjusted for credit risk

A
  1. Exposure = Par Value / (1+RFR)^(T-t)
  2. Recovery = Exposure x Recovery Rate
  3. LGD = Exposure - Recovery
  4. POD = Hazard rate - POS(t-1)
  5. POS = (100% - Hazard Rate)^(T-t)
  6. Expected Loss = LGD x POD
  7. Discount Factor = 1 / (1+RFR)^(T-t)
  8. PV of expected loss - Expected loss x DF
  9. CVA = sum of PV of expected loss
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10
Q

Bond Duration

A

Measures the sensitivity of the bonds full price (including accrued interest) to SMALL changes in the bond’s YTM or benchmark rates

Modified Duration - used only for option-free bonds; assumes bond’s expected cash flows do not change when yield changes

Effective Duration - used for straight and embedded option bonds

Change in P = -D x (change in R / 1 + R)

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11
Q

Effective Duration

A

Indicates the sensitivity of the bond’s price to a 100 bps PARALLEL shift of the benchmark yield curve (govt. par curve)

= (PV_) - (PV+) / [2 * (change in rate) x (PV of bond)]

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12
Q

Effective Duration (Callable Bonds)

A

Effective duration of a callable bond cannot exceed that of a straight bond

If R > Coupon rate, call option is out of the money

Effect of an interest rate change on price of a callable bond is similar to otherwise identical option-free bond

When interest rate decreases, price increases and call option is in the money; issue will limit the price appreciation by retiring the bond and therefore, call option reduces the effective duration relative to straight bond

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13
Q

Effective Duration (Putable Bond)

A

Effective duration of a putable bond cannot exceed that of straight bond

If R < Coupon R, put option is OTM; effective duration of put is similar to straight bond

Put option reduces the effective duration of the putable bond relative to straight bond

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14
Q

Credit Spread Migration

A

Typically reduces the expected return for 2 reasons:

  1. Probabilities for change are not symmetrically distributed around the current rating. They are skewed toward a downgrade rather than upgrade
  2. Increase in credit spread is much larger for downgrades than the decrease in the spread for upgrades
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15
Q

Convexity

A

Measures the sensitivity of a bond’s duration to large changes in interest rates and long holding periods

Bond’s duration + Convexity =

-D x (change in rate / 1 + rate) + [C x change in rate^2 / (1+rate)^2] / 2

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16
Q

Market conversion premium ratio

A

allows investors to identify the premium or discount payable when buying the convertible bond rather than the underlying common stock

(Market conversion price / share price of common share) - 1

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17
Q

Change of control price

A

Price at which the bond holder can convert the bond if the firm is merged with or acquired by another firm and is unaffected by a cash dividend to shareholders

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18
Q

Convertible bond

A

Hybrid security that presents the characteristics of an option-free bond and an embedded conversion option

The conversion option is a call option on the issuer’s common stock

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19
Q

Conversion ratio

A

The number of shares of common stock that the bondholder receives from converting the bonds into shares

20
Q

Conversion value

A

This value of a convertible bond indicates the value of the bond if it is converted at the market price of the shares

Underlying share price * conversion ratio

21
Q

Market conversion price

A

Represents the price that investors effectively pay for the underlying common stock if they buy the convertible bond and then convert it into shares

Convertible bond price / conversion ratio

22
Q

Value of a convertible bond

A

Value of a straight bond + call option on issuer stock

23
Q

Value of a callable bond

A

Value of straight bond - call option

24
Q

Value of a callable convertible bond

A

Value of straight bond + value of call option on issuer stock - value of call option

25
Q

Value of a callable putable convertible bond

A

Value of straight bond + value of call option on issuer stock - value of call option + value of investor put option

26
Q

Busted Convertible

A

When underlying share price is well below the conversion price, it exhibits mostly bond risk-return characteristics

share price movements do not significantly affect the price of the call option or price of the convertible bond

27
Q

When does convertible bond exhibit mostly stock risk-return characteristics?

