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57 Cards in this Set

  • Front
  • Back

to effectively IMMUNIZE a Single Liability

1) Select a bond or portfolio with effective duration equal to duration of the liability. For any liability payable on a single date, duration is taken to be the time horizon until payment; bond payable in 3 years has a duration = to 3

2) set the Present Value of the bond equal to the present value of the liability

example: $100mln liability with duration of 8.0 and present value of $56mln -> the strategy is to select a bond with duration of 8.0 and PV of $56mln

Capital Allocation Line (CAL)

-CAL is the straight line drawn from the Risk-Free rate to the TANGENCY PORTFOLIO on the efficient frontier, where the tangency portfolio is the corner portfolio with the HIGHEST SHARPE RATIO

-if the investor's required rate of return is LOWER than the expected return on the tangency portfolio, the investor will invest a portion of the funds in the risk free asset and the remainder in the tangency portfolio

*change to asset allocation folder

Asset classes have been appropriately specified if:

1) Assets in the class are similar from a descriptive as well as a statistical perspective

2) they are NOT highly correlated; so they provide diversification

3) individual assets CAN'T be classified into more than 1 class; if they can, description of classes is too vague

4) they cover a majority of all possible investable assets

5) they contain a sufficiently large % of liquid assets

* change to asset allocation folder

Strategic Asset Allocation

-combines capital mkt expectations with investor's risk, return, and investment constraints


-a conscious effort to gain the desired exposure to systematic risk via specific weights to individual asset classes

-exposures to specific asset classes in specific proportions enables PMs to effectively monitor and control their systematic risk exposure

IMMUNIZATION RISK and immunization against non-parallel shifts

Immunization Risk; risk that the terminal value may fall short of its target value as a result of non-parallel changes in interest rates

-immunized portfolios with cash flows that are concentrated around the investment horizon have the lowest immunization risk

-an immunized portfolio consisting entire of zero-coupon bonds that mature at the investment horizon will have zero immunization risk b/c there is zero reinvestment risk


strategy used to minimize interest rate risk (both PRICE RISK and REINVESTMENT Rate risk)

CLASSICAL Immunization -> when price risk and reinvestment risk exactly offset each other

-if rates rise, then gain in reinvestment income > loss of portfolio value

construct portfolio where Effective Duration=Liability Horizon

portfolio ceases to be immunized for single liability when: 1) rates move more than once 2) time passes

If portfolio duration is LESS than duration of liability, the portfolio is exposed to ______ Risk

If portfolio duration is > liability duration, then the portfolio is exposed to ______ Risk

Portfolio Duration < Liability Duration -> Reinvestment Risk

-if rates fall, the losses from reinvested coupon and principal will be greater than any gains in the value of outstanding bonds

if portfolio duration > liability duration, portfolio is exposed to PRICE Risk

ways by which an enhanced indexer may seek to align the risk exposures of the portfolio with those of the benchmark bond index

1) Effective Duration - measures exposure to interest rate risk as measured by small parallel changes in yield curve; match convexity for larger changes; CELL MATCHING duration minimizes both interest rate (general level) and yield curve (non-parallel changes) risk

2) Key Rate Duration: same result as cell matching and PV Distribution of CF matching

3) Sector and Quality % matching

4) Quality Spread Duration Contribution

5) Sector Duration Contribution

6) Sector/Coupon/Maturity Cell weights

7) Issuer Exposure: for Event Risk

common rationales for Secondary trading

1) YIELD/SPREAD PICKUP: flaw is that yield measures are not based on Total Return Framework

2) CREDIT UPSIDE: identify issues likely to be upgraded

3) CREDIT-DEFENSE: reduce exposure to sectors with expected credit Downgrades

4) NEW ISSUE SWAPS: managers often prefer new issues, particularly on the run Treasuries due to perceived better liquidity


6) YIELD-CURVE ADJUSTMENT TRADES: attempt to align portfolio duration with anticipated shifts in the yield curve; if LT rates expected to fall, manager may want to shift into longer durations to maximize positive effect of change in rates

