CFA Level 3 - Fixed Income

Total Return Mandates

1. Active management (allows for larger risk factor mismatches relative to a benchmark index) 2. Enhanced Indexing (close link to benchmark but seeks to generate some outperformance relative to benchmark) 3. Pure Indexing (full replication)

Key Factors Affecting Credit Spreads

1. Carry 2. Defense 3. Momentum 4. Value

Liability Based Mandates (4)

1. Cash flow matching = match expected liability payments with future projected portfolio CF 2. Contingent Immunization = When A>L, Immunization + Active Management Option 1 - immunize part of liability with CF ($10M) of duration matching, then pursue with rest of $2M with active management Option 2: active management with all $12M until A=L and then immunization 3. Derivatives Overlay = close duration gaps with futures and swaps 4. Duration Matching = match duration of assets and liabilities

Alternatives to Direct Investing

1. FI mutual funds = lower investment req'm w/o sacrificing diversification (redemption at NAV rather than a need to sell particular securities) 2. ETFs = greater liquidity vs. MFs vs. underlying bonds 3. Total Return Swaps = synthetic index position - carries counterparty risks - less initial cash outlay than direct investment plus exposure to difficult to access securities

Methods to establish Passive Bond Market Exposure

1. Full replication 2. Enhanced indexing/stratified sampling - reduces construction and maintenance costs - larger tracking error vs. full replications

Enhanced Indexing/Stratified Sampling Strategies

1. Lower Cost Enhancement - tight controls on trading and mgt fees 2. issue selection enhancement - identify and select undervalued securities, select possible 'credit upgrade' issues, avoid possible 'credit downgrade' issues 3. YC enhancement - o/w undervalued areas of the curve, u/w overvalued area of the curve 4. sector/quality enhancement - periodic over/under weighting of sectors/qualities across the business cycle 5. call exposure enhancements - u/w callable bonds if rates are expected to drop

Structural Instruments offers exposure to collateral that investor cannot access directly

1. Mortgage Backed Securities backed by mortgages 2. Asset backed securities (ABS) backed by credit card, auto, and other types of loans 3. Covered bonds - senior debt obligations of commercial bank backed by a pool of mortgages or loans managed by the bank - non performing assets replanced - full recourse to issuer: The investors have recourse to other assets of the bank should the bank fail to make payments to the covered bond.

Methods to Assess Tail Risk

1. Parametric 2. Historical 3. Monte Carlo

Empirical duration

A measure of interest rate sensitivity that is determined from market data.

Money duration

A measure of the price change in units of the currency in which the bond is denominated given a change in its yield-to-maturity.

decrease duration

buy put options decrease duration short futures contract

Laddered Portfolios

can be used in CF matching multiple liabilities Has a roughly equal par amount across different maturities Advantages: Regular liquidity as bonds mature each period Diversification across maturities, thus of price risk (LT) & reinvestment risk (ST) Convexity: Barbell > Laddered > Bullet Better protection against twists / shifts (non parallel) ETF laddered portfolios = alternatives to buying individual bonds Advantages: Create a laddered approach using fixed maturity, target date ETFs ETFS passively replicate bond performance ETFs have cost advantages and increased liquidity Disadvantages: Mutual funds may provide more cost efficient diversification across maturities

Decreasing Convexity

sell call and put decrease convexity

derivative overlay

used to adjust portfolio and maintain the duration match without expense of adjusting the underlying assets. Futures contracts are often used. Long an interest rate futures contract increases a portfolio's sensitivity to interest rates (increase duration) Short --> decrease sensitivity = decrease duration Trade on both short term(Tbills, Eurodollars) and long term (treasury notes, bonds)

Macaulay duration

weighted average of the time to receipt of the bond's promised payments, where the weights are the shares of the full price that correspond to each of the bond's promised future payments

FI Indexing Risk Factors

1. Portfolio modified adjusted duration & convexity 2. Key rate duration Alternative to key rate duration = PV of distribution of CFs -Each CF can be seen as ZCB -Portfolio being managed will largely be protected from deviation from the benchmark associated with YC changes Matching key rate duration instead of just EffDur will decrease tracking risk 3. Sector and quality % = match % weight in the various sectors and qualities of the index -Further away, greater tracking risk 4. Sector and quality spread duration = matches sector &. Quality duration exposure Combined with #3 matches spread risk change in yield for other than rate changes 5. Sector/coupon/maturity call weights = match optionality exposure of sectors 6. Issuer exposures = match issuer event risk

if downward parallel shift in YC, what is the most profitable?

