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CFA Level II 2020 COPY (552) > Fixed Income > Flashcards

Fixed Income Flashcards

1
Q

Fixed Income Spot Rates

A

are the yields on zero-coupon bonds

No coupons –> no reinvestment risk

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2
Q

Zero Coupon Bond Price

A

Pt = 1 / (1 + St)^T

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3
Q

YTM

A

Price today: Calculate the PV of the cash flows

Yield: Put everything into the calculator and solve

Example:

Calculate the price and YTM on a three-year, 4% annual-pay, $1,000 face. S1 = 5%, S2 = 6%, S3 = 7%

Price = 40 / (1.05) + 40 / (1.06)² + 1040 / (1.07)^3 = $922.64

Then use calculator

N = 3, PV = -922.64, PMT = 40, FV = 1,000 CPT I/Y = 6.94%

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4
Q

Return will be equal to the bond’s yield only when:

A
  1. Held to Maturity
  2. All payments are made on time
  3. All coupons are reinvested at the original YTM (least realistic since the YTM changes)
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5
Q

Forward Pricing Model (zero-coupon)

A

Based on arbitrage-free pricing; basically says that the same timeframe yields the same

Step One: Calculate discount factors for each
1 / (1 + r)^t

Step Two: Calculate Forward Price
F = Discount(long) / Discount(short)

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6
Q

Fixed Income: Implied Forward Rate

A

[(Rlong * t) - (Rshort * t)] / timplied

Example: S2 = 4%, S5 = 6%, calculate 3 year implied

Long: 6 * 5 = 30 Short: 4 * 2 = 8

30 - 8 = 22

22 / 3 = 7.33

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7
Q

Riding the Yield Curve

A

Purpose: Purchasing bonds with maturities longer than your investment horizon.

Think: I want a bond for 5 years, so I purchase a 30 year bond and then sell it in 5 years

Increases interest rate risk

AKA “rolling down the yield curve”:

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8
Q

What is a Swap Rate Curve?

Why do people use them?

A

Definition: One party makes a payment based on a fixed rate, the other makes a payment based on a floating rate

Formula: 1 = SFR / (1 + S1) + 1 / (1 + S1) Plug in for SFR

Used because:

  1. Reflects credit risk of banks (not governments)
  2. Not regulated (makes it easier to compare across countries)
  3. More maturity ranges
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9
Q

Swap Spread

A

Swap Spread = swap rate - treasury yield

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10
Q

I-spread

A

Definition: amount by which the yield on the risky bond exceeds the swap rate for the same maturity

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11
Q

Interpolation

A

Definition: finding a rate between 2 listed spot rates

Formula: Rshort + (Rlong - Rshort) * [(Xt - Tshort) / (Tlong - Tshort)]

Example: 2 year swap at 2.0% and 2.5 year swap at 2.3%

Calculate 2.2 year

.02 + (.023 - .02) * [(2.2 - 2.0) / (2.5 - 2.0)]

So = 2.12%

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12
Q

Z-spread

A

Definition: the spread over the entire spot rate curve. Should be added to each spot rate

Think: I need to add 50 bps to each spot to equal the risk for this particular bond

Cannot be used when a bond has options,

Used for corporate bonds and ABS

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13
Q

TED Spread

A

Formula: 3 Month LIBOR - 3 Month T Bill

  1. Seen as indication of the level of credit risk in the economy

Analysis: Higher = banks more likely to default on loans and lower liquidity

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14
Q

LIBOR-OIS Spread

A

OIS is the overnight indexed swap

Formula: LIBOR - OIS rate

LIBOR includes credit risk, OIS does not

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15
Q

Traditional Theories

A
  1. Unbiased (Pure) Expectations Theory
  2. Local Expectations Theory
  3. Liquidity (biased) Preference Theory
  4. Segmented Markets Theory
  5. Preferred Habitat Theory
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16
Q

