MIP Ch 6: Fixed Income Portfolio Management Flashcards
What are the 4 key activities in the investment management process?
- Setting the investment objective (return, risk, and constraints)
- Developing and implementing a portfolio strategy
- Monitoring the portfolio
- Adjusting the portfolio
List and describe the 5 strategies for managing against a bond market index, from the
least tracking error to most (i.e. passive vs active strategies).
- Pure bond indexing (or full replication)
Attempts perfect match (own all bonds in index)
Rare: expensive and inefficient - Enhanced indexing by matching primary risk factors
Primary risk factors: interest rate level, yield curve twists, and spreads
Cheaper than pure indexing and allows opportunity for higher yield - Enhanced indexing by small risk factor mismatches
Match duration, while actively managing smaller risk factors (sector, quality, etc.) - Active management by larger risk factor mismatches
- Full-blown active management (most aggressive mismatches)
List the 3 reasons for using indexing
- Lower fees than managed accounts
- Outperforming an index (after costs) is difficult to do consistently
- Excellent diversification
Describe the risk factors to consider when choosing an index.
- Market value risk of portfolio should be similar to benchmark
Longer portfolios tend to have higher MV risk - Income risk should be similar to benchmark
Longer portfolios tend to have less income risk - Liability framework risk – should match A/L investment characteristics
Use longer bonds for longer liabilities
Describe the 3 risks that a manager should consider when assessing an index’s
sensitivity.
- Interest rate risk – changes in level of interest rates (parallel shifts)
Largest risk source (90%) - Yield curve risk – changes in yield curve shape (twists, curvature)
- Spread risk – changes in spread over Treasuries (credit risk)
List the primary bond risk factors.
- Duration and convexity – price sensitivity to parallel yield shifts
- Key rate duration and present value distribution of cash flows
- Sector and quality percent
- Sector duration and contribution
- Quality (credit) spread duration contribution
- Sector/coupon/maturity cell weights
- Issuer exposure (manage event risk)
Describe tracking risk and its formula components
Tracking risk = standard deviation of the portfolio’s active return over time
T = total number of time periods (or final time period)
ARt = active return for period t = PortfolioReturnt BenchmarkReturnt
AR = average AR for all time periods
Describe the main disadvantage of using enhanced bond management strategies
Enhanced strategies add costs , must be earned on top of a passive return
Describe strategies to overcome the high costs of enhanced indexing.
- Lower cost enhancements – reduce trading costs and management fees
- Issue selection enhancements – attempt to find undervalued securities
- Yield curve positioning – find consistently mispriced maturities
- Sector and quality positioning (2 forms)
Tilt toward short corporates (high yield spread per unit of duration risk)
Periodic over- or under-weighting of sectors or qualities - Call exposure positioning – e.g. under-weight in callable bonds if you expect
falling interest rates
Describe some additional activities that are carried out by active managers
- Exploit index mismatches (based on manager’s expertise)
- Extrapolate market expectations from market data (e.g. analyze forward rates)
- Independently forecast inputs and compare with market’s expectations
Example: manager may believe forward rates are too high ñ increases duration
mismatch by increasing portfolio duration - Estimate relative values of securities to identify areas of under- or over-valuation
Define total return with respect to bond returns
Total return accounts for coupon income, reinvestment income, and change in price
Semiannual Total Return
Total Future Dollars
Full Price of Bond
1{n
1
n = total semiannual periods in investment horizon
Describe the benefits of scenario analysis
- Assess distribution of possible outcomes (wider distribution = more risk)
- Reverse scenario analysis: determine the IR movements that would trigger
acceptable outcomes - Calculate contribution of individual components (e.g. impact of a yield twist)
- Evaluate merits of entire trading strategy
Describe 2 types of dedication strategies
- Immunization – classical single period and 4 extensions
1.1 Extensions for non-parallel shifts
1.2 Relax the fixed horizon requirement
1.3 Return maximization (risk and return trade-offs)
1.4 Contingent immunization - Cash flow matching
Exact (basic) cash flow matching
2 extensions: symmetric and combination (horizon) matching
List the 2 requirements for classical single period immunization
- Portfolio duration = liability horizon (duration)
- PV of portfolio cash flows = PV of liability cash flows
List the important characteristics of immunization.
- Specified time horizon
- Assured rate of return over a fixed holding period
- Portfolio value at the horizon date is insulated from interest rate changes
Describe 2 ways that a portfolio’s duration can change.
- As market yields change (convexity effects)
- With the passage of time (as the bond approaches maturity)
Define the immunized target rate of return.