1. long a callable 2. short a putable 3. long an option free The value of a bond with an embedded option is equal to the sum of the value of an option free bonds + value of the embedded option. callable bond, call option is owned by the issuer of the bond, who can exercise this option if YTM decreases putable bond, the embedded put option is owned by the bond investor, who can exercise the option if YTM increase. For a decrease in YTM, the value of the embedded call option increases and value of embedded put option decreases. This means that a long position in the callable would underperform compared to a long position in a option free bond. a short position in a putable bond would underperform a long position in an option free bond primarily b/c YTM declining, although the declining value of the embedded put option would mitigate some of the loss.

Effective convexity

A curve convexity statistic that measures the secondary effect of a change in a benchmark yield curve on a bond's price. A pricing model is used to determine the new prices when the benchmark curve is shifted upwards and downwards by the same amount, holding other factors constant.

Convexity

A second order effect that describes a bond's price behavior for larger yield movements. It captures the extent to which the yield/price relationship deviates from a linear relationship Positive convexity = E(R) of bond will be higher than then return of an identical duration, lower convexity bond if interest rate change. Higher convexity = lower YTM compared to a similar duration bond with less convexity

Increase Convexity

Buy call and put increase convexity buy futures contracts

Divergent YC Slope View

Active manager expects a steepening curve with LT rates rising and ST rates falling Strategy: sell long dated bonds, buy short dated bonds Active manager expects a flattening curve with LT rates falling and ST rates rising Strategy: buy long dated bonds, sell short dated bonds Duration Neutral Choose this option if there is no view on change in the level of rates Strategy: buy ST bonds, short sell LT bonds GAINS FROM CHANGE IN SLOPE Downside Risk: YC flattening Bull Steepener: ST rates will fall by more than LT rates Strategy: buy ST bonds, short sell LT bonds Portfolio duration: net positive Downside Risk: YC flattening and/or higher yields Bear Steepener: LT rates will rise by more than ST rates Strategy: buy ST bonds, short sell LT bonds Portfolio duration: net negative Downside: YC flattening and/or lower yields Duration Neutral Choose this option if there is no view on change in the level of rates Strategy: buy LT bonds, short sell ST bonds GAINS FROM DECREASE IN SLOPE Downside Risk: YC steepening Bull flattener: LT rates will fall by more than ST rates Strategy: buy LT bonds, short sell ST bonds Portfolio duration: net positive Downside Risk: YC steepening and lower yields Bear flattener: ST rates will rise by more than LT rates Strategy: buy LT bonds, short sell ST bonds Portfolio duration: net negative Downside Risk: YC steepening and higher yields

Cashflow matching

Advantages: Can improve company's credit ratings May be able to use accounting defeasance (ability to remove both A+L from B/S) Disadvantages: Cash in advance constraints = maturity timing mismatches mean funds must be available before each liability payments May lead to large cash holdings--> reinvestment risks (esp. with steep YC)

Price value of a basis point (PVBP)

An estimate of the change in a bond's price given a 1 bps change in YTM. PVBP "scales" money duration so that it can be used to see the money gained/lost for each basis point change in the reference interest rate

Butterfly

Butterfly shift refers to yield curve Butterfly trade refers to the position of the bullet and barbell Butterfly spread refers to a trade using options

Static yield curve

Buy and Hold = Buy bonds with a duration greater than the benchmark *Add Duration Income = coupon income Objective = add duration beyond target given static yield curve view Advantage = low turnover + transactions cost Higher yield + illiquidity premium (off the run bonds) Rolling Down the YC = Buy bond with a maturity beyond IH *Add Duration Income = coupon income + rolldown return Objective = add duration and increased return if future ST yield is below current YTM Total return > maturity matching strategy Repo carry trade = Buy a bond financed in the repo market *Add Leverage Income = coupon income + rolldown return - financing costs Objective = generate repo carry return if coupon plus rolldown exceeds financing cost

Credit Default Swaps

CDS spread = fair periodic payment that should be paid by the protection buyer to the seller for the credit protection, given current conditions Fixed coupon =actually paid periodically by the protection buyer to the protection seller. The payment is standardized to 1% for IG and 5% for HY. Expect credit spreads to narrow: Protection buyer = long CDS = short credit quality Expect credit spread to widen: Protection seller = short CDS = long credit quality If CDS spread > fixed coupon --> buyer pays seller upfront fee If CDS spread < fixed coupon --> seller pays buyer upfront fee