7) STRUCTURE TRADES: swap into structures that will have strong performance given an expected movement in volatility and yield curve shape; higher volatility tends to result in lower prices for callable securities bc of increased value to the issuer of embedded option


IMPLICATIONS of CYCLICAL supply/demand changes in PRIMARY corp bond mkt and IMPACT of SECULAR changes in market's dominant product structures

CYCLICAL CHANGES: increases in # of new corp bond issues sometimes associated with NARROWER spreads and STRONG returns

-valuation of new issues may validate price of outstanding issues

SECULAR CHANGES: in mkts other than high yield, intermediate and bullet bonds (no embedded options) have come to dominate mkt

3 implications:
1) security with embedded options may trade at premium due to scarcity

2) credit managers seeking longer durations will pay a premium for them bc of tendency toward intermediate term bond issues now

3) credit-based derivatives will be increasingly used to take advantage of return and/or diversification benefits across sectors, structures, etc

differences btwn Cash Flow matching and multiple liability immunization

1) CF matching depends on ALL CF of the portfolio, so expectations of ST reinvestment rates or borrowing rates are critical; must use CONSERVATIVE ASSUMPTIONS; deviations from true CF match should be modest and be associated with significant expected cost saving; Immunization by matching duration is less restrictive and may cost less

2) only asset flows from a CF matched portfolio that occur PRIOR to the liability may be used to meet the obligation. Immunized portfolio is only required to have sufficient VALUE on the date of each liability bc funding in achieved through portfolio rebalancing

*CF matching is MORE RESTRICTIVE, SIMPLER, SAFER, but generally makes the purchase price of the required portfolio HIGHER

4 extensions to Classical Immunization

Immunization strategies also Risk-Minimizing Strategies

4 extensions to address deficiencies in classical immunization:

1) MULTI-FUNCTIONAL DURATION (aka KEY RATE DURATION) MBS and callable corporates do not increase in value as much as non-callables when rates fall below coupon rates, so the portfolio's sensitivity to changes in different rate maturities can be unique

2) MULTIPLE-LIABILITY IMMUNIZATION: goal is to ensure the portfolio contains sufficient liquid assets to meet all the liabilities as they come due

3) INCREASED RISK allowance: relaxes the minimum risk requirement of classical immunization

4) CONTINGENT IMMUNIZATION: mixes active and passive strategies

Potential Sources of Excess Return of an INTERNATIONAL Bond Portfolio

Excess Return implies active management

1) MARKET SELECTION: selecting appropriate national bond mkts

2) CURRENCY SELECTION: manager must determine amount of active currency mgmt vs amount of currency hedging; manager should remain unhedged or employ hedging strategies to capture value ONLY if they feel confident in ability to forecast interest rate changes and their impact on fx rates

3) DURATION MANAGEMENT: after countries, determine optimal maturities


5) CREDIT ANALYSIS: analysis of individual securities

6) MARKETS OUTSIDE BENCHMARK: large foreign bond indices usually comprised of sovereign issues; with increasing availability of corp issues, manager may try to add value through enhanced indexing by adding corporates

Types of Credit Derivative Instruments

1) CREDIT OPTIONS: Binary (based on underlying asset's price) or Spread (a call provides protection to buyer if asset's spread over relevant risk-free benchmark increases beyond strike spread)

2) CREDIT FORWARD: payment at settlement is a function of the credit spread over the benchmark at the time the contract matures: FV=payoff to buyer of credit spread Fwd

FV=(spread at maturity - contract spread) x notional x risk-factor

zero-sum game

3) CREDIT SWAPS (mainly CDS): protection buyer pays seller a periodic fee in exchange for a commitment to stand behind an underlying bond or loan should its issuer experience a credit event

critiques of using the following as measures of Fixed-Income Portfolio Risk

1) standard deviation

2) target semivariance

3) shortfall risk

4) VaR

1) SD: measures dispersion of returns around mean; square root of variance

Drawbacks: bond returns not normally distributed around mean

-the # of inputs (variances and covariances) increases significantly w larger portfolios

