The standard approach is to define an objective that maximizes the portfolio-weighted average of an alpha signal. That could be a standardized score, an expected return, a spread measure like option-adjusted spread (OAS), or the output of a proprietary model. The optimizer then tilts the portfolio toward bonds with better scores, subject to whatever constraints are in place.

What's easy to miss is that position bounds are also a form of alpha expression. A bond your credit analyst has flagged as a "sell" can be capped at zero weight, and a high-conviction "buy" can be given a positive lower bound. This lets qualitative analyst views sit alongside a quantitative signal in the same optimization problem, without requiring any manual reconciliation afterward.

The most commonly constrained characteristics in credit strategies are effective duration, key rate durations, convexity, spread duration and duration times spread (DTS). Beyond the portfolio level, these can also be constrained at the sector, rating, and issuer levels. In practice, that means a single rebalancing problem can easily require satisfying hundreds of inequalities.

The right answer depends on the strategy. A strategy that wants most of its active risk to come from credit selection, not rates, will want tight bounds around benchmark duration at both the portfolio and sub-segment level. A more macro-oriented strategy might loosen those considerably. The key discipline is being explicit about which constraints are load bearing and which are just defaults that have never been revisited.

Both, in most cases. But recognize that they behave differently.

Characteristic constraints control exposures. A constraint on duration tells the optimizer how much interest rate sensitivity the portfolio can have, but comparatively little about the volatility of rates and how those rates correlate with other risk factors the portfolio may be exposed to. On the other hand, the relative simplicity of these constraints makes them quite attractive.

A factor risk model captures exposures, volatilities, and correlations simultaneously. A single tracking error constraint can therefore replace a cluster of characteristic constraints while also accounting for diversification effects that characteristic constraints ignore. For example, if US investment-grade (IG) and high-yield (HY) credit spreads are highly correlated, as they historically have been, a risk model will reflect the amplification effect of being long both simultaneously, whereas separate spread duration constraints would not.

In practice, the most effective setups use characteristic constraints for the risks the manager cares most about controlling explicitly (e.g. duration matching at the portfolio level), and a tracking error bound as a catch-all for everything else.

Again, there's no universal answer, but the question to ask is: how much active risk is the strategy designed to take and how much of that should come from factor exposures versus idiosyncratic (bond-specific) bets?

A useful calibration approach is to run the optimization at several tracking error levels and examine the decomposition of active risk at each. Most factor risk models will break tracking error into contributions from interest rate, credit, FX, and other factors alongside the idiosyncratic component. If the strategy is a credit selection strategy, you generally want the majority of active risk to be idiosyncratic. If the tracking error bound is so tight that the optimizer has no room to take meaningful active positions, you'll see this in both the decomposition and in the transfer coefficient.

A tracking error bound set too tight is one way to over-constrain the problem discussed above. More often, though, infeasibility comes from stacking characteristic constraints too aggressively. Fixed income optimization problems are particularly susceptible to this because the number of constraints tends to be high, especially in less liquid markets where position sizes are lumpy and the universe is large but not infinitely divisible.

A few diagnostics worth running: first, check whether any individual constraint is trivially infeasible given the investment universe (e.g. a minimum issuer weight that can't be satisfied because the bond is excluded on liquidity grounds). Second, look at whether multiple constraints are effectively saying the same thing. Tight KRD constraints at every tenor alongside a tight overall duration constraint, for instance, can be redundant in a way that collapses the feasible region without adding meaningful protection.

The structural fix is to identify which constraints are truly non-negotiable and soften the rest. Soft constraints allow the optimizer to violate a bound if the cost in objective terms is worth it, rather than treating every constraint as an absolute barrier.

Once the constraint set has been softened where it should be, confirm it's actually working as intended. Look at the constraint status report after each optimization. The key question for any given constraint is whether it is binding (the portfolio is sitting at the bound) or slack (the bound is not active). A constraint that is consistently slack across multiple rebalancing cycles is either too loose to influence the optimizer’s decision making or redundant given other constraints already in place. In either case, it merits further consideration.

The transfer coefficient is a useful complement to this. It measures the correlation between the constrained and unconstrained optimal portfolios. In other words, it measures how much the constraint set is impeding the manager's ability to fully translate their alpha signal into portfolio weights. A transfer coefficient well below 1 isn't necessarily cause for alarm, but it should prompt the question of whether the constraints driving the gap are intentional and justified.