The reputation of full-blown active portfolio management waned during the 1970s: the reliance on the manager’s gut feeling proved too narrow and insecure a basis to build consistent performance on. Furthermore, the sponsors wanted to exert a stricter risk control on their fund managers.
There are several reasons for considering passive management, including excellent diversification and predictable behaviour, straightforward assessment of the portfolio management, lower management fees and transaction costs which make passive management competitive with respect to an active stance, and its consistent relative performance.
Pure passive management consists of selecting and managing a portfolio that tracks the performance of a particular index portfolio by duplicating some or possibly all of the index’ characteristics (composition, average coupon, average maturity and so on). It is obvious that the choice of a benchmark index is of paramount importance in this investment strategy. Remarkably enough, this step is often overlooked.
A sponsor should use the index that is best suited to their risk/return profile. A ‘good’ index should reflect these considerations:
o It should provide a comprehensive picture of the markets that are relevant to the underlying investment.
o Since the benchmark will be used to measure the performance of the management, it should be replicable, or ‘fair’.
o The index should be stable, that is the periodical revision to update the benchmark to the broad market it represents should not happen unpredictably or too often.
o The defining rules concerning inclusion of market segments and individual issues, pricing and return calculation, reinvestment methodology, expenses and so on, should be clear in advance and easily understood.
It may seem strange that, given the fact that outstanding fixed income value largely exceeds combined equity value, bond indices and their use are very much younger than equity indices: the first bond indices and index funds were not developed until the 1970s. A possible reason may be the difficulty in building and maintaining a bond index. The universe is much broader and more diverse than in the case of stocks, and this universe changes constantly. In addition, pricing is a notorious problem in fixed income, and price volatility - important for bonds with embedded options – varies widely across issues and over time.
Once the sponsor has defined an investment policy and has chosen a representative benchmark index, the manager can set up the portfolio.
First, a detailed analysis of the index is made in terms of the relevant risk factors: overall statistics like average maturity or coupon will not suffice to the portfolio manager when trying to replicate the index. He will need to partition the index in segments or cells with respect to term structure, quality, sectors, currency, cash flow distribution, and so on. The aim is then to match the allocation per segment between the portfolio and the benchmark. Any divergence between the characteristics of portfolio and benchmark can lead to return difference.

We thus come the second task of the manager: to quantify the contribution of a cell mismatch to the overall return and risk. These are not necessarily equal: the largest mismatches do not implicitely lead to the largest return difference nor do they necessarily carry the most risk. There might be correlations among the mismatches in the various risk factors. The goal is to identify a number of ‘key’ risk factors, such as duration.
Finally, the portfolio is constructed. In most cases, the number of issues in the portfolio will be (much) smaller than the number of index issues. There exist several methods to select the portfolio among the benchmark issues; we list a few:
o Stratified sampling. The index allocations to each are matched by a small number of liquid issues. Normally the benchmark duration or additional risk factors of the cell are targeted in the selection. This procedure is simple and flexible, yet labour-intensive.
o Linear programming. This is a more quantitative extension of the previous method. It applies a constrained optimisation algorithm over a specified universe from which issues can be selected. The objective function can be of various nature: a yield measure, transaction cost, expected total return. Its extremum value should correspond to a minimal tracking error. The constraints fulfil multiple purposes: first, they implement the cell partitioning and the aggregate characteristics of the benchmark but additional constraints can arise from diversification or other concerns that would enhance the replication.
o Variance minimisation. This is a quadratic optimisation method that maximises utility, defined as the difference between expected return and risk.
o Gradient descent. This method ranks all issues from a specified universe by the sensitivity of the tracking error to a change in the issue position.
o Scenario analysis. In this method, the portfolio is optimised as before, but now with respect to the deviation from the benchmark in a number of possible scenarios.
Every time the benchmark index is updated, a similar procedure is needed to rebalance the portfolio to the new index composition. A no-trade zone should be considered around the exact figure in which no rebalancing transactions occur; an issue that has wandered outside of this no-trade zone, should be rebalanced but not to the new benchmark weight but to the relevant frontier of the no-trade zone.
As was noted before, the benchmark does not incur any transaction costs due to the management nor any other deductable expenses – custody fees, taxes among others. Pure passive management will then necessarily result in a tracking error due to these expenses.
Enhanced passive management of a fixed income portfolio allows for mismatches in risk factors like sector weights, credit quality weights, cash flow distribution or call exposure to achieve higher returns that could compensate for the implicit tracking error of passive management. This introduces market view, yet it is still called passive management, since no bets are taken against ‘key’ risk factors; in particular, total portfolio duration remains exactly equal to the benchmark duration.
Instead of trying to replicate the index, enhanced management aims at replicating the return of the index. When the management becomes less and less passive, it is clear that both risk and expected return increase, and thereby the management fee.
However, the portfolio was constructed, managed and rebalanced, in the end one needs to compare its return relative to the benchmark. Two approaches exist: return attribution and performance attribution.
Return attribution breaks down the return of each individual issue with respect to the market influences encountered, for example yield curve movement, spread changes or interest accrual. Strictly speaking, no reference benchmark is needed for return attribution.
Performance attribution seeks to analyse the return differences between index and portfolio, due to allocation mismatches in the various cells (maturity cells, sector cells, quality cells etc).
Even with these quantitative tools in hand, it remains a delicate matter to evaluate the manager of the portfolio. We mention but a few pitfalls:
o As was mentioned before, a manager’s strategy can only stand trial before the relevant index. Furthermore, the return and performance attribution must of course adhere to the same methodology as is used by the benchmark.
o Before comparing with the benchmark figures, portfolio returns always need to be adjusted for pricing discrepancies among sources and deductable expenses. Transaction costs however, form part of the management and must be included in the evaluation.
o Beware of interpreting historical performance data. Even in the active management case, one would need several decades of data to unambiguously decide whether a consistent performance comes from skill or luck! On average, too recent data over too short a period is extrapolated too far in the future.
There is a tendency among sponsors and managers alike, towards a more nuanced assessment of performance, instead of the sole simple return figure. A more complete picture of the investment process has emerged involving the risk taken corresponding to the return earned.

Recent years have seen a shift from ‘risk awareness’ to a more active stance of ‘risk control’, and this evolution will assuredly continue.
Risk measurement is not the same as risk management. Risk measurement quantifies the risk in a portfolio at a given time instant; risk management tries to determine a dynamic risk strategy in line with the investment objectives.
Two questions need to be answered in risk measurement: what are the relevant sources of risk to our portfolio, and how do we measure this risk?
A risk measure tries to capture how data move through time. It characterises the fitted statistical distribution of the data series. Standard measures for risk are volatility, value at risk and expected tail loss.
Volatility seems the most relevant to passive portfolio management. The issue is to come up with a correct volatility measure.
Suppose a valid framework is set up in which the portfolio risk can be measured, the sponsor’s risk/return profile can then be restated in terms of appropriate risk measures, and his objectives will lead to a risk target for the manager. This risk target can then be managed in a way similar to the (dynamic) management of the performance or return targets we discussed in the previous sections. Ongoing research tends to indicate that risk management should be enhanced.
Bond portfolio management, like all asset management, tends to become more and more process-driven: verifiable, transparant, rational and consistent. Quantitative tools have become crucial in the course of the entire investment process: from determining an investment policy, setting the objectives, to the actual management, and reporting back to the sponsor and the regulator. This evolution will assuredly continue in view of the more difficult times ahead.
Koen Van Der Borght is chief investment officer and Karel Volckaert is quantitative analyst at Bank Corluy-Effectenbankiers in Antwerp