Portfolio Construction for Systematic Fixed Income: Signals, Optimization, and Constraints

Book: Systematic Fixed Income: An Investor’s Guide Author: Scott A. Richardson, Ph.D. Publisher: John Wiley & Sons, 2022 ISBN: 9781119900139

Having a good signal is only part of the job. You also need to turn that signal into an actual portfolio. Chapter 8 of Richardson’s book walks through the portfolio construction process, and honestly, this is where the real craftsmanship happens. There are way more decisions to make than you might expect.

The Investment Process Visualization

Richardson presents a simple visual of the investment process. It has multiple steps, and the previous three chapters only covered one of them: ranking the relative attractiveness of assets. Now we need to think about everything else. Defining the eligible universe, processing signals, building a risk model, setting constraints, and actually optimizing.

Step One: Define Your Sandbox

Before you do anything else, you need to decide which bonds you are allowed to buy. For a US high-yield corporate bond mandate using the ICE/BAML H0A0 index as a benchmark, that index had 2,003 bonds as of late 2020. Not all of them belong in your systematic process.

Liquidity is the first filter. If a bond has not traded in six months, there is no point modeling it. Your trading desk will never be able to buy it at your target price. The good news is that filtering out illiquid bonds does not reduce your expected returns. There is no evidence of a liquidity premium in public corporate bond markets.

Seniority matters too. Bonds in the same index can range from senior secured to junior unsecured. If you keep all of them, you need to adjust for expected recovery rates in your carry and value signals. Otherwise your cross-sectional comparisons break down.

Remaining time to maturity affects turnover. Bonds die when they mature. Buying short-duration bonds that will exit the index soon is a poor use of your limited turnover budget.

Private issuers make up 29 percent of the US HY index. It is harder to get data on them, so you need at least a minimum information threshold. And domicile matters because some USD-denominated bonds are issued by companies based in emerging markets, which introduces different risks.

Every exclusion creates tracking error relative to your benchmark. You need to measure that tracking error and understand where it comes from.

The Investment Cube

Richardson introduces a useful visual he calls the “investment cube.” The front face spans breadth (how many investment themes you cover) and depth (how many measures you have within each theme).

On the vertical axis you have the usual themes: carry, defensive, momentum, valuation. But you could add sentiment, smart money, liquidity provision, and more. Across the horizontal axis, each theme can range from simple to complex. Momentum can start with price returns and extend to fundamental measures. Valuation can start with linear regressions and extend to structural models or machine learning.

Smart beta approaches cover only the simple end of this face. A full systematic process tries to span the entire face and keep expanding it. The backward dimension of the cube represents portfolio construction and implementation, which is what this chapter is all about.

Signal Processing: Z-Scoring and Sector Neutrality

Raw signals need to be processed before you can use them. Richardson walks through a concrete example using equity momentum for corporate bonds.

Step 1: Z-score across the full cross-section. Take your raw momentum signal, subtract the mean, divide by the standard deviation. This normalizes the signal but preserves the rank ordering. Problem: the Z-scored signal has a negative association with DTS (a proxy for beta), and there is a sector imbalance between long and short positions.

Step 2: Z-score within sectors. Instead of normalizing across all 195 issuers at once, normalize within each sector. Now the sector imbalance disappears completely. But the negative beta tilt remains.

Step 3: Beta neutralize. Regress the within-sector Z-scored signal onto DTS. The residual removes the beta tilt entirely. This introduces a tiny sector imbalance, so ideally you regress onto both sector indicators and DTS at the same time.

After all these transformations, the modified signal still has a 0.77 correlation with the original raw signal. You keep most of the information while removing unintended exposures.

Signal Weighting

Once you have processed individual signals, you need to combine them. Richardson recommends equal weighting across themes unless you have strong conviction otherwise. That conviction might come from unique data access or a demonstrably superior methodology.

A warning about factor timing: trying to adjust signal weights based on recent performance is tempting but dangerous. In credit markets, the turnover cost can eat up any benefit. And a diversified set of signals already provides some implicit timing for free, because the correlation structure between themes is dynamic.

The Optimization

At the core is an objective function. Richardson presents a linear program that captures the essentials. You are trying to maximize expected returns subject to constraints.

The constraints include: no shorting (for long-only portfolios), portfolio weights must sum to one, individual bond weights cannot deviate more than 0.25 percent from benchmark, aggregate spread deviation is capped at 50 basis points, aggregate duration deviation is capped at 0.5 years, and turnover is limited to 10 percent.

When you feed a signal through this optimizer, the correlation between the resulting portfolio weights and your original signal (called the “transfer coefficient”) will be less than 1. In Richardson’s example it is about 0.60. That is normal. Liquidity limits, position size caps, and risk constraints all create distance between what you want and what you can actually hold.

Risk Modeling

Risk models estimate the volatility and correlation structure across all eligible bonds. For a universe of 2,000 bonds, you need 2,000 volatility estimates and many more correlations.

Two common approaches: asset-level historical returns (good for small universes like government bonds) and common factor models (necessary for large universes like corporate bonds). Commercial options exist (BARRA, Axioma, Northfield), but building your own gives you transparency and flexibility.

Rebalancing and Turnover

Systematic portfolios rebalance at discrete intervals, traditionally monthly but increasingly more often. Rebalancing happens because of fund flows, coupon accumulation, and portfolio drift.

The optimal turnover depends on signal speed. Faster signals need more turnover. But corporate bonds are expensive to trade, so you have to weigh the benefit of getting closer to the optimal portfolio against the cost of trading.

Other Constraints and Crowding

Beta constraints ensure your portfolio matches the benchmark’s risk profile. Trade-size and position-size constraints reflect the realities of bond market liquidity. Sustainability constraints are increasingly common as ESG considerations grow.

Richardson warns against adding constraints too aggressively. Every constraint lowers your transfer coefficient. On crowding: systematic strategies in fixed income account for roughly 3 percent of assets in systematic equity strategies. Not a pressing concern yet.

Beta Completion

The portfolio needs to match the benchmark’s rate, credit, and currency exposures. Rather than distorting your security selection to achieve this, use derivatives. Interest rate swaps and futures for rate risk, credit index derivatives for credit risk, and currency forwards for FX risk. These are much cheaper to trade than individual bonds, so they are the efficient way to complete your beta.

This post is part of a series retelling Systematic Fixed Income: An Investor’s Guide by Scott A. Richardson.

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