-obtaining estimates for each input is problematic

2) SEMIVARIANCE: only measures dispersion of returns below target return

Drawbacks: difficult to computer for large bond portfolio

-if returns are symmetric, results are ranked the same as using variance

-if not symmetric it's difficult to forecast downside risk

-estimated with only half the distribution, so sample size is smaller, less accurate

3) SHORTFALL RISK: Probability that actual return < target return

Drawback: does not consider impact of outliers, so the magnitude of shortfall below target return is ignored

4) VaR: probability of return less than the given amount over the specified time period

Drawback: also does not provide magnitude of losses

Factors that affect the REPO Rate

1) if borrower's CREDIT RISK increases (when delivery is not required, the Repo Rate Increases

2) as QUALITY of collateral INCREASES, repo rate DECREASES

3) as TERM of repo INCREASES, repo rate INCREASES

4) DELIVERY: if collateral is physically delivered, repo rate is Lower; if held by borrower's bank, rate Higher; if no delivery rate is Highest

5) COLLATERAL: if availability of collateral is limited, rate is LOWER; lender accepts lower rate to obtain security they need for another trade

6) FED FUNDS RATE: benchmark for repo rate; as it Increases, repo rate increases

7) SEASONAL FACTORS: affect demand for funds at institutions, and thus will affect rate

Investing in Foreign Assets -> currency hedging options

when selecting among foreign mkts, the mkt with the HIGEST excess return (local mkt return - local mkt risk free rate) will provide BEST currency hedged return

1) Invest in foreign asset, DON'T HEDGE, earn LMR+LCR

LMR= local mkt return LCR= local currency return

2) buy foreign asset and FWD hedge the currency (sell it) to earn LMR + investor's domestic rate - foreign currency rate

hedged LCR= domestic interest rate - foreign interest rate

3) buy foreign asset, PROXY HEDGE currency; used when fwd contracts on asset's currency are expensive or not traded

4) buy foreign asset and CROSS HEDGE the currency; sell foreign currency fwd to buy a different foreign currency fwd; this is taking active risk based on an expectation the 2nd currency will perform better; CHANGES RISK rather than eliminating it

Criteria utilized in determining OPTIMAL MIX of active managers

1) STYLE ANALYSIS: explains majority of active returns; primary concern is any addt'l risk exposure due to style

2) SELECTION BETS: decompose manager's excess returns to determine ability to generate superior selection returns

3) INVESTMENT PROCESSES: type of research, how alpha is attained, who/how decisions made

4) ALPHA CORRELATIONS: alphas should also be diversified; sponsor should find mix of active managers that optimizes avg alpha with alpha vol

Ratios of Fees to Alpha usually higher for FI mangers


-unlike govt's, emerging corporations don't have tools to offset negative events

-EMD returns can be volatile and negatively skewed

-lack of transparency and regulations=higher credit risk

-may have under-developed legal systems that don't protect against gov't actions (lack of seniority protection)

-lack of standardized covenants; each issue must be studied

-GEOPOLITICAL RISK: political instability; changes in taxation or regulations; currency restrictions; relaxed bankruptcy regulations that increase likelihood; pegged fx rates

-lack of diversification of main index, which is concentrated in Latam


duration contribution =

duration contribution = weight x duration x country Beta

IMMUNIZATION Strategies for SINGLE liability vs MULTIPLE liability vs GENERAL Cash Flows

SINGLE LIABILITY: bullet strategy: minimize the distribution of the maturities of bonds around the single liability date

barbell strategy: 1st bond matures several years before liability date, the other several years AFTER

maturity variance: (M2): minimize M2, which is the variance of the differences in maturities of the bonds used in the immunization strategy and maturity date of liability; if all bonds have same maturity date M2=0

MULTIPLE LIABILITIES: key is to decompose portfolio payment streams in such a way that the component streams separately immunize each liability

possible if:

1) A and L have same PV

2) A & L have same aggregate duration

3) range of duration distribution of individual assets in portfolio > distribution of liabilities; necessary to use CF generated rom our assets to meet outflow needs

GENERAL CASH FLOWS: using cash as part of the immunization strategy, even if cash has not yet been received; Duration of cash in 6 months = 0.5