Dynamic YC with interest rate volatility

Callable bonds, embedded call options is owned by issuer of the bond, who can exercise this option if YTM decreases (bond investor is short the call option) Decrease in YTM, value of embedded call options increases Long position in callable would underperform compared to a long position in an option free bonds Putable bonds, embedded put option is owned by bond investor, who can exercise this option if YTM increases Decrease in YTM, value of embedded put option decreases Short position in putable bond would underperform compared to a long position in an option free bonds primarily b/c YTM decreases If upward shift in yield = will cause option free bonds to fall more than bonds with embedded options The putable bonds will fall less than an option free bonds b/c embedded long put option will increase in value and place a floor beneath the bond price The callable bond will fall by less than an option free bonds b/c embedded short call option will decrease in value and partially offset losses on the underlying bond

Structured instruments issues different tranches of security, each with different risk profile, allowing investor to create risk exposures not available through investing directly in the collateral

Collateralized debt obligations: with general debt obligations as collateral Collateralized loan obligations: with leveraged loans (loans to non IG companies) as collateral

CDS Based Alternatives to Corporate Bonds

Single name CDS = long or short credit quality of an issuer Index based CDS = long or short index credit (IG or HY) Payer option on CDS index = right to buy protection (pay premiums) Receiver option on CDS index = right to sell protection (receive premiums)

Repurchase Agreements

Dollar Interest = Principal amount x Repo Rate x (Term of repo in days/365)

Structural Credit Risk Model

Estimate the future value of assets, liabilities, and equity of a company. The size of equity cushion and volatility of the assets is used to estimate the distance to default -The likelihood of default is defined as prob. Of assets falling below that of liabilities -Ex. EDF - Expected Default Frequency (Moody), DRSK (Bloomsburg) -Default is assumed to occur when A=L (E=0) -Higher equity cushion, higher DtD, lower POD

Zero Discount Margin

However, for zero DM, ST reference rate is allowed to fluctuate. It incorporates forward MRR. for upward sloping YC, Z-DM < DM; the flatter the curve, the closer the Z-DM and DM will be.

Monte Carlo Simulation

Involves generating random outcomes using portfolio measures and sensitivities Adv: randomly generate results from a probability distributions, accommodates options Disadv: highly depend on model assumptions and less transparent

Derivatives Based on Static YC

Long futures position = Purchase contract for future bond delivery Income = (change In Price/change in bond yield) - Margin Cost Objective = synthetically increase duration (up front margin and daily MTM valuation) Receive - fixed swap = Fixed rate receiver on an interest rate swap Income = (swap rate - MRR) + (change in swap MTM / change in swap yield)Objective = synthetically increase portfolio duration (up front/MTM collateral) +/- swap carry MRR = Market reference rate MTM = Market to market

Reduced Form Credit Risk Models

Look for relationships b/w macroeconomic conditions and borrowers Credit model that solve for default probability over a specific time period using observable company specific variables such as financial ratios & macroeconomic variables. Solves for default intensity, POD over periods of time Ex. Altman z-score --> lower score = higher likelihood of financial stress Z-score > 3 = 3 low chance of default 1.8</ z-score </3 = some risk of default Z-score <1.8 = likely to default POD = Credit Spread/LGD

Key rate duration

Measure of a bond's sensitivity to a change in the benchmark yield curve at a specific maturity segment.

Modified duration

Macaulay's duration divided by 1 + yield to maturity. Measures interest rate sensitivity of bond. % change in MV given a change in YTM

BPV of a portfolio

Mod Dur x MV of portfolio x 0.0001

Explain risks associated with managing a portfolio against liability structure

Model risks = whenever assumptions are made about future events & approximations are used to measure key parameters Measurement Error = use weighted average duration instead of portfolio duration Assuming that change in yields are equal for A, H, L Spread risks = future contracts uses Treasuries even though liabilities are corporate obligations Counterparty credit risk = when OTC derivatives are not collateralized Collateralization risk = available collateral becomes exhausted Asset liquidity = for CI, if active strategy fails Cash management and collateral ability rise = arise with the use of exchange traded futures contracts

Negative Butterfly Shift

Negative butterfly shift = non parallel shift in YC in which short and long rates increase by less than mid rates. This leads to increase in curvature (which favors a barbell). The portfolio wanted to be positioned to have less exposure to the mid key rates and more exposure to short/long key rates. This expectation is met with a butterfly trade that is long barbell (wings) and short the bullet (body).

