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Flashcards in S10 Deck (67):

Two negatives of using leverage in fixed income investing

- Negative impact on return if rate of return is smaller than cost of leverage
- Higher dispersion of portfolio returns


Return formula using leverage

Rportfolio = Rinvestment + B/E* (Rinvestment - CostofBorrowedFunds)


Duration formula using leverage

De = (Di*I - Db*B) / E


Risks to REPO lender is collateral remains in borrowers custody

Borrower sells collateral
Goes bankrupt
Use collateral for a different loan


Ways of reducing REPO risk

Physical delivery to lender
Depositing collateral in a custodial account at borrowers bank
Electronic security transfer
No action is borrower's credit risk is low or if transaction is short term


REPO rate factors

Credit risk
Quality of collateral
Term of the repo
Collateral Delivery
Federal funds rate
Funds demand seasonality factors


Drawbacks of standard deviation

- Bond returns are often not normally distributed
- The number of inputs increases with number of bonds in portfolio (N*(N+1)/2 assumptions needed)
- Historical calculations may not be applicable today


Drawbacks of semivariance

- difficult to compute for large portfolios
- yields same results as standard deviation if returns are symmetric
- if returns are not symmetric, downside risk forecast is difficult to forecast
- uses just half of distribution so sample size is smaller - and less accurate statistically


Criticism of shortfall risk

Ignores outliers, so magnitude of shortfall below target return is ignored

Not as commonly used as standard deviation

Statistical properties are not well known

Does not take form of $ amount (while VAR does)


Criticism of VAR

like Shortfall Risk, VAR ignores the magnitude of losses


CTD Cheapest to Deliver price is =

=Quoted futures price X conversion factor


Advantages of using futures over cash market instruments

- more liquid
- less expensive
- easier to short vs actual bonds


number of futures to be bought to alter DOLLAR duration to target

nr = (DDt - DDp) / DDf


number of futures to be bought to alter DOLLAR duration to target (using CTD)

nr = (Dt-Dp) * Pp * CTDconversionFactor / (Dctd * Pctd)


Price basis =

= spot (cash) price - futures delivery price


hedge ratio =

= exposure of bond risk factor / exposure of futures to risk factor


hedge ration of yield spread is not constant =

DpPp * CTDconversionFactor * Yield Beta / (Dctd * Pctd)


3 sources of error in hedging

- forecast of basis at the time the hedge is lifted
- estimated durations
- estimated beta


option delta measures the change in

price of the option relative to the change in the underlying contract


credit spread option value =

max (actual spread - strike spread) x notional x risk factor, 0)


six sources of excess return for an international bond portfolio

market selection (country),
currency selection,
duration management ,
sector selection ( = industries, ratings, maturity),
credit analysis ,
markets outside the benchmark


foreign yield change (function of domestic yield change) =

change in foreign yield = beta X change in local yield + contrantE


contribution of foreign bond to total duration

=Fweight in portfolio X Fduration X Fbeta


Forward exchange rate (dom/for) =

Interest rate PARITY !!!

Spot exchange rate X (1 + domestic short term rate ) / (1 + foreign short term rate)


covered interest arbitrage
Covered interest differential exists if =

(1 + dom rate) - (1+foreign rate) X (Forward exchange rate / Spot exchange rate)


Proxy hedge

Using 2nd foreign currency (with high correlation to 1st foreign) forwards to hedge FX risk


Cross hedge

Using a forward contract to deliver original foreign currency for a different foreign currency to hedge FX risk


Foreign bond return =

R = R of bond in local currency + R from currency change ( 1 + return from bond in local currency)


foreign bond breakeven formula

(Foreign return - Domestic return ) / - (max of duration (foreign or local)

Discussion: yield on foreign should increase QWE over holding period for the decrease in price to wipe out yield advantage


core plus fixed income approach

holding core investment grade debt plus adding bonds perceived to have potential for generating added return.


Advantages of investing in emerging market debt

Diversification benefit
Return enhancing
Increased quality in EM sovereign bonds
Increased resiliency


Risks associated with investing in EM debt

Corporations do not have tools to offset negative events
EM debt returns are volatile and with negative skewedness
Higher credit risk due to lower transparency and weaker regulations
Under-developed legal system not protecting against adverse government action
Lack of standard covenant
Political risks
Lack of diversification in certain indexes


Political risks in EM debt

Political instability
REGULATIONS: Changes in taxation and regulations
REGULATIONS: Relaxed regulations on bankruptcy
CURRENCY: Imposed changes in exchange rate (pegging)
CURRENCY: Potential currency conversion difficulties due to various Gov restrictions