Cash Flow Matching to fund a set of FUTURE LIABILITIES

-CF matching will also cause durations to be matched, but is more stringent

-REBALANCING should NOT be needed

1) select bond with maturity date = last liability payment

2) buy enough in par value such that principal + final coupon fully fund the liability

3) work backward, choose another bond with maturity value + final coupon + coupon on longer bond fully fund 2nd to last liability payment, etc, until all liabilities have ben addressed

-an easy way is to buy face amounts of zero-coupon bonds equal to each liability on needed payout dates -> VERY RESTRICTIVE and EXPENSIVE

-bond with CF just after liability date could be used with assumption it could be used as collateral to borrow funds needed for distribution

Immunization RISK

-a measure of the relative extent to which the terminal value of an immunized portfolio falls short of its target value as a result of non-parallel changes in rates

-select portfolio that minimizes Immunization Risk which is a portfolio with cash flows concentrated around the investment horizon

Problems with using Bond Mkt Indexes as a benchmark

if an index is not investable, it is NOT a valid benchmark

1) bonds are more heterogeneous and illiquid; many issues don't trade and pricing data is frequently based on appraisals and not publicly reported

2) indexes from vendors can appear similar but are actually very different in characteristics with risks not readily apparent (sinking funds, callable vs non-callable, countries in a global index)

3) risk characteristics can change quickly over time as new issues of bonds are added and those approaching maturity are deleted from the index

4) BUMS problem as cap-weighted indexes may carry increased exposure to credit downgrades; large issuance leads to greater index weight, but increased issuance also related to excessive leverage; index may impose weight limits

5) can be difficult for investors to match their risk profile

classical single-period immunization

IMMUNIZATION: strategy used to minimize interest rate risk, made up of price risk and reinvestment rate risk

-buy bonds that results in the effects of price risk and reinvestment risk exactly offsetting each other

-construct a portfolio with an effective duration = liability horizon

-duration works for small, immediate, parallel shifts in yield curve

-without rebalancing, only works for one-time instantaneous change in rates: the passage of time causes portfolio duration and its target liabilities to change, but not usually at the same rate; so not a buy and hold strategy

-if portfolio duration < liability duration -> reinvestment risk; if rates fall the losses from reinvested coupons would more than offset gains from an increase in value

-if portfolio duration > liability duration -> PRICE RISK; if rates rise, the LOSSES from mkt value of bonds would more than offset any gains from additional revenue from reinvested coupons and principal

Advantages of investing in emerging mky debt

-provide diversification benefits

-increased quality in emerging sovereign bonds; gov'ts can potentially engage in monetary or fiscal activity to offset negative events

-Resiliency has increasee; bounce back from taking hit after an event

-an Undiversified index offers return-enhancing potential

Decision to hedge or not hedge foreign currency

Start by calculating fwd differential expected by the mkt for the foreign currency

f=i(d) - i(f) = -0.8% means a fwd currency hedge would lock in 0.8% depreciation in foreign currency

If manager expects USD to increase by 0.4% this means he expects foreign currency to depreciate by 0.4%

The 0.8% loss that occurs on the hedge is worse than the expected loss so it's best to remain unhedged

As long as the bonds are similar in maturity and other risk characteristics, choosing btwn them is determined solely by the bond that offers the greatest...

Domestic return on foreign bond = R(b)

Currency return = R(c) =

Choose bond that offers greatest excess return denominated in its local currency; so

R(l) - i(f) = (local return on foreign bond in its local ccy) - (foreign interest)

R(b) = R(l) + R(c) = nominal local return + currency return implied by fwd ccy differential

R(c) approx= i(d) - i(f)

Interest Rate Parity = F =

Approx FWD premium or discount =

If Foreign Rate is higher than investor's domestic rate, foreign currency trades at a forward ________; and

If foreign rate is higher than investor's domestic rate, foreign currency will trade at a forward discount and selling foreign currency fwd to hedge currency risk will earn a negative currency return

Estimate change in price of foreign bond given 100bps change in domestic rate


Yield Beta measures relationship btwn change in one set of foreign rates and another set of domestic rates

3 Credit-Related risks that can be addressed with Credit Derivative Instruments

DEFAULT RISK: unique in that it results from a potential action of the debt issuer (failure to pay)

CREDIT SPREAD RISK: a function of potential changes in the market's collective evaluation of credit quality, as reflected by the spread


Duration of a Bond Option

=option delta x duration of underlying x (price of underlying/price of option)

Out of the money option will be cheaper and provide more leverage than ITM options

But OTM options are less sensitive to the underlying and thus have a lower delta


delta and duration of a put negative

Receiving FIXED in a swap ______ duration

What is the duration for floating rate bonds?