A

When the underlying share price is above the conversion price

The call option on the issue is in the money and the price of the call option and convertible bond is significantly affected by share price movements but unaffected by interest rates

28
Q

Interest rate volatility impact on a bond with an embedded call option

A

Call option increases in value with interest rate volatility (positive correlation)

As interest rate volatility increases, the value of the callable bond decreases because:

Callable bond = OFB - call option

29
Q

Interest rate volatility impact on a bond with an embedded put option

A

The put option increases in value with interest rate volatility

As interest rate volatility increases, the value of the putable bond increases because:

Putable bond = OFB + put option

30
Q

Effects of Yield Curve Level and Shape on Bonds with Embedded Call Options

A

Yield Curve Level:

As interest rates decline (increase), value of a call option increases (decreases) and the value of the callable bond decreases (increases)

Call option limits the upside potential for investor when rates decline

Yield Curve Shape:

As the yield curve moves from upward sloping -> flat -> Downward sloping, value of call option increases (more opportunity for issue to call back the bond to refinance at lower rate)

31
Q

Effects of Yield Curve Level and Shape on Bonds with Embedded Put Options

A

Yield Curve Level:

Put option is considered a hedge against rising interest rates

Value of straight bond will decline as rates increase but will be partially offset by rising value of put option (sell back to issuer and lend at the higher rate)

Yield Curve Shape:

As the slope of the yield curve moves from upward sloping -> flat -> downward sloping, value of put option will decrease

32
Q

Z-spread

A

A fixed spread that is estimated from the market prices of suitable bonds of similar credit quality

This is added to the forward rates derived from the default-free benchmark yield curve

33
Q

Define Option Adjusted Spread (OAS)

A

A constant spread that is added to all the one-period forward rates on interest rate tree when valuing risky bonds with embedded options

This makes the arbitrage-free value of the bond equal to its market price

Often used a measure of value relative to the benchmark

34
Q

What is the consideration of the bond’s value if the OAS on the bond is greater than the OAS on a bond with similar characteristics and credit quality?

A

The bond would be considered underpriced

A higher OAS results in a lower valuation for the bond because the purpose of the OAS in the model is to match the market price and

35
Q

What is the effect of a decline in interest rate volatility on OAS and a callable bond?

A

Decline in volatility of interest rate means that the value of the call option will decrease and the value of the callable bond will increase (OFB-call option)

The higher valuation of bond will require a higher OAS because less adjustment is required to match the market price of the bond

36
Q

Define One-sided durations

A

They are better at capturing the interest rate sensitivity of a callable or putable bond than two-sided effective duration, particularly when the embedded option is near the money

37
Q

What does one-side durations explain about sensitivity of bonds with embedded options to interest rate changes?

A

Callable bonds are more sensitive to interest rate increases than decreases

When rates are declining, a call option is ITM and there is limited upside potential because the issuer will recall the bond. This results in a lower one-sided down duration

When rates are increasing, call option is OTM and there is no downside protection. This results in a higher one-sided up-duration

38
Q

Define Key Durations (aka partial durations)

A

Reflects the sensitivity of a bond’s price to changes in specific maturities on the benchmark yield curve

Helps to identify shaping risk - i.e. whether the yield curve is steepening or flattening

39
Q

How to assess the fair value for the bond under provided assumptions

A
  1. Determine the value for the corporate bond assuming no default
  2. Calculate the credit value adjustment

FV of bond =

VND - CVA

40
Q

How to determine Value no Default (VND)

A

Option 1:

Using the binomial tree

Option 2:

Sum (coupon x benchmark discount factors for each year) + (principal + coupon * DF at maturity)

41
Q

How to calculate the expected return on a bond that is expected to have its credit rating notched?

A

[-Duration * (new - old spread)] + annual coupon (if applicable)

42
Q

Explain Structural model of Credit Risk and model components

A

When a company defaults (value of assets < liabilities), the probability of default has features of an option

Equity = call option purchases on the assets of the company

Strike price = face value of debt

Assumes assets on which the options are written are actively traded

Aims to explain WHY default occurs

Best used for internal risk management by managers of the company

43
Q

Explain reduced form model and its components

A

Default is an external variable that occurs randomly

Aims to explain WHEN default occurs statistically

Key parameter is default intensity, which is the probability of default over the next time increment

Should be used to value risky debt securities and credit derivatives

44
Q

Advantage of Structural Model

A

Provides insight into the nature of credit risk

45
Q

Disadvantages of Structural Model

A

Burdensome to implement

Difficult to determine default barrier due to limitations in available data

Assets of company typically do not trade in market

46
Q

List the advantages of reduced-form model

A

Inputs are observable variables and includes historical data

Default intensity can be estimated using regression analysis on company-specific and macroeconomic variables

Allows the model to reflect the business cycle in the credit risk measure

47
Q

List the disadvantages of reduced-form model

A

Doesn’t explain the economic reason(s) for default

Model assumes default comes at a surprise and can occur at any time, which is not realistic

CFAI Flashcards (10 decks)

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