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CFA Level III > Fixed Income > Flashcards

Flashcards in Fixed Income Deck (50):
1

Pure Bond Indexing

Advantages/Disadvantages

Advantages

Low tracking error & fees
Same risk as index

Disadvantages

Lower return than index due to fees
Costly to implement

 

2

Enhanced Indexing

Advantages/Disadvantages

Advantages

Exposure to primary & small risk factors
Less costly to implement

Disadvantages

Higher tracking error & fees
Lower expected return than index
Higher risk

3

Active Bond Management

Advantages/Disadvantages

Advantages

Higher return
Less restrictions
Can control duration

Disadvantages

Higher tracking error & fees
Increased risk

4

Selecting an Appropriate Benchmark (Fixed Income)

Choose a benchmark that matches risk exposures;

  1. Market value risk (e.g. interest rates): control with duration
  2. Income risk - longer term bonds reduce income risk
  3. Liability framework risk - matching liabilities if needed
  4. Credit risk

5

Issues with Bond Indexes

 

  1. New issues create new risks
  2. Investability (unique and illiquidity)
  3. Irregular pricing 
  4. "Bums" problem (issuers with large weightings)

6

Methods Aligning Risk Exposures

 

  1. Cell matching (stratified sampling) - matching weights but not every security
  2. Multifactor models - modeling risk factor exposures and then matching
  3. Duration
  4. Key Rate Duration
  5. PV distribution of cash flows

7

Effective Duration & Yield Curve Risk

Effective Duration: exposure to interest rate risk (parallel changes in YC).

           Matching effective duration minimizes risk

 

Yield Curve Risk: Non-parallel changes

           Matching key rate and PV of cash flows minimizes risk

 

Example: duration of 5.8 means a 1% change in rates the market value will drop 5.8%

8

Spread Duration Calculations

Just the weighted average of duration (weight * duration)

Important: Treasuries have 0 spread duration

Example:

Sector             Weight            Duration
Treasury          47.74               0.00                   0.00
Agency            14.79               5.80                   0.86
Corporate        12.35              4.50                   0.56
MBS                 25.12              4.65                    1.17 
                                                             Total:    2.59

9

Key Rate Duration

Purpose: capture the interest rate sensitivity of a bond to changes in yields for specific rates (e.g 5 year key rate of 1.27 means if interest rates increase 1% the bond will decline 1.27%)

Matching key rate minimizes interest and YC risks.

 

 

 

10

Scenario and Total Return Analysis

1. Total return - compare initial value with FV for one security at a time
                            Looks at time, ending price, reinvestment rate

2. Scenario analysis - multiple total return analyses based on multiple sets of assumptions

3. Combining 1 and 2 can asses returns and volatility (distribution)

 

11

Total Return Analysis Steps

Step 1: compute PV (FV is 100)

Step 2: Compute FV of coupons

Step 3: Add 1 & 2 and compute interest (return) for holding period

 

Example: 30 Year, 8% bond at par ($100), reinvest at 6%, 1 yr hold, YC flat

Step 1: Price is $100
Step 2: bond pays 2 $4 coupons. FV = 4(1.03) + 4 = 8.12
Step 3: Total value = 108.12 which is 8.12% return
Need semi-annual so √1.0812 - 1 = 3.98% * 2 = 7.96%

12

Total Return Analysis Example

Investor owns a 10-year, 6% bond. Currently at 101.50 with YTM of 5.8%
Reinvestment rate = 5% with a 2 yr holding period. YTM of 5.4%
Calculate the investors expected bond equivalent return.
BEY is 2 * 6-month periodic return

Step 1: Compute horizon price
FV: 100, n: 16, PMT: 3, i: 2.7     PV = 103.86

Step 2: Compute end-of-period value of reinvested income
n: 4, PMT: 3, i: 2.5    FV = 12.46

Step 3: Compute semiannual total return in 2 years
FV = 103.86 + 12.46 = 116.32
FV = 116.32, n = 4, PV: -101.50,      CPT i: 3.466
3.466 * 2 = 6.93%

13

Classical Immunization

Offsetting price and reinvestment risk by matching effective duration with your time horizon. (parellel shifts)

