Fixed Income

Question 1

•••••••Fixed Income•••••••

Incremental Return (XR)

Answer 1

XR = (s x t) - (Δs x SD) - (t x p x L)

• s = spread
• t = time
• SD = Spread duration
• p = prob of loss
• L = Loss severity

Question 2

•••••••Fixed Income•••••••

Duration Matching for Single / Multiple Liabilities

Answer 2

• For a single liability:
  
  • PV_A ≥ PV_L
  • Match Macaulay D; D_A = D_L
  • Minimize asset convexity (make it closer to a zero-coupon bond)
• For multiple liabilities:
  
  • PV_A ≥ PV_L
  • BPV_A = BPV_L
  • Convexity_Assets slightly exceeds Convexity_Liabilities

Question 3

•••••••Fixed Income•••••••

4 Types of FI Liability-Based Mandates

Answer 3

1. Cash flow matching - buy zero-coupon bonds for each cash flow
2. Duration matching - only works for parallel shifts, requires rebalancing,
   
   1. For a single liability = minimize asset convexity
   2. For multiple liability = Convexity_Assets > Convexity_Liabilities
3. Contingent immunization - active strategy when MV_Assets > PV_Liabilities
4. Horizon matching – short term is cash flow matched and long term is duration matched

Question 4

•••••••Fixed Income•••••••

Fixed Income Expect Returns

(Decomposing Bond Returns)

Answer 4

ALWAYS DIVIDE ANNUAL COUPON BY CURRENT BOND PRICE

Question 5

•••••••Fixed Income•••••••

Levered Return

Answer 5

Rp = R_Asset + [(V_Debt/V_Equity) * (R_Asset − R_Debt)]

Question 6

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Yield curve Curvature

Butterfly spread

Answer 6

Butterfly Spread = -Short + 2 * Intermediate - Long

Question 7

•••••••Fixed Income•••••••

Δ Slope

Answer 7

Δ Slope (30s – 2s) = Flatter/Steeper

Question 8

•••••••Fixed Income•••••••

$ Duration and PVBP

Answer 8

$ Duration = Modified Duration x MV x 0.01

PVBP = Modified Duration x MV x 0.0001

Question 9

•••••••Fixed Income•••••••

Macaulay (D)

Answer 9

Macaulay (D) = ∑ (PV of CFs weighted by length of time to receipt) / MV_Bond

Question 10

•••••••Fixed Income•••••••

Modified Duration (MD)

Answer 10

Macaulay D_Annual / (1 + CF yield_Annual/2)

Question 11

•••••••Fixed Income•••••••

Duration gap

Answer 11

|BPV_A − BPV_L|

Question 12

•••••••Fixed Income•••••••

Yield Curve portfolio strategies

Answer 12

1. Buy and hold: increasing duration to obtain higher income yield.
2. Ride the yield curve (a more active version of buy and hold): Buy higher-yield bonds with longer durations and sell them for a gain as they roll down to a lower-yield portion of the curve (assuming steep YC).
3. Sell convexity (for low vol scenario): buy callable and M_ortgageB_ackedS_ecurities for higher yield or sell options for premium income.
4. Carry trade: buy higher yield (longer-duration or higher-yield currencies) and borrow at lower yield (inverse).

Question 13

•••••••Fixed Income•••••••

Yield Curve portfolio types

Answer 13

Bullet-like: Cash flows concentrated at a single point in time. Lower convexity (undesirable), but higher yield (desirable)

Barbell-like: Cash flows concentrated in shorter and longer durations. With > dispersion, higher convexity but lower yield

Ladder-like: Equal amounts of bonds in each period, more liquidity and diversification

Question 14

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Spread measures:

Answer 14

Benchmark spread: Bond – Closest Dur. Gov. Bond

G-spread: Bond – Interpolated Gov. Bond

I-spread: Bond – Interpolated Swap rate yield

OAS: trial-and-error estimation of average expected incremental return. Best for bonds with embedded options.

Question 15

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zero replication

Answer 15

zero replication is when the interest rate risk has been immunized (i.e. duration match)

Question 16

•••••••Fixed Income•••••••

Yield change using Duration and Convexity

Answer 16

Yield change = (–ModDur * ΔYield) + (½ * Convexity * ΔYield²)

Question 17

•••••••Fixed Income•••••••

Sensitivity to changes: High yield vs Investment Grade

Answer 17

High Yield - more affected by spread change

Investment Grade - general market (risk-free) interest rate change

Question 18

•••••••Fixed Income•••••••

Bums problem

Answer 18

Bums problem = less creditworthy issuers with a lot of outstanding debt constitute a larger part of a Value-Weighted Index (use an Equally Weighted Index instead)