Receiving Fixed in swap INCREASES DURATION

-swaps used to hedge interest rate risk bc they are lower in cost than futures or other contracts

-floating rate bonds have low duration

3 basic sources of hedging error

Error in:

1) FORECAST of the BASIS at the time the hedge is lifted



Target Dollar Duration = DDt =

# of contracts to achieve DDt

To INCREASE Dollar Duration _______ futures contracts

BUY futures contracts

DD = (effective duration)(.01)(value)

Calculate the Effect of Leverage on Duration

D(E) = duration of equity =

Just as leverage increases portfolio return variability it also increases duration

Due to negative convexity, callable bonds outperform non-callable bonds when rates are ______

Callable bonds outperform when rates are RISING as the probability of bonds being called FALLS

-when current rate is lower than coupon rate, negative convexity makes callable bonds respond less to increasing rates

-call has value to the issuer


if yield spread is expected to Narrow choose the _____ yield bond

Focusing on overall spread duration:

If yield spread is expected to Narrow ______ spread duration

If yield spread is expected to NARROW choose Higher yield bond

For overall spread duration:

If yield spread is expected to Narrow, then INCREASE SPREAD DURATION

If rates are expected to RISE, ______ shorter duration bonds and ______ longer duration

If rates expected to RISE, BUY shorter duration and SELL longer duration

Contingent Immunization hints

-assume semiannual compounding unless told otherwise

-if asset duration and convexity MATCH the liability's, the surplus will be relatively stable (i.e. the portfolio is immunized); if duration and convexity of assets and liabilities do not match, the surplus will change as mkt conditions change and time passes

-BEFORE the surplus becomes NEGATIVE, portfolio must be immunized and active management is no longer allowed; once surplus goes negative, it's no longer possible to immunize and reach target value at prevailing mkt immunization rates

Bond characteristics that must be considered with immunization

1) Credit Rating: immunizing a portfolio, it is implicitly assumed bonds will NOT DEFAULT

2) Embedded Options: for bonds with embedded options, it may be difficult to estimate duration bc cash flows are difficult to forecast

3) Liquidity: if a portfolio is to be rebalanced, it will be necessary to sell some of the bonds

Problems with using Bond Mkt Indexes as Benchmarks

If index is NOT investable, it's not a valid benchmark

1) Bond mkt securities are heterogeneous and illiquid; pricing data frequently based on appraisals

2) indexes from different vendors can appear similar but have very different characteristics (callable vs non, sinking fund bonds, etc)

3) Risk characteristics can change over time as new issues of bonds are added and ones approaching maturity cut

4) BUMS: cap weighted index may be exposed to credit downgrade as large issuance may indicate increased leverage (may impose weight limit)

5) difficult for investors to find index match for risk profile

5 classifications of Bond portfolio management

1) Pure Bond Indexing: easy to describe, costly and difficult to implement

2) Enhanced Indexing by matching primary risk factors; sampling approach due to illiquidity of certain bonds, Outperforms Pure Bond

3) Enhanced Indexing by small risk factor mismatches; 1st level designed to earn same return as index; small relative value tilts to cover admin costs

4) Active Mgmt by Larger risk factor mismatches; higher degree of risk factor mismatches and possibly duration; increased transactions costs

5) Full-Blown Active Mgmt: no restrictions; increased expected return; increased risk, tracking error and fees

3 characteristics when moving from Pure Bond Indexing to Full Blown Active Management

1) Increasing Active Management

gradual relaxation of restrictions on a manger's actions to allow him to exploit superior forecasting abilities

2) Increasing Expected Return of the portfolio from actions taken by the managers

3) Increasing Tracking Error: the degree to which the portfolio return tracks that of the index

Immunization definition/concept

Strategy for 'locking in' a guaranteed rate of return over a particular time horizon regardless of interest rate changes

As interest rates increase, the decrease in the price of a fixed-income security is usually at least partly offset by a higher amount of reinvestment income.