Works best with lower reinvestment risk

STOPS when interest rates flucuate more than once 
OR
Time passes

 

14

Immunization of a Single Obligation

Select a bond with matching effective duration and set PV to match liability

Unrealisticly assumes: one small shift in YC, liabilities don't change, no defaults

Must consider costs of rebalancing

 

Example: $50M liability due in ten years. Ten-year zero coupon bonds yield 6% semi-annually compounded.
$50,000,000 / (1.03)20 = 27,683,788 required to immunize

 

15

Immunization Risk

  • If duration < liability: exposed to reinvestment risk
  • If duration > liability: exposed to price risk
  • None for cash flow matching with default free bonds

Minimize risks bracketing cash flows around liability dates

16

Dollar Duration and Rebalancing Ratio

Dollar Duration = (duration)(0.01)(price)

Rebalancing Ratio

target DD
new DD

Then - 1 to get the % (e.g 1.52 = 52%)

Example: DD of liabilities: 1,000,000, DD portfolio = 950,000
MV of bond A: 2,250,000, D = 7.5

DD Bond A: 2,250,000(7.5)(0.01) = 168,750
Need to get 950K to 1M liability: 50,000 / 168,750 = 29.6%
Bond A: 2,250,000 * 1.296 = 2,916,000 (so buy 666K)

17

Spread Duration

Measures sensitivity of non-treausry issues to a change in their spread above treasuries

3 Types of Measures:

  1. Nominal: spread between issue and treasury
  2. Static: spread added to treasury to force PV to be equal
    1. doesnt look at options
  3. OAS: Constant spread added to all rates in binomial tree so model price = market price

18

Immunization Extensions

  1. Increasing risk: to try and increase value
  2. Multifunctional duration: focus on key rate durations to minimize non-parrellel shifts
  3. Combination matching: cash flow match closer liabilitiess, duration match longer liabilities
  4. Contingent Immunization: combo of active and passive immunization (PV must exceed PV of liabilities)

19

Contingent Immunization

With a surplus you have a cushion spread. No need to immunize unless surplus declines to 0.

 

Example: Liability in 2 years of 10,952,229, immunization rate is 6%, client funds $10M

Minimum acceptable return = PV -10M, FV 10,952,229, N 4 CPT R= 2.3 * 2 = 4.6%
Cushion spread = 6 - 4.6 = 1.4%
Initial surplus = FV 10,952,229, N 4, R 3. CPT PV = 9,730,914 - 10M = 269,086

20

1. Cyclical Changes (Supply/Demand)

 

2. Secular changes

Cyclical

  • Increase in new corporate bonds = narrow spreads/strong return
  • New issues validates prices of outstanding bonds
  • Decreasing supply is the reverse (make prices go down)

Secular

  • Intermediate bonds and bullet maturity bonds dominate corporate bonds
    • Scarcity of callable/putable bonds and long-term bonds gets a premium
  • HY dominated by callable bonds
  • Increased use of credit derivatives to get what you want

21

Liquidity and Price Relationship

Higher liquidity = higher prices (lower yields)

Lower liquidity = lower prices (higher yield)

22

Reasons for Secondary Market Trading

  • Additional yield
  • Credit upside/defense trades: attempt to identify issues likely to be upgraded or downgraded
  • New issue swaps: new issues have better liquidity
  • Structure trades: trading between bullet and option bonds
  • YC adjustments: going up/down YC based on views
  • Invest excess cash

23

Relative Value Strategy

Ranking credit, stuctures, issuers, by expected performance

Relative value =   -Duration*▲s      

Yield spread expected to narrow

  • choose higher yield
  • increase spread duration

Yield spread expected to widen

  • choose lower yield
  • decrease spread duration

24

Methods for Analyzing Spreads

Mean Reversion

Definition: Reverts to average

(Currend Spread - Historical spread) / Stdspread

Higher = spread will fall more (more return)

25

Structured Based Issues

  1. Callable Bonds - interest rates decline, underperforms
    1. Creates negative convexity due to the limit on price appreciation
  2. Sinking Bonds - has callable feature but isser forced to "call" at the specified time. Could benefit bond holder
  3. Putable Bonds - very scarce and illiquid

26

Leverage Effects on Return

RP = Ri + [L/E) * (Ri - cost to borrow)]

More leverage = higher variability of returns

 

Example: Portfolio = 100M, $70M of which is borrowed.
Return = 6%, cost of borrowing = 5%.