Immunized target rate of return = total portfolio return assuming no change in the
term structure
Will only equal YTM if the yield curve is flat
If yield curve is positively sloped, total return < YTM
If yield curve is negatively sloped, total return > YTM
Define portfolio duration and dollar duration
Portfolio Duration
°ni
1 Di Vi
VP
Dollar Duration Portfolio Duration Portfolio Value 0.01
Describe the steps required for rebalancing to the desired level of dollar duration
- Calculate the new (or current) portfolio DD
- Calculate the rebalancing ratio:
Target DD
New DD - Calculate amount of cash needed for rebalancing:
pRebalancing Ratio 1q MV of Portfolio
Define spread duration
Spread duration = change in price if the yield spread changes by 100 bps
Describe how classical immunization can be extended for non-parallel interest rate
shifts
Key rate duration (a.k.a. “multi-functional duration”)
Arbitrary interest rate changes
Set portfolio duration = investment horizon
Changes in portfolio value depend on:
1. Structure of investment portfolio
2. M2 = immunization risk measure (“maturity variance”)
If M2 is small, immunization risk is small
Describe the steps under multiple liability immunization
- Set DA DL
- Asset cash flows must “bracket” liability cash flows
Shortest asset < shortest liability; longest asset > longest liability
Describe the steps for immunizing general cash flows
- Assume future assets are a hypothetical investment
- Invest available funds to mature beyond liability horizon
Portfolio duration should match liability horizon - When the future assets become available:
Invest new funds in assets that will mature at the liability horizon
Sell existing longer assets and reinvest at the liability horizon
What is the goal of return maximization for immunized portfolios?
Goal: maximize the lower bound return given the investor’s risk tolerance
Expected Return 2
Describe contingent immunization
Goal: pursue active management as long as there is a positive safety margin
Safety margin = Current Portfolio Value Min Value Required for Immunization
Cushion spread = maxp0, i sq
i = available immunized return
s = safety net rate of return = required return to reach required terminal value
Initial minimum portfolio value required for immunization:
Required Terminal Value at T
1
i2
2T
Initial Portfolio Value
1
s2
2T
1
i2
2T
s and i are bond-equivalent yields above (but don’t have to be)
Describe the sources of liability funding risk
- Interest rate risk – reinvestment and disintermediation risk
- Contingent claim risk (call and prepayment provisions)
Call/prepayment features add reinvestment risk - Cap risk (floating rate securities with caps)
If market rates ¡ cap, investor loses additional interest and bond behaves like a
fixed bond
Describe the importance of reinvestment risk
Portfolios with the least reinvestment risk have the least immunization risk
Describe the differences between cash flow matching and multiple liability
immunization.
Main problem with cash flow matching:
Exact matching is usually not possible
Reinvestment will be required ñ liability funding risk
Cash flow matching is inferior to multiple liability immunization because it
requires:
1. Relatively high cash balance with a conservative rate of return
2. Funds available when or before each liability is due
Cash flow matching is still used sometimes because it is easy!
Describe the 2 extensions of basic cash flow matching
- Symmetric cash flow matching
Borrow short-term money to meet liability
Invest in longer assets that will mature after the liability - Combination matching (a.k.a. horizon matching)
Duration-match portfolio and cash flow match initial years
Ensures short-term cash flows are met (e.g. first 5 years)
Reduces risk of non-parallel shifts
Disadvantage: increases cost of funding liability
List the considerations when applying dedication strategies
- Universe considerations (credit risk, embedded options, liquidity)
- Optimization
- Monitoring (periodic performance measurement)
- Transaction costs (initial and rebalancing)
Describe 2 combination dedication strategies
Active/passive combination
Large core passive portfolio with smaller actively managed portfolio
Active/immunization combination (e.g. contingent immunization)
Define the portfolio rate of return formula, accounting for leveraging
rF return on funds invested
B borrowed funds
E amount of equity (existing funds that are not borrowed)
k cost of borrowing (like a loan rate)
Leverage creates more potential for higher returns but also more downside risk
RP rF
B
E
prF kq
portfolio rate of return
Define a repo agreement
Repo – sell a security (e.g. T-bill) and agree to purchase it back (usually the next day)
Repo interest = Repurchase Price Sale Price
What are the characteristics of a repo agreement?
Repos offers a low cost way to borrow short-term funds
Term to maturity is usually overnight or a few days
Can be extended by rolling over
Methods of transferring securities between parties:
Physical delivery (highest cost and usually not practical)
Credit and debit accounts with banks (cheaper but still has fees)
Deliver to custodial account at seller’s bank (reduces costs)
No delivery (OK if parties trust each other)
What are the factors that increase the repo rate?
- Lower quality collateral (securities being exchanged)
- Longer repo term (if upward sloping yield curve)
- No physical delivery (higher risk of default)
- Collateral is in high supply or easy to obtain (less attractive for buyer/lender)
- Higher prevailing interest rates in the economy
- Seasonal factors that restrict supply or increase demand for repos
Describe the non-duration risk measures and their disadvantages.
Standard deviation (or variance) – useful only if returns are normal
Most portfolio returns are not normal
The number of variances and covariances becomes very large as the number of
bonds n increases:
npn 1q
2
Bond characteristics change over time
Semivariance – measures dispersion of returns below the target return
Not widely used: computationally challenging and unreliable for asymmetric returns
Shortfall risk
Does not account for the magnitude of losses
Value at risk (VaR) – estimates the loss at a given percentile
Does not capture magnitude of losses beyond the specified percentile
List the products used in derivatives-enabled strategies
Interest rate futures and forwards (bond futures)
Interest rate swaps (e.g. fixed for floating)
Interest rate options (calls and puts on physicals or futures, caps)
Credit risk instruments (forwards, spread options, swaps)
Define interest rate futures and forwards.
