Fixed Income Flashcards
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
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
Active Bond Management
Advantages/Disadvantages
Advantages
Higher return
Less restrictions
Can control duration
Disadvantages
Higher tracking error & fees
Increased risk
Selecting an Appropriate Benchmark (Fixed Income)
Choose a benchmark that matches risk exposures;
- Market value risk (e.g. interest rates): control with duration
- Income risk - longer term bonds reduce income risk
- Liability framework risk - matching liabilities if needed
- Credit risk
Issues with Bond Indexes
- New issues create new risks
- Investability (unique and illiquidity)
- Irregular pricing
- “Bums” problem (issuers with large weightings)
Methods Aligning Risk Exposures
- Cell matching (stratified sampling) - matching weights but not every security
- Multifactor models - modeling risk factor exposures and then matching
- Duration
- Key Rate Duration
- PV distribution of cash flows
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%
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
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.
Scenario and Total Return Analysis
-
Total return - compare initial value with FV for one security at a time
Looks at time, ending price, reinvestment rate - Scenario analysis - multiple total return analyses based on multiple sets of assumptions
- Combining 1 and 2 can asses returns and volatility (distribution)
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%
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%
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
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
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
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)
Spread Duration
Measures sensitivity of non-treausry issues to a change in their spread above treasuries
3 Types of Measures:
- Nominal: spread between issue and treasury
-
Static: spread added to treasury to force PV to be equal
- doesnt look at options
- OAS: Constant spread added to all rates in binomial tree so model price = market price
Immunization Extensions
- Increasing risk: to try and increase value
- Multifunctional duration: focus on key rate durations to minimize non-parrellel shifts
- Combination matching: cash flow match closer liabilitiess, duration match longer liabilities
- Contingent Immunization: combo of active and passive immunization (PV must exceed PV of liabilities)
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
- Cyclical Changes (Supply/Demand)
- 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
Liquidity and Price Relationship
Higher liquidity = higher prices (lower yields)
Lower liquidity = lower prices (higher yield)
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
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
Methods for Analyzing Spreads
Mean Reversion
Definition: Reverts to average
(Currend Spread - Historical spread) / Stdspread
Higher = spread will fall more (more return)
Structured Based Issues
-
Callable Bonds - interest rates decline, underperforms
- Creates negative convexity due to the limit on price appreciation
- Sinking Bonds - has callable feature but isser forced to “call” at the specified time. Could benefit bond holder
- Putable Bonds - very scarce and illiquid
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%
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
Repurchase Agreements (repos)
Definition: a collaterilized loan
Interest Calculation: borrowed * r * (days/360)
Risks: credit risk
Factors Affecting Repo Rate
- Credit risk
- Quality of collateral
- Availability of collateral (more difficult to obtain ↓ rate)
- Physical delivery = lower rate
- Repo term (Term ^, rate ^)
- Fed funds rate
Bond Risk Measures
Duration is not accurate for l_arge yield changes_ or bonds with _negative convexit_y. 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
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
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)
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
Duration of a Bond Option
option delta * Dunderlying * (Punderlying / Poption)
buy calls = ^ duration
buy puts = lower duration (have negative delta and duration)
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
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
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
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
International Bond Source of Excess Returns
- Market Selection
- Currency Selection - hedged or unhedged
- Duration Management
- Sector Selection
- Credit Analysis
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
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 Rf = 5%, GBP Rf = 2.5%. Domestic = GBP
5 - 2.5 = 2.5%, EUR is expected to dep. 2.5% against GDP
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)
Forward Differential
Forward Differential: Fd,f = (F - S0) / S0
Discount/Premium Hedged Return
If Foreign > Domestic discount negative
If Foreign < Domestic premium positive
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
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 ▲y<sub>domestic</sub> = -0.40% / -6.5 = 0.06% ▲y<sub>foreign</sub> = 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
Pros and Cons of EM Debt
Pros
- Diversification
- Increased quality/resiliency in sovereign bonds
Cons
- EM Corporates are more risky
- Highly volatile
- Lack of trasparency
- Political risk/legal systems
- Negative skewness in returns
Criteria for Selecting a FI Manager
- Style Analysis - sources of risk and return
- Selection Bets - attribution
- Investment Process
- Alpha Correlations
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
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.
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