Unbiased (Pure) Expectations Theory

A
  1. Investors expectations determine the shape of the yield curve
  2. Forward rates = expected future spot rates
  3. If yield curve is upward sloping, short-term rates are expected to rise
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17
Q

Local Expectations Theory

A
  1. Not every maturity strategy should have the same return
  2. Risk-neutrality is preserved for only short-term

Remember: only applies to short-term, does not work

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18
Q

Liquidity (biased) Preference Theory

A
  1. Forward rates reflect expectations plus a liquidity premium
    a. If YC is flat, the liquidity premium would push it upward sloping
  2. Longer-term bonds more sensitive to rate changes
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19
Q

Segmented Markets Theory

A
  1. Yield at each maturity is determined independently
    (e.g. Banks have to play in short-term bonds
    HF may like to play in the l/t bonds)
  2. The supply and demand of each segment effects rates.
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20
Q

Preferred Habitat Theory

A
  1. Forward rates are expected future spot rates plus a premium
  2. Investors prefer a particular maturity but will jump to different segments
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21
Q

Modern Theory: Vasicek

A
  1. Vasicek Model: suggest that interest rates mean revert over time

a. Interest rates can become negative
b. Volatility does not increase as interest rates does

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22
Q

Duration

A

approximate change in value based on a 1% increase/decrease in interest rates

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23
Q

Effective Duration Definition

Approximate Percent Price Change Formula

A

Definition: measures the sensitivity of a bond’s price

Formula: -D x change in Yield

Example: Duration of 5.0 and change of .5 would be:

-2.5% change

24
Q

Yield Curve shifts

A

In order of importance:

  1. Change in level: a parallel increase or decreases of interest rates
  2. Change in steepness: long maturity interest rates increases, short rate decrease
  3. Change in Curvature: short and long rates increase, intermediate rates don’t change

Important: S/t rates change more

25
Q

Value additivity and dominance

A

Additivity: when the value of the whole differs from the sum of the parts

Dominance: when one asset trades at a lower price than another with identical characteristics

26
Q

Stripping and Reconstitution

A

Stripping: If a bond is worth less than its component parts, one could purchase the bond, break it into a portfolio of strips then sell

Reconstitution: the opposite - buy all the strips and combing (reconstitute) into a full bond

27
Q

Binomial Interest Rate Tree

A

Valuation is done backwards

Formula at each ending node:

(Par + Coupon) / (1 + r)

Formula for every other node:

(Previous Value Upper + Coupon) / (1 + r)

+

(Previous Value Lower + Coupon) / (1 + r)

Then divide by 2

28
Q

Pathwise Valuation

A

Just go down each path:

Coupon / (1 + r) + Coupon / (1 + r)(1 + r2) + Coupon / (1 + r)(1 + r2)(1 + r3)

29
Q

Types of Embedded Options

A

Callable Bonds: issuer can call back the bond

European style option: option can only be exercised on a single day

American style option: anytime after lockout period

Bermudan-style option: option can be exercised at fixed dates after lockout period

Putable bonds; allow the investor to put back the bond to the issuer

30
Q

Valuation of Embedded options

A

Call rule: the issuer will call the bond if the price is OVER 100.

Put rule: the investor will call the bond if the price is LOWER than 100

31
Q

Interest rate volatility

A

Straight bonds unaffected

32
Q

Option Adjusted Spread (OAS)

Comparison to Z spread

A

Constant spread added to all rates in binomial tree so model price = market price

Accounts for credit and liquidity risk

Z spread = OAS spread it is a straight bond

Z spread > OAS spread callable bond

Z spread < OAS spread putable bond

33
Q

Effective Duration

A

Duration of call or put bonds < Duration of straight bond

Duration zero = bond maturity

Duration fixed-rate < Bond maturity

Duration floater = time (years) to next reset

34
Q

Effective convexity

A

Convexity

Straight Bond Positive

Putable Bond Positive

Callable Bond Negative

35
Q

Key Rate Duration

A

Purpose: capture the interest rate sensitivity of a bond to changes in yields

  1. Captures shaping risk
  2. However the key rate will change if an embedded option is near the money

Formula: -Rate Duration * change in yield

36
Q

When the underlying option is near money

A

Callable bonds will have a lower one-sided down-duration

Putable bonds will have higher one-side down duration

37
Q

Market conversion price

A

Market price of bond/conversion ratio

38
Q

Conversion value

A

market price of stock after conversion * conversion ratio

Minimum value of a convertible bond: Greater of conversion value and straight value