Interest Rate Swaps

Pay floating, receive fixed = adds duration Pay fixed, receive floating = reduces duration

Floating Rate Note Credit Spread Measures

QM = Quoted Margin = yield spread over MRR on issuance (generally doesn't reflect credit risk change over time) DM = Discount Margin (what the market expects) - reflects changes in credit risk MRR = floating rate FRN Price: QM = DM: Par GM > DM: Premium GM < DM: Discount Assumptions made: ST reference rate is constant over the life of the bond for QM and DM. Coupon is constant However, for zero DM, ST reference rate is allowed to fluctuate.

Historical Stimulation

Price existing portfolio using historical parameters and ranking results Adv: actual results; accommodates options, with no probability distribution assumed Disadv: highly dependent on historical period and repetition of historical market trends

Dynamic yield curve - Rates Expects to Drop

Rates expected to drop = extend duration to maximum value gained Cash bond purchase "bullet" = Extend duration with longer dated bonds Expected excess return = price appreciation as YTM declines Downside risks = higher yield levels Receive fixed swap = Fixed rate receiver on an interest rate swap Expected excess return = swap MTM gain plus "carry" (fixed minus floating rate) Downside risks = higher swap yield levels and/or higher floating rates Long futures = Purchase contract for forward bond delivery Expected excess return = futures MTM gain minus Margin Costs Downside risks = Higher bond yields and/or higher margin cost

Dynamic yield curve - Rates Expects to Rise

Rates expected to rise = reduce duration to minimize losses Cash bond sell "bullet" = Reduce duration with shorter dated bonds Expected excess return = smaller price decline as YTM increases Downside Risk = lower yields Pay fixed swap = Pay fixed, receive market rate Expected excess return = swap MTM gain plus "swap carry" (MRR minus fixed swap rate) Downside Risk = swap MTM loss amid lower swap yield levels and/or lower floating rates Sell futures = Sell contract for forward bond delivery Expected excess return = futures MTM gain minus Margin Costs Downside Risk = futures MTM loss amid lower bond yields and/or higher margin costs

Single Liability Immunization

Set duration of portfolio (MacDur of Asset = IH) Initial PV of portfolio CFs >/ PV of future liabilities Portfolio convexity is minimized (to minimize variance)

Immunization

Short futures contract = decrease duration receive floating, pay fixed = decrease duration payer swaption (buy) = decrease duration buy payer swaption, sell receiver swaption = -D - (+D) = decrease duration

GENERAL RULES

Short rate increases, long rate decreases, YC will flatten Barbell outperforms, bullet underperform Interest rate volatility increases Narrowing spreads Greater convexity but lower yields (compared to bullet) More curvature Indicates economic weakness as it signals inflation and interest rate will stay low for awhile Short rate decreases, long rate increases, YC will steepen Bullet outperforms, barbell underperforms Interest rate volatility decreases Widening spreads Lower convexity but higher yields (compared to barbell) Less curvatures Indicates strong economic activity and rising inflation expectations Higher interest rates - bank borrow at lower interest rate, lend at higher interest rates CDS when steepening Buy long maturity "buy protection" Sell short maturity "sell protection" YC when steepening Short long maturity and buy short maturity = to add duration

discuss various portfolio positioning strategies that managers can use to implement a specific credit spread view

Static credit spread curve strategies = belief spreads are correctly priced and curves will remain unchanged over some IH Lower portfolio credit quality for same SD or extend SD for the same credit quality 1) buy and hold 2) carry and roll down Derivatives to add spread duration Sell CDS (single name or index based) Dynamic credit spread curve strategies -Strategies for change in level, change in slope, and change in shape -Expect upward sloping CDS curve to flatten Buy ST CDS protection = Win if spread increase Sell LT CDS protection = Win if spread narrow Economic Recovery = HY spreads narrow more than IG spreads Cash: buy HY bonds, sell IG bonds CDS: sell HY protection, buy IG protection Economic Recovery = HY credit curve steepens Cash: buy ST HY bonds, sell LT HY CDS: sell CDS ST HY, buy CDS LT HY Economic Slowdown = HY spreads widen more than IG spreads Cash: buy IG bonds, sell HY bonds CDS: sell IG protection, buy HY protection Economic Slowdown = HY credit curve flattens/inverts Cash : sell ST HY bonds, buy LT HY CDS: buy CDS ST HY, sell CDS LT HY

Type of Cashflows

Type I = certain amount and dates for its CF (govt bonds) Type II = known amount but uncertain dates (demand and time deposits, callable and putable bonds) Type III = specified dates but uncertain amounts (floating rate notes) Type IV = uncertain dates and amounts (residential mortgage loans)

Effective duration

The sensitivity of a bond's price to a change in a benchmark yield curve.