Long party agrees to buy a bond from short party in the future at the futures price
What is the formula to approximate the number of interest rate futures contracts to a
target duration?
The number of futures needed to adjust initial portfolio duration pDIq to a target pDT q:
Approximate No. of Contracts
Change in DD Desired
DD Per Futures Contract
pDT DIqPI 0.01
DCTDPCTD 0.01 Conversion Factor
Change in DD Desired
DD of CTD Bond Conversion Factor
PCTD and DCTD = price and duration of the CTD bond
Define basis risk.
Basis = Bond Cash Price Futures Price
Basis risk = risk of unpredictable changes in the basis
Define cross hedging
Cross hedging – hedged bond bond underlying the futures contract
Increases basis risk
Define hedge ratio
Hedge Ratio
Factor exposure of the bond to be hedged
Factor exposure of hedging instrument
DHPH
DCTDPCTD
Conversion Factor
List the 3 major sources of hedging error
Incorrect duration
Projected basis
Yield beta
Define an interest rate swap.
Contract between two parties to exchange periodic interest payments based on a
notional principal amount
Interest Payment Specified Interest Rate Notional Amount
Define the dollar duration (DD) of an interest rate swap
Swap DD Fixed Rate Bond DD Floating Rate Bond DD
Fixed Rate Bond DD (since a floater’s duration is very small)
List the 3 ALM applications of swaps
Alter asset and liability cash flows
Adjust the portfolio duration
Cheaper/easier alternative to using a package of forward contracts
Define option duration
Option Duration Duration of Underlying Option Delta
Price of Underlying
Price of Option Instrument
List 3 ways that hedging can be done with options
- Buying protective puts – protects against rising interest rates
- Selling covered calls – generates premium income on out-of-the-money calls
- Interest rate caps, floors, and collars
Caps pay off if rates ¡ cap rate; floors pay off if rates floor rate
Collar = cap + floor
Describe credit spread options
Credit spread options only pay off if ITM at maturity
Payoff maxrpSpread at Option Maturity Kq Notional Risk Factor, 0s
Risk Factor = change in security value per 1 bps change in credit spread
Describe credit forwards.
Credit forwards have similar payoffs to credit spread options, but no downside
protection
Payoff pSpread at Forward Maturity Kq Notional Risk Factor
where K = “contracted credit spread”
Describe credit default swaps (CDS).
Shifts credit risk based on a reference entity from the protection buyer to the
protection seller
Protection buyer pays regular swap premiums to the protection seller
If a defined credit event causes a loss on the reference entity bond, the protection
seller pays the loss to the protection buyer
List the advantages and uses of CDS
Reduce credit risk concentration without selling or shorting assets
Hedge non-publicly traded debts
Protection seller does not have to make an upfront investment
Can be tailored to specific needs since over-the-counter
State Ways the Active Manager can Add Value
- Bond market selection
- Currency selection
- Duration management{yield curve management
- Sector selection
- Credit analysis of issuers
- Investing in markets outside the benchmark
Define currency risk.
Currency risk is the risk associated with the uncertainty about the exchange rate at
which proceeds in the foreign country can be converted into the investor’s home
currency
State how to compute the forward discount/premium based on the spot and forward
exchange rates.
f
FS0
S0
F is the forward exchange rate (stated as domestic currency/foreign currency)
S0 is the spot exchange rate (stated as domestic currency/foreign currency)
f is the forward discount/premium (it is a premium if positive and a discount if
negative)
State the interest rate parity (IRP) equation.
f id if
State the three methods of currency hedging
- Forward hedging
Use forward contract between bond’s currency and home currency
Most popular approach - Proxy hedging
Use forward contract between home currency and highly correlated currency with
bond’s currency
Often used when forward markets in the bond’s currency are relatively undeveloped,
or because it is otherwise cheaper to hedge using a proxy - Cross hedging
Hedge two currencies other than the home currency
Technique used to convert the currency risk of the bond into a different exposure that
has less risk for the investor
State Criteria for the Selection of a Fixed-Income Manager
- Style analysis
A style analysis looks at how the portfolio differs from the benchmark - Selection bets
A manager that believes they have superior credit/security analysis skills may
deviate weights based on credit or security analysis - The organization’s investment process
Need to understand the support staff and investment processes of the manager’s
organization - Correlation of alphas
Plan sponsors will prefer low correlation among managers’ alpha to control/diversify
portfolio risk
State similarities between fixed-income and equity manager selection
- Both frequently use a consultant to identify a universe of suitable manager
candidates - Both realize past performance is not a reliable guide for future results
- Qualitative factors are important for both
- Management fees and expenses are important for both