39
Q

Market conversion premium

A

Market conversion premium: market conversion price - market price of stock

Market conversion premium ratio: market conversion premium / market price

40
Q

Recovery rate

Loss given Default

Expected Loss

A

Recovery rate: % of money received upon default

Loss given default (%) = 100 - recovery rate

Expected Loss = probability of default * loss given default

41
Q

Ordinal rankings

A

Purpose: categories of borrowers from highest to lowest risk

e. g. FICO Score
1. Does not explain degree of risk, just order

42
Q

Credit Rating Types, Strengths/Weaknesses

A

Types:

  1. Standard & Poors: BBB and above is investment grade
  2. Moody’s: Baa3 and above is investment grade

Strengths

  1. Simple
  2. Stable over time (this reduces volatility)

Weaknesses

  1. Stability means reduced correlation with default
  2. Ratings do not adjust with the business cycle (i.e. the economy tanks)
  3. Conflicts of interest
43
Q

Structural Model Assumptions

A
  1. Company assets are tradable considering a perfect world (arbitrage free, etc.)
  2. Rf and volatility are constant over time
  3. Simple balance sheet that includes zero-coupon debt
44
Q

Structural Models Weaknesses

A
  1. Balance sheet cannot be modeled realistically using a single zero-coupon bond
  2. Company assets are not traded
  3. Assumes constant volatility and risk-free rate
45
Q

Reduced Form Model Differences from Strucural

A
  1. No assumption on structure of balance sheet
  2. Volatility and risk-free rate vary
  3. Can use historical data
46
Q

Calculate the PV of expected loss

A

Formula: Coupon * log^ minus time * rate

Example:

25 * e^ -.5 * 0.0112 = 24.86

25 = coupon

-.5 is 6 months

.0112 is the rate (1.12%)

47
Q

Modern Theory: Cox-Ingersoll-Ross (CIR)

A
  1. Cox-Ingersoll-Ross (CIR): same as Vasicek BUT can’t be negative
    a. Volatility IS related to interest rates
48
Q

Modern Theory: Ho-Lee Model

A
  1. Ho-Lee Model
    a. Must be calibrated using market prices
    b. Can be used to price zero-coupon bonds
    c. Produces a normal distribution of rates
49
Q

Bootstrapping

A

Purpose: Build up method for interest rates

Formula: 100 = Coupon / (1 + r) + (Par + coupon) / (1 + x)²

Think: Solve for X to get the bond to 100

50
Q

Calculate the forward rates based on spot rates

A

[(1 + Slong)^t / (1 + Sshort)^t] - 1

51
Q

Calculate Swap Fixed Rates

A

Formula: (1 - P3) / (P1 + P2 + P3)

52
Q

Busted Convertibles

A

embedded call option is so far out of the money that a small change in the price of common stock will have a minimum impact on the value of the convertible bonds.

53
Q

Calculate Forward Interest Rate

A

[(1 + Rlong)^t / (1 + Rshort)^t] - 1

Example:

Forward rate starts in 2 years, and last 1 year

[1 + r(3)]³ / [1 + r(2)]² - 1

54
Q

Convertible Bonds

A
  1. Conversion option is NOT interest-rate sensitive
  2. Minimum value of a convertible bond: great of conversion value and straight value
55
Q

Stocks vs. Convertible Bonds

A
  • Stock price lower –> CV bond outperforms
  • Stock price higher –> CV underperforms stock
  • Stock flat –> CV bond outperforms (b/c of coupons)

CFA Level II 2020 COPY (552) (13 decks)

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