Multiple Liability Immunization

Three conditions are needed for multiple liabilities: MVA >/ MVL BPVA = BPVL Dispersion of CF and convexity of assets must be greater than those of liabilities

Structured Alternative to Individual Bonds

Two primary reasons investor invest in structured credit: 1. Structured instruments issues different tranches of security, each with different risk profile, allowing investor to create risk exposures not available through investing directly in the collateral - Collateralized debt obligations - with general debt obligations as collateral - Collateralized loan obligations - with leveraged loans (loans to non IG companies) as collateral 2. Structured instrument offers exposure to collateral that investor cannot access directly, such as: -Mortgage backed securities (MBS) backed by mortgages -Asset backed securities (ABS) backed by credit card, auto, or other types of loans -Covered bonds - senior debt obligations of commercial bank backed by a pool of mortgages or loans made by the bank. *non performing assets replaced *Full recourse to issuer - The investors have recourse to other assets of the bank should the bank fail to make payments on the covered bond.

CDS Spread

Underweight an issuer = buy protection and sell credit quality - we benefit if CDS spreads widen Overweight an issuer = sell protection and buy credit quality - we benefit if CDS spreads narrows

Parametric Method

Uses expected value and standard deviation of risk factors assuming normal distribution Adv: simple and transparent calculation Disadv: not well suited for non-normally distributed returns or option based portfolios

Positive Butterfly Shift

a positive butterfly shift = non parallel shift in YC in which short and long rates increase by more mid rates. This leads to decrease in curvature (which favors a bullet) The portfolio wanted to be positioned to have more exposure to the mid key rates and less exposure to the short/long key rates. This expectation is met with a butterfly trade that is long the bullet (body) and short the barbell (wings)

Spread duration

determine portfolio's sensitivity to changes in credit spreads - % increase in bond prices expected for a 1% decrease in credit spread

increase duration

long position in interest rate swap buy call options

Duration Time Spreads

modification of SD to incorporate empirical observations that spread changes across the credit spectrum tend to occur on a proportional % rather than absolute bps changes

Duration matching

more flexible and practical approach to funding multiple liabilities. It matches sensitivities of asset portfolio to insurance the liability portfolio. Conditions are:

Structural Risk

potential for a non parallel shifts and twists to YC, which leads to changes in the cashflow yield that do not track the change in the yield on the zero coupon bond. This risk is minimized by selecting the portfolio with the lower convexity and dispersion of cashflows.

Fixed Rate Bond Credit Spread Measures

yield spread = corporate YTM - nearest on the run treasury yield Slope and maturity mismatch Not a good measure of carry/return (i.e. long credit, short UST) Yield spread = G-spread when the spot curve is flat G-spread = corporate YTM - maturity matching UST YTM 9Interpolated if needed) Use constant maturity T-yield as benchmark Incorporates term structure of interest rates I-spread = corporate YTM - maturity matching swap rate (interpolated if needed) *estimate of spread over MRR for a new par bond from bank issuer, with the difference largely reflecting premium or discount of the outstanding bond P More accurately measure carry for leveraged position Quoted across all maturities Can be used as a duration hedge directly Asset swap spread = (corporate bond coupon - swap fixed rate) + MRR *estimate of spread over MRR vs. bond's original coupon rate to maturity Synthetic FRN Full duration hedge, which means no/low price volatility Z-spread (zero volatility) = constant spread over spot or swap rates, not YTMs More accurate than G or I spreads CDS basis = CDS spread - z-spread If CDS spread < z spread, sets up a negative basis trade (buy bond, buy CDS) OAS (Option adjusted Spread) = constant spread over fwd rates in a pricing model Can compare all bonds --> option free or not (option free, callable, putable, structured FI securities) Highly dependent on volatility and model assumptions