6% + [(70/30) * (6%-5%)] = 8.33%

27

Leverage Effects on Duration

DE = [(Di)(Notional) - (DL)(L)]  /  E

 

 

Example: Portfolio = 100M, $70M of which is borrowed.
Duration = 5.0, Duration of borrowing = 1.0.

DE = (5.0)(100) - (1.0)(70)  /  30 = 14.33

28

Repurchase Agreements (repos)

Definition: a collaterilized loan

Interest Calculation: borrowed * r * (days/360)

Risks: credit risk

29

Factors Affecting Repo Rate

  1. Credit risk
  2. Quality of collateral
  3. Availability of collateral (more difficult to obtain ↓ rate)
  4. Physical delivery = lower rate
  5. Repo term (Term ^, rate ^)
  6. Fed funds rate

30

Bond Risk Measures

Duration is not accurate for large yield changes or bonds with negative convexity. Other risk measures are:

         Risk Measure                                                 Problems           

  • Standard Deviation                                 Not normally distributed
  • Semivariance* (return stats below target)    Less accurate
  • Shortfall Risk (probability below target)   Degree of loss ignored
  • Value at Risk                                              Degree of loss ignored

*Semivariance is the left side of the tail

31

Number of Contracts Formula

Nf = [(DT - DP) * VP /  DCTD * PCTD]  * CF  *  Yield Beta

 

Note: Yield Beta = 1 unless specified

 

Example: $50M portfolio, D = 7.51, DT = 8.5
Futures priced at 110,000 with D of 7.6, CF = .98

# of contracts = [(8.5 - 7.51) * 50M / 7.60 * 110,000] * 0.98 * 1.0 = 58.03

32

Basis

Basis Risk

Cross Hedging Risk

Basis = spot price - futures delivery price

Basis risk is the variability of the basis (spot vs future). Makes hedging results change

Cross hedge risk = underlying security not iidentical to asset being held (Using T-bond futures to hedge corporate bonds)

33

Interest Rate Swaps

Receiving fixed = Higher duration
Paying fixed = lower duration

Always add duration of what you RECEIVE
Subtract duration that replicates what you PAY

There are options on bond prices AND interest rates

 

Example: receive fixed and pay floating
Add duration of fixed and subtract duration of floating

34

Duration of a Bond Option

option delta * Dunderlying * (Punderlying / Poption)

 

buy calls = ^ duration

buy puts = lower duration (have negative delta and duration)

35

Credit Options

&

 Binary Credit Options

Credit put option on price = receive if price declines

Credit call option on spread = receive if the spread widens

Binary credit option: structured with a specified event
No payoff if the event doesn't occur

Example: 1 year credit put option is purchased on a AA bond 10M if falls below investment grade, Strike = 92, option premium = 100,000, Bond rating drops to BB, price declines to 87.50. Calculate payoff
(92 - 87.50)/100 * 10,000,000 = 450,000

36

Credit & Binary Options Formula

Used for credit and spread events

Credit Spread & Credit Forward

(actual spread - strike spread) * notional * risk factor

Example: 1,000 bonds, MV of $1M, Spread is 200 bps.
Manager buys option; strike = 250 bps, notional = $1M, RF = 10
Option matures and bond price is 900, implying spread of 350.

Value = (0.035 - 0.025) * $1M * 10 = 100,000

37

Credit Forward

Same as credit option but no premium

Example: Hi-Fi bonds trade at a 200 bp spread. Buys a 6-month credit forward on $5M par at the current spread with a risk factor of 4.3. Calculate payoff if spread is 150 bp OR 300 bp. Then calculate max loss

150 bp: (.015 - 0.20)(4.3)(5,000,000) = 107,500 paid (none received)

300 bp: (0.030 - 0.020)(4.3)(5,000,000) = 215,000 received

max loss = (0.00 - 0.020)(4.3)(5,000,000) = 430,000 paid

 

38

Credit Default Swap (CDS)

One time payment for event protection

 

Example: 3 yr CDS on $20M bond, swap premium 50 bps, event = fall below BBB
After 6 months bond falls to BB and 80% of par.

