S10 Flashcards
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 = (DiI - DbB) / 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
