MIP Ch 6: Fixed Income Portfolio Management

Question 1

What are the 4 key activities in the investment management process?

Answer 1

1. Setting the investment objective (return, risk, and constraints)
2. Developing and implementing a portfolio strategy
3. Monitoring the portfolio
4. Adjusting the portfolio

Question 2

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).

Answer 2

1. Pure bond indexing (or full replication)
   Ÿ Attempts perfect match (own all bonds in index)
   Ÿ Rare: expensive and inefficient
2. Enhanced indexing by matching primary risk factors
   Ÿ Primary risk factors: interest rate level, yield curve twists, and spreads
   Ÿ Cheaper than pure indexing and allows opportunity for higher yield
3. Enhanced indexing by small risk factor mismatches
   Ÿ Match duration, while actively managing smaller risk factors (sector, quality, etc.)
4. Active management by larger risk factor mismatches
5. Full-blown active management (most aggressive mismatches)

Question 3

List the 3 reasons for using indexing

Answer 3

1. Lower fees than managed accounts
2. Outperforming an index (after costs) is difficult to do consistently
3. Excellent diversification

Question 4

Describe the risk factors to consider when choosing an index.

Answer 4

1. Market value risk of portfolio should be similar to benchmark
   Ÿ Longer portfolios tend to have higher MV risk
2. Income risk should be similar to benchmark
   Ÿ Longer portfolios tend to have less income risk
3. Liability framework risk – should match A/L investment characteristics
   Ÿ Use longer bonds for longer liabilities

Question 5

Describe the 3 risks that a manager should consider when assessing an index’s
sensitivity.

Answer 5

1. Interest rate risk – changes in level of interest rates (parallel shifts)
   Ÿ Largest risk source (90%)
2. Yield curve risk – changes in yield curve shape (twists, curvature)
3. Spread risk – changes in spread over Treasuries (credit risk)

Question 6

List the primary bond risk factors.

Answer 6

1. Duration and convexity – price sensitivity to parallel yield shifts
2. Key rate duration and present value distribution of cash flows
3. Sector and quality percent
4. Sector duration and contribution
5. Quality (credit) spread duration contribution
6. Sector/coupon/maturity cell weights
7. Issuer exposure (manage event risk)

Question 7

Describe tracking risk and its formula components

Answer 7

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

Question 8

Describe the main disadvantage of using enhanced bond management strategies

Answer 8

Enhanced strategies add costs , must be earned on top of a passive return

Question 9

Describe strategies to overcome the high costs of enhanced indexing.

Answer 9

1. Lower cost enhancements – reduce trading costs and management fees
2. Issue selection enhancements – attempt to find undervalued securities
3. Yield curve positioning – find consistently mispriced maturities
4. Sector and quality positioning (2 forms)
   Ÿ Tilt toward short corporates (high yield spread per unit of duration risk)
   Ÿ Periodic over- or under-weighting of sectors or qualities
5. Call exposure positioning – e.g. under-weight in callable bonds if you expect
   falling interest rates

Question 10

Describe some additional activities that are carried out by active managers

Answer 10

1. Exploit index mismatches (based on manager’s expertise)
2. Extrapolate market expectations from market data (e.g. analyze forward rates)
3. Independently forecast inputs and compare with market’s expectations
   Ÿ Example: manager may believe forward rates are too high ñ increases duration
   mismatch by increasing portfolio duration
4. Estimate relative values of securities to identify areas of under- or over-valuation

Question 11

Define total return with respect to bond returns

Answer 11

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

Question 12

Describe the benefits of scenario analysis

Answer 12

1. Assess distribution of possible outcomes (wider distribution = more risk)
2. Reverse scenario analysis: determine the IR movements that would trigger
   acceptable outcomes
3. Calculate contribution of individual components (e.g. impact of a yield twist)
4. Evaluate merits of entire trading strategy

Question 13

Describe 2 types of dedication strategies

Answer 13

1. 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
2. Cash flow matching
   Ÿ Exact (basic) cash flow matching
   Ÿ 2 extensions: symmetric and combination (horizon) matching

Question 14

List the 2 requirements for classical single period immunization

Answer 14

1. Portfolio duration = liability horizon (duration)
2. PV of portfolio cash flows = PV of liability cash flows

Question 15

List the important characteristics of immunization.

Answer 15

1. Specified time horizon
2. Assured rate of return over a fixed holding period
3. Portfolio value at the horizon date is insulated from interest rate changes

Question 16

Describe 2 ways that a portfolio’s duration can change.

Answer 16

1. As market yields change (convexity effects)
2. With the passage of time (as the bond approaches maturity)

Question 17

Define the immunized target rate of return.

