Fixed Income

Question 1

What are the Yield Curve strategies for: 1) Stable Yield Curve

Answer 1

1) Buy and Hold
2) Ride the yield curve
3) Sell Convexity
4) Carry Trade

Question 2

What are the Yield Curve strategies for:

2) Changes expected in
- Level (rising or falling interest rates)
- Slope (steepness or flattening) - 30s and 2s
- Curvature - -2 + 2(10) - 30

Answer 2

1) Duration Management
2) Buy convexity
3) Bullet/Barbell structures
4) Butterfly 5) Condor

Question 3

How do you sell convexity?

Answer 3

• Sell Calls on bonds in the portfolio - Write puts on bonds you’re willing to own anyways Negative convexity - Buy Callable bonds - Buy MBS

Question 4

Duration Management - rising/falling rates? - methods

Answer 4

Rising rates = shorten duration

Falling rates = lengthen duration

Derivatives overlay

• long int rates futures to increase
• short int rate futures to decrease Leverage
• borrow very short, invest long Swaps
• Rec FX, Pay Fl to lengthen
• Pay FX, Rec Fl to shorten

Or, just buy longer date bonds to lengthen and sell shorter dated bonds to shorten If constrained from changing dur, can buy or sell convexity

Question 5

What is the “Bums” problem?

Answer 5

If a FI index is weighted by Market Cap, higher issuers of debt will have a higher weighting. Higher issuers = higher default risk and potentially less creditworthy issuers constituting a large part of the index.

Question 6

What is a Condor and when would you use it?

Answer 6

Condor 1) Long2yr/Short5yr and Short10yr/Long30yr *use when more curvature or 2) Short2yr/Long5yr and Long10yr/Short30yr The outside wings (2yr/5yr and 10yr/30yr) must be duration neutral

Question 7

Carry Trade - when do you use it? - Intra vs Inter? - types

Answer 7

Used when a stable YC expected, and if using across two countries, entered to avoid currency risk by buying and selling both currencies - intra = 1 country - inter = multiple countries

1) Buy a bond that earns high yield, by financing it in the repo market (short, low rates)
2) Int rate swap - Receive Fixed, Pay Floating in the market with steeper curve and - Pay Fixed, Receive Floating in the market with flatter curve
3) Int rate futures - Long position in futures in steeper market, short position in futures in flatter market

Question 8

Expected Excess Return - formula? - what is it telling us?

Answer 8

EXR = (S x t) - (ChangeS x SD) - (t x p x l)

It is a relative value, therefore look at the change in spread to see it’s value relatively. If z-spread for instance is increase, %changeS = +25%, the credit spread widening means a loss, therefore relatively the best value would be the smallest loss

Question 9

Butterfly Spread - Formula? - What does it show you?

Answer 9

Butterfly spread = -2yr + 2(10yr) - 30yr Tells us whether there has been a change in curvature

Given term structures for Jan, Feb and March (each has 2,10,30) calc butterfly spread and the change is the change in curvature

Question 10

Total E(R)

Answer 10

Total E(R)

Yield income Coupon/Current Bond Price + Reinvestment Income

Rolldown Yield Bondend/Bondbeg - 1

Question 11

Laddered Portfolio

Answer 11

Laddered Portfolio

1) spreads bonds maturities more or less evenly along the YC

Advantages

• protection from shifts and twists: cash flows diversified across the time spectrum
• as bonds mature, they are reinvested at the longer end of the ladder, typically at higher rates so over time, have bonds at higher rates and lower rates: maintains duration
• provides a balanced position between cash flow reinvestment and market price volatility risk
• liquidity management

Question 12

Change in portfolio value using PVBP

Answer 12

Change in Port Value = Key-rate PVBP x Portfolio Par Value x curve shift bps/100

Question 13

Shifts, twists and Butterfly

• explain

Answer 13

1) Shifts
1. 1) parallel
1. 2) non-parallel:
- non-parallel increase/decrease in all yields
2) Twists
- steepening
- flattening
3) Curve
- butterly: short and long increase, middle decrease or other way
- more curve: Barbell outperforms
- less curve: Bullet outperforms

Question 14

Repurchase Agreements

Answer 14

Repo agreement

• “sell” a security for cash (at a haircut) & simultaneously agree to “buy” it back (usually overnight)
• stock = collateral for the loan

Cost (interest) = amount received x repo rate x ¹/₃₆₀

Borrower = repo

Lender perspective = reverse repo

Question 15

Single Liability Immunization

Rules

Answer 15

Single Liability

1) Initial Portfolio MVa >= PVliab
2) Portfolio MacDur matches due date of liability
3) Minimize Portfolio Convexity

*4) Regular rebalancing

Question 16

Multiple Liabilities Immunization

Rules

Answer 16

Multiple Liabilities Immunization

1) PVa >= PVl
2) BPVa = BPVl
3) Dispersion of Cashflows and Convexity higher than Liab, but minimize thereafter

*for = durations, higher convexity outperforms

Question 17

Interest Rate Swap - managing a duration gap

1) Formula

Answer 17

Interest Rate Swap - working out the notional amount

NA = BPV_Liab - BPV_Port x 100

BPV_Swap

* remember, there is no underlying bond, therefore the 100 is to express it per unit of 100

Question 18

Futures Contracts - to manage a duration gap

1) Formula

Answer 18

Futures Contracts - number of futures contracts to buy/sell

N_f = BPV_liab - BPV_portfolio

BPV_futures

BPVfutures = BPV_CTD

CF_CTD

Question 19

Portfolio positioning in anticipation of a parallel upward shift in YC

Answer 19

Paralell upward shift

• remember - upward shift means it’s not a stable curve, therefore the market thinks the spot curve will evolve into the forward curve
• so, you’ll get your 1-year HPR (as you would)

+

• additional bps or less bps depending on the
  1) Implied Forward Yield vs Forecast Yield

If our forecast is < Implied Fwd Yield, theres room for rolling!

Max - (Imp Fwd yield - Forecast yield) x Dur@ horizon end = bps to add or subtract from hpr