CFA Level 3 Fixed Income Portfolio Management

Below, you’ll find my personal CFA level 3 fixed income portfolio management notes…

You can find a list of the other categories here: CFA Level 3 Notes, Formulas, and Weights.

Cash Flow Matching and Duration Matching are two immunization approaches. With a proper setup, companies can remove both the matched assets and liabilities through Accounting Defeasance.

Immunization (zero replication) is structuring a portfolio to minimize return variance over a known time horizon to meet liability obligations.

Contingent Immunization combines an immunization approach with an active management component… more common if there’s a positive surplus (assets – liabilities)

Three primary yield curve movements for fixed income portfolio management… change in Level, Slope, and Curvature.

Pure Indexing (Full Replication index) is not practical in fixed income markets due to liquidity issues, transaction fees, etc. Enhanced Indexing is more common and involves the attempt to slightly outperform the index… for example, Stratified Sampling or Cell Approach.

Mutual Funds and ETFs can be a useful way to gain bond exposure due to the illiquidity and large minimums on many issuances. Capital requirements have reduced brokers’ incentives to hold inventory in thinly traded securities.

Matrix Pricing is a way to value illiquid assets by looking at comparable securities.

Fixed Income Expected Returns

+ Yield Income

+ Rolldown Return

+ Yield Curve Change Return (-MD × ∆Yield + ½ × Convexity × ∆Yield2)

± Credit Change Return

± Forex Return

Rolling Yield = Yield Income + Rolldown Return

Fixed Rate Swap payers (floating receivers) are short a fixed rate bond. Useful for lowering portfolio duration.

Repurchase Agreements (Repos) are collateralized loans

CFA Liability Classifications

Macaulay Duration is the weighted average of the times to receipt of cash flow. Dispersion is the weighted variance.

Modified Duration Formula
Convexity Formula with Dispersion

Convexity ≈ (Macaulay Duration)^2

Increasing portfolio convexity usually requires giving up some yield.

Reduce Structural Risk by minimizing dispersion (Barbell –> Bullet)

Laddered Bond Portfolios offer diversification over the yield curve.

3 Requirements for Single Liability Immunization

  1. Market value exceeds present value of the liability
  2. Macaulay duration matches liability due date
  3. Minimize convexity statistic (opposite for multiple liability immunization)

Derivatives Overlays can be used to rebalance immunized portfolios in a cost-effective way.

Basis Point Value (BPV) is Money Duration times 0.0001… helps make the numbers of large portfolios more manageable.

Assets BPV + Nf × Futures BPV = Liability BPV

Nf = (Liability BPV – Asset BPV) / Futures BPV

Futures BPV Formula Cheapest-to-Deliver and Conversion Factor
Accumulated Benefit Obligation Formula
Projected Benefit Obligation Formula

G = Years Worked
T = Remaining Years to Retirement
Z = Numbers of Years to Live after Retirement
W0 = Current Annual Wage
m = Multiplier
r = Discount Rate

Effective Duration Formula

International Swaps and Derivatives Association (ISDA) master agreements are often supported by collateral or by a Credit Support Annex (CSA) which can also require collateral.

Swap BPV Duration Adjustment Formula

Immunization Hedging Ratio is the percentage of the duration gap that’s closed.

Tracking Risk is deviations on portfolio returns that differ from the index returns.

Active Return = Portfolio Return – Benchmark Return

Key Rate Duration accounts for a specific rate change along the curve while holding the others unchanged.

Empirical Duration is duration derived from historical market data.

Total Return Swaps (TRS) are one of the most common OTC derivative strategies. The Total Return Receiver receives both underlying index cash flows and any index appreciation. In return, the receiver pays Libor plus a pre-determined spread… and also pays if the underlying index price drops.

Strategic Asset Allocation targets specific asset class weightings. Tactical Asset Allocation lets portfolio managers deviate from those weights in the short-term.

The Bums Problem occurs as investors allocate more to more-levered borrowers. Value weighting bond indexes plays into the Bums Problem. Also, as funds take on more leverage, their credit ratings can drop.

If bonds drop to Negative Coupon Rates, the duration will be longer than the maturity.

Butterfly Spread = -(2-Year Yield) + (2 × 10-Year Yield) – 30-Year Yield

The Butterfly Spread is a larger number when the yield curve is more curved. And when there’s an upward level shift, the yield curve usually flattens.

Stable Yield Curve Strategies

  • Buy and Hold (Ride the Yield Curve)
  • Sell Convexity (Sell Calls on Owned Bonds and Puts on Bonds Willing to Own)
  • Carry Trade (Buy High Yielding and Finance with Lower-Yielding)

Buying Mortgage Backed Securities is similar to writing options.

Portfolio managers use a Barbelled Portfolio if they expecting a yield curve flattening. They use a more Bulleted Portfolio if steepening is expected.

Credit Risk is the risk from a counterparty’s possible failure to make a promised payment. The two credit risk components are Default Risk (probability of default) and Loss Severity (amount of loss if default happens).

High-Yield bonds have higher credit risk exposure and aren’t as sensitive to interest rate moves. Investment grade are more sensitive to interest rate moves.

Credit Spreads and Risk-Free Rates tend to have a negative correlation.

Benchmark Spread is a simple method… subtract the security yield on a bond with little to no credit risk from a bond with a similar duration.

G-Spread is derived from actual or interpolated government bonds.

I-Spread is similar to the G-Spread but uses swap rates instead. The advantage is that swap curves can be smoother.

Z-Spread is the zero-volatility spread. It’s a spread that’s added to every implied spot yield curve point to make the present value of the bonds cash flows equal to the bond’s market value.

Option-Adjusted Spread (OAS) is similar to the Z-Spread but it adjusts for features such as options. It’s a theoretical measure and realized will be different due to option exercises.

Excess Return (XR) ≈ (s × t) – (∆s × SD)

Expected Excess Return (EXR) ≈ (s × t) – (∆s × SD) – (t × p × L)

Bottom-Up Credit Strategy Approach

  • Looks at relative value of comparable bonds (start by narrowing sectors)
  • Compare credit related risks and then credit spreads
  • Also consider… issue size, bond structure, supply, and issue date

Top-Down Credit Strategy Approach

  • Determine macro trends such as corporate default rates and economic growth
  • Sector divisions used by top-down are often broader than bottom-up
  • Determine credit quality by factoring in credit cycle and credit spread changes
  • Looks at average credit ratings, average spread duration, and EXR of indexes

Tail Risk is the risk of more events in the probability tail than the probability model predicts.

Please comment below if you have any suggestions or questions. Also, the next category in my CFA level 3 study list is Equity Portfolio Management.

Invest mindfully,

Brian Kehm

Sharing is caring...


  1. Shwetank Jain May 27, 2019
    • Brian Kehm June 2, 2019

Leave a Reply