Answer 17

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

Question 18

Define portfolio duration and dollar duration

Answer 18

Portfolio Duration
°ni
1 Di Vi
VP
Dollar Duration Portfolio Duration Portfolio Value 0.01

Question 19

Describe the steps required for rebalancing to the desired level of dollar duration

Answer 19

1. Calculate the new (or current) portfolio DD
2. Calculate the rebalancing ratio:
   Target DD
   New DD
3. Calculate amount of cash needed for rebalancing:
   pRebalancing Ratio 1q MV of Portfolio

Question 20

Define spread duration

Answer 20

Spread duration = change in price if the yield spread changes by 100 bps

Question 21

Describe how classical immunization can be extended for non-parallel interest rate
shifts

Answer 21

Key rate duration (a.k.a. “multi-functional duration”)

Arbitrary interest rate changes
Ÿ Set portfolio duration = investment horizon
Ÿ Changes in portfolio value depend on:
1. Structure of investment portfolio
2. M2 = immunization risk measure (“maturity variance”)
Ÿ If M2 is small, immunization risk is small

Question 22

Describe the steps under multiple liability immunization

Answer 22

1. Set DA DL
2. Asset cash flows must “bracket” liability cash flows
   Ÿ Shortest asset < shortest liability; longest asset > longest liability

Question 23

Describe the steps for immunizing general cash flows

Answer 23

1. Assume future assets are a hypothetical investment
2. Invest available funds to mature beyond liability horizon
   Ÿ Portfolio duration should match liability horizon
3. When the future assets become available:
   Ÿ Invest new funds in assets that will mature at the liability horizon
   Ÿ Sell existing longer assets and reinvest at the liability horizon

Question 24

What is the goal of return maximization for immunized portfolios?

Answer 24

Goal: maximize the lower bound return given the investor’s risk tolerance
Expected Return 2

Question 25

Describe contingent immunization

Answer 25

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 Ÿ i = available immunized return Ÿ 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)

Question 26

Describe the sources of liability funding risk

Answer 26

1. Interest rate risk – reinvestment and disintermediation risk 2. Contingent claim risk (call and prepayment provisions) Ÿ Call/prepayment features add reinvestment risk 3. Cap risk (floating rate securities with caps) Ÿ If market rates ¡ cap, investor loses additional interest and bond behaves like a fixed bond

Question 27

Describe the importance of reinvestment risk

Answer 27

Portfolios with the least reinvestment risk have the least immunization risk

Question 28

Describe the differences between cash flow matching and multiple liability immunization.

Answer 28

Main problem with cash flow matching: Ÿ Exact matching is usually not possible Ÿ 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!

Question 29

Describe the 2 extensions of basic cash flow matching

Answer 29

1. Symmetric cash flow matching Ÿ Borrow short-term money to meet liability Ÿ Invest in longer assets that will mature after the liability 2. Combination matching (a.k.a. horizon matching) Ÿ Duration-match portfolio and cash flow match initial years Ÿ Ensures short-term cash flows are met (e.g. first 5 years) Ÿ Reduces risk of non-parallel shifts Ÿ Disadvantage: increases cost of funding liability

Question 30

List the considerations when applying dedication strategies

Answer 30

1. Universe considerations (credit risk, embedded options, liquidity) 2. Optimization 3. Monitoring (periodic performance measurement) 4. Transaction costs (initial and rebalancing)

Question 31

Describe 2 combination dedication strategies

Answer 31

Active/passive combination Ÿ Large core passive portfolio with smaller actively managed portfolio Active/immunization combination (e.g. contingent immunization)

Question 32

Define the portfolio rate of return formula, accounting for leveraging

Answer 32

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

Question 33

Define a repo agreement

Answer 33

Repo – sell a security (e.g. T-bill) and agree to purchase it back (usually the next day) Repo interest = Repurchase Price
Sale Price

Question 34

What are the characteristics of a repo agreement?

Answer 34

Repos offers a low cost way to borrow short-term funds Ÿ Term to maturity is usually overnight or a few days Ÿ Can be extended by rolling over Methods of transferring securities between parties: Ÿ Physical delivery (highest cost and usually not practical) Ÿ Credit and debit accounts with banks (cheaper but still has fees) Ÿ Deliver to custodial account at seller’s bank (reduces costs) Ÿ No delivery (OK if parties trust each other)

Question 35

What are the factors that increase the repo rate?

Answer 35

1. Lower quality collateral (securities being exchanged) 2. Longer repo term (if upward sloping yield curve) 3. No physical delivery (higher risk of default) 4. Collateral is in high supply or easy to obtain (less attractive for buyer/lender) 5. Higher prevailing interest rates in the economy 6. Seasonal factors that restrict supply or increase demand for repos

Question 36

Describe the non-duration risk measures and their disadvantages.