Swap premium = .005 * $20M = $100,000

Payment = (1 - 0.8) * $20M = $4M

39

International Bond Source of Excess Returns

  1. Market Selection
  2. Currency Selection - hedged or unhedged
  3. Duration Management
  4. Sector Selection
  5. Credit Analysis

40

International Yield Change and Duration

▲ in Yield

%▲ = duration x ▲y x B

Duration

weight * duration * beta

Remember: standardized duration is duration * beta

Example: 20% of GBP bond portfolio is invested in German bonds, D = 6, country beta = 0.42. Calculate the duration contribution:

Duration contribution when UK rates change: (6)(0.42) = 2.52
Duration contribution to fund: (0.2)(2.52) = 0.504

41

Interest Rate Parity

 

Higher yielding currency depreciates. 

IRP:  F = S0(1 + RD / 1 + RF)

OR

Rf foreign - Rf domestic

Example: US 7%, Euro 5%, exchange is 2.35 $/E

2.35(1.07 / 1.05) = 2.395

Then 2.395 / 2.35 = 1.91% premium

EUR R= 5%, GBP Rf = 2.5%. Domestic = GBP

5 - 2.5 = 2.5%, EUR is expected to dep. 2.5% against GDP

42

Selecting the Best Market and Currrency

Step One - Best market is highest excess return (RM - Rf)

Step Two - Best Currency: Compare expected change (higher is better)
 

43

Forward Differential

Forward Differential: Fd,f = (F - S0) / S0

                                      Discount/Premium          Hedged Return

If Foreign > Domestic         discount                         negative

If Foreign < Domestic         premium                         positive

44

Currency Hedging Techniques

  • Forward hedge - used to eliminate currency risk
  • Proxy hedge - contract with a similar currency
  • Cross Hedge - sell foreign currency for a third countries currency (speculation)

Currencies with higher return over Rf will have higher return

Example: UK investor buys CAD bond
Forward hedge: Sell CAD forward to buy GBP
Proxy hedge: Sell USD forward to buy GBP
Cross Hedge: Sell CAD forward to buy JPY

45

Breakeven Spread Analysis

bps / -duration and -bps / -duration

Make sure to breakdown the bps per quarter

 

Example: Domestic 7.65%, duration 6.5
Foreign 6.85%, duration 5.3
Holding period 6 months

Domestic = 80 bps better yield, 20 per quarter
▲ydomestic = -0.40% / -6.5 = 0.06%
▲yforeign = 0.40 / -5.3 = -0.08%

 foreign bond would need to decrease 8 bps to wipe out its yield advantage or domestic increase by 6 bps

46

Pros and Cons of EM Debt

Pros

  1. Diversification
  2. Increased quality/resiliency in sovereign bonds

Cons

  1. EM Corporates are more risky
  2. Highly volatile
  3. Lack of trasparency 
  4. Political risk/legal systems
  5. Negative skewness in returns

47

Criteria for Selecting a FI Manager

  1. Style Analysis - sources of risk and return
  2. Selection Bets - attribution
  3. Investment Process
  4. Alpha Correlations

48

Hedge or not Hedge example

Assume that the short-term interest rates are 1.6 percent in Japan and 2.7 percent in Canada. Yen will appreciate 1.5% against CAD and 0.5%. Hedge or not?

2.7 - 1.6 = 1.1     anything above 1.1 should NOT be hedged

49

Hedge or Not Hedge

Hedged: (Forward / spot) - 1

Non Hedged: (Forecast / spot) - 1

If only given one, take the difference if the Rf for hedged.

Example:

Rf = 1.8%EUR, 4%US
Forecast = 1.97EUR/1 US, Spot = 2EUR/1 US
EUR YTM = 4.30, US YTM = 7.5%

(1.97 / 2) - 1 = -1.5% Not hedged

4.30 - 7.5 = -2.2% Hedged

Would NOT hedge.

50

Impact of Economy and YC Projections for Trades

Economy   YC shift   Trade to Make     Reasons

Stronger     Upward    Less quality        ↑ liquidity
                                                   ↑ change for an update 

Stronger    Upward     ↓ duration     Lessen impact of ↓price