For an arbitrary time horizon the proce and reinvestment effects generally do not exactly offset each other. The purpose of immunization is to identify the portfolio for which the change in price is exactly equal to the change in reinvestment income at the time horizon of interest

To immunize a portfolio's target value or target yield against a change in the mkt yield, a manager must invest in a bond or bond portfolio whose:

1) duration is equal to the investment horizon; AND

2) initial present value of all cash flows equals the present value of the future liability

# of futures contracts needed to achieve the portfolio's target dollar duration (fixed income)

Basis Risk

The outcome of a hedge will depend on the relationship btwn the cash price and the futures price both when a hedge is placed and when it is lifted.

The difference btwn the cash price and the futures price is called the BASIS.

The risk that the basis will change in an unpredictable way is called basis risk

There is potentially substantil basis risk in cross hedging bc the two products may not move as expected

Rebalancing Ratio =

for Dollar Duration

Rebalancing Ratio = (target DD/new DD)

to readjust back to original DD AND maintain the current proportions of each bond in the portfolio, subtract 1 from rebalancing ratio to arrive at the necessary increase in value of each bond in the portfolio, and thus the TOTAL increase in the value of the portfolio (requires additional cash)

Dollar Duration=

if portfolio has mkt value of 47.5mln, par value=50mln and duration=7; manager uses cash in the portfolio (cash has 0 duration) to purchase 1mln mkt value and par of a bond w duration=4.0

what are initial and after purchase dollar durations?

measures $ duration in value for 100bps change in rates


initial DD=(47.5)(.01)(7.0)= 3,325,000

DD of purchased bond=(1mln)(.01)(4.0)= 40,000

DD after purchase=3,325,000 + 40,000= 3,365,000

Rebalancing a portfolio to reestablish a desired $ duration

1) calculate new DD=(mkt value)(.01)(duration)

2) calculate rebalancing ratio

Rebalancing Ratio = (target DD/new DD) then subtract 1 to get the necessary increase in the value of each bond in portfolio; and thus required additional $

More Practical Solution is making the adjustment in only 1 bond

if rates increase, find bond w longest duration

desired increase in DD=(target DD) - (new DD)

new DD of control bond=old DD + desired increase

required new value of control bond=

(new DD/old DD) x (mkt value of control bond post rate change)

Spread Duration

measures sensitivity of non-Treasury issues to a change in their spread above treasuries of the same maturity

-allows manager to forecast future performance of the sector and select superior bonds to represent each sector in the portfolio

-if spread forecast to widen for one sector, reduce weight before prices fall

3 measures used for fixed-rate bonds:

1) Nominal Spread

2) Z-spread (static spread)

3) OAS; approx % change in price for 100bps change in OAS

Using a CONTROLLING POSITION to return portfolio back to its original dollar duration

Use bond with LONGEST DURATION, which becomes the controlling position, and allows you to use the least amount of cash

Return to a domestic investor

Breakeven Spread Analysis

(-)Higher Yielding bond's yield advantage = (-)Duration of comparison bond x BE spread(-)Higher Yielding bond's yield advantage = (-)Duration of highest yielding bond x BE spread

So we can absorb 5.7 bps of spread widening before breaking even btwn the 2 bonds

The higher yielding bond will underperform when the spread widens

Caution: if the case specifies which bond will change, use its duration

New duration of local bonds needed to keep duration the same after adding foreign bond with country beta

Step 1) Adjusted foreign duration = foreign bond duration x country beta

Step 2) calculate new duration of local component (NDL) using weighted avg

Target duration of portolio = (weight of foreign bonds x adjusted foreign duration) + (weight of local bond x NDL)

Solve for NDL