Criteria that should be utilized in determining the optimal mix of active managers

Style analysis,
Selection bets (credit spread analysis),
Investment processes (decision making, research process)
Alpha correlations.


instruments for default risk hedging

credit options
credit swaps


instruments for credit spread risk hedging

credit options
credit swaps


instruments for downgrade risk hedging

credit options
credit swaps


ALWAYS adjust the spread advantage to

investment period as it is often less than one year in Schweser tests


Credit spread forward contract - the payout is ignoring the

time number of months until settlement.


current forward exchange discount =

= (Forwarx fx - spot fx) / spot fx


impact on portfolio duration after increasing leverage by using 2yr REPO (compared to using overnight REPO)

the longer the repo the larger NEGATIVE impact on levered portfolio duration


leveraged portfolio duration formula denominator

$ of equity (not total portfolio)


hedged return for foreign bond =

domestic rfr + local risk premium =
domestic rfr + local Bond rate - local rfr


contingent claim exists even if liabilities are funded from a portfolio with

noncallable bonds.


Hedging MBS with two contracts better

matches the dispersion of MBS cash flows


Spread Risk of MBS: Definition, when to hedge

- Risk that spread over corresponding Tbond will widen, thus lowering the value of MBS.
- Usually not hedged, but taken when spread is attractive (when likely to narrow)


Interest rate risk of MBS: Definition, when to hedge

- Risk of interest rate increase to impact MBS value.
- might be selectively hedged via duration hedging
- non parallel changes in interest rate curve can be hedge with 2 bond hedge


Prepayment risk of MBS: Definition, when to hedge

- is the cause of negative convexity (smaller benefit from lower interest)
- can be hedged via:
--- dynamic hedging (continuous futures trading)
--- options


Volatility risk of MBS: Definition and when to hedge

- MBS can be evaluated as being composed of an option free bond and a short call option
- higher volatility increases value of call option and as a result causes a decline in MBS value
- if volatility is underestimated - buy options
- if volatility is overestimated - use dynamic hedging


model risk of MBS: definition and when hedging needed

- risk of incorrectly estimating MBS cashflows
- cannot be hedged


benefit/drawback from 2 bond MBS hedging

- better simulates the more evenly distributed and front loaded cash flows of MBS compared to one bond hedge
- doesn't address the negative convexity risk that arises from prepayment (could be hedged via options or dynamic hedging)


assumptions of 2 bond hedge

- incorporates reasonable possible yield curve shifts
- used an adequate model for predicting prepayments given certain changes in yield
- includes reliable assumptions in the monte carlo simulations of interest rates
- knows the security's price change given a small change in yield
- knows that the average price change method yields good approximations.


drawback of 2 bond hedging

- hedging is as good as the assumptions for the amount of rate change an curve reshapening


steps in 2 bond hedging

- determine average absolute price change per 100$ for a given SHIFT in yield curve
- same for a given TWIST in yield curve
- solve system of equations for the required amounts of bond 1 and bond 2


cuspy coupon MBS

- a MBS for which changes in interest rates have large effects on prepauments and hence on price
- given large negative convexity, adding calls and puts may be needed to better hedge in addition to 2 bond hedge


MBS is more exposed to yield curve risk (changes in shape of the curve) compared to bonds because

MBS cash flows are more evenly distributed (i.e. not bullets)


MBS adjustable-rate are still exposed slightly to

interest rate risk between reset periods.


MBS backed by adjustable-rate mortgages, are subject to cap risk if

underlying mortgage rates adjust upward to the point that they reach the cap


Effective duration of a mortgage will drop precipitously when interest rates do

drop because the effective maturity of the bond decreases sharply as the
bond is more likely to be called


A barbell strategy exploits

a flattening of the yield curve and
can immunize the duration of a portfolio just as a bullet bond portfolio could


Due to negative convexity, MBS are considered to be

market directional investments


Yield of a MBS =

+ yield of equal interest rate risk Treasury
+ spread (= option cost + option adjusted spread)


Assessing impact of a change in the yield curve on the price of MBS, using effective duration is inferior to using

interest rate sensitivity, and this is why it is used in 2-bond hedge


MBS investors usually want to capture value from changes in

mortgage spread (OAS) and not from changes in interest rates.

this is why risk related to changes in interest rate is being hedged using 2 bond hedge


market directional feature of MBS can be removed by

2 bond hedging


H2 and H10 determined for 2 bond hedge are multiplied to

par amount (not market price) of relevant two bonds


2 bond hedge equations

do not forget about minus !!!!!
aX + bY = MINUS Z
cX + dY = MINUS W