Answer 36

Standard deviation (or variance) – useful only if returns are normal Ÿ Most portfolio returns are not normal Ÿ The number of variances and covariances becomes very large as the number of bonds n increases: npn 􀀀 1q 2 Ÿ Bond characteristics change over time Semivariance – measures dispersion of returns below the target return Ÿ Not widely used: computationally challenging and unreliable for asymmetric returns Shortfall risk Ÿ Does not account for the magnitude of losses Value at risk (VaR) – estimates the loss at a given percentile Ÿ Does not capture magnitude of losses beyond the specified percentile

Question 37

List the products used in derivatives-enabled strategies

Answer 37

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)

Question 38

Define interest rate futures and forwards.

Answer 38

Long party agrees to buy a bond from short party in the future at the futures price

Question 39

What is the formula to approximate the number of interest rate futures contracts to a target duration?

Answer 39

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

Question 40

Define basis risk.

Answer 40

Basis = Bond Cash Price
Futures Price Basis risk = risk of unpredictable changes in the basis

Question 41

Define cross hedging

Answer 41

Cross hedging – hedged bond  bond underlying the futures contract Increases basis risk

Question 42

Define hedge ratio

Answer 42

Hedge Ratio  Factor exposure of the bond to be hedged Factor exposure of hedging instrument  DHPH DCTDPCTD  Conversion Factor

Question 43

List the 3 major sources of hedging error

Answer 43

Incorrect duration Projected basis Yield beta

Question 44

Define an interest rate swap.

Answer 44

Contract between two parties to exchange periodic interest payments based on a notional principal amount Interest Payment  Specified Interest Rate  Notional Amount

Question 45

Define the dollar duration (DD) of an interest rate swap

Answer 45

Swap DD  Fixed Rate Bond DD
Floating Rate Bond DD  Fixed Rate Bond DD (since a floater’s duration is very small)

Question 46

List the 3 ALM applications of swaps

Answer 46

Alter asset and liability cash flows Adjust the portfolio duration Cheaper/easier alternative to using a package of forward contracts

Question 47

Define option duration

Answer 47

Option Duration  Duration of Underlying  Option Delta  Price of Underlying Price of Option Instrument

Question 48

List 3 ways that hedging can be done with options

Answer 48

1. Buying protective puts – protects against rising interest rates 2. Selling covered calls – generates premium income on out-of-the-money calls 3. Interest rate caps, floors, and collars Ÿ Caps pay off if rates ¡ cap rate; floors pay off if rates   floor rate Ÿ Collar = cap + floor

Question 49

Describe credit spread options

Answer 49

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

Question 50

Describe credit forwards.

Answer 50

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”

Question 51

Describe credit default swaps (CDS).

Answer 51

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

Question 52

List the advantages and uses of CDS

Answer 52

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

Question 53

State Ways the Active Manager can Add Value

Answer 53

1. Bond market selection 2. Currency selection 3. Duration management{yield curve management 4. Sector selection 5. Credit analysis of issuers 6. Investing in markets outside the benchmark

Question 54

Define currency risk.

Answer 54

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

Question 55

State how to compute the forward discount/premium based on the spot and forward exchange rates.

Answer 55

f  F
S0 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)

Question 56

State the interest rate parity (IRP) equation.

Answer 56

f  id
if

Question 57

State the three methods of currency hedging

Answer 57

1. Forward hedging Ÿ Use forward contract between bond’s currency and home currency Ÿ Most popular approach 2. Proxy hedging Ÿ Use forward contract between home currency and highly correlated currency with bond’s currency Ÿ Often used when forward markets in the bond’s currency are relatively undeveloped, or because it is otherwise cheaper to hedge using a proxy 3. Cross hedging Ÿ Hedge two currencies other than the home currency Ÿ Technique used to convert the currency risk of the bond into a different exposure that has less risk for the investor

Question 58

State Criteria for the Selection of a Fixed-Income Manager

Answer 58

1. Style analysis Ÿ A style analysis looks at how the portfolio differs from the benchmark 2. Selection bets Ÿ A manager that believes they have superior credit/security analysis skills may deviate weights based on credit or security analysis 3. The organization’s investment process Ÿ Need to understand the support staff and investment processes of the manager’s organization 4. Correlation of alphas Ÿ Plan sponsors will prefer low correlation among managers’ alpha to control/diversify portfolio risk

Question 59

State similarities between fixed-income and equity manager selection

Answer 59

1. Both frequently use a consultant to identify a universe of suitable manager candidates 2. Both realize past performance is not a reliable guide for future results 3. Qualitative factors are important for both 4. Management fees and expenses are important for both