Making the implicit explicit: A framework for the active-passive decision

29 June 2017 | Portfolio management


 Research brief  Research paper


The portfolio construction debate around active versus passive investments tends to focus on all-or-nothing views and recommendations. Vanguard believes that both active and passive investments have potential benefits in a portfolio. Passive funds offer low-cost efforts to track benchmarks, leading to a tight range of relative returns. Active funds offer the potential for outperformance, albeit with greater uncertainty (including the possibility of underperformance relative to a benchmark) and typically higher costs.

We created a quantitative framework for how to approach and evaluate a mix of active and passive investments.1 Such a combination could allow for both active's potential for outperformance and passive's low-cost benchmark tracking.

The active-passive decision framework

Vanguard sees talent, low costs and patience as the tenets of success in active management. Our active-passive decision framework considers four related variables.

  • Gross alpha expectation. Actual future alpha is uncertain, so the level of expected alpha is subjective. In our framework, "alpha expectation" carries a statistical meaning that acknowledges a distribution around the median and weighs the risk that active funds may underperform the benchmark.
  • Cost. Subtracting cost from the gross alpha expectation produces the net alpha expectation. Cost is thus an important factor in deciding which active fund to choose.
  • Active risk. An inconsistent pattern of relative returns can be quantified as active risk, or tracking error, the volatility of a fund relative to its benchmark. Active risk can be thought of as the uncertainty attached to a particular active manager. Compounded over time, it can lead to performance that differs substantially from the gross alpha expectation for a manager.
  • Active-risk tolerance. The trade-off between an investor's subjective alpha expectation and his or her subjective tolerance for downside risk is at the heart of the active-passive framework. The active-passive decision arises from balancing the two.

Where the active-passive allocation addresses the active risk-return trade-off, one can think of indexing as a diversifier of active manager risk. Figure 1 addresses how assumptions around each of the four variables might influence the active-passive mix.

Figure 1. Key decision factors and their impact on the active-passive mix

Figure 1. Key decision factors and their impact on the active-passive mix

Source: The Vanguard Group, Inc.

Our quantitative model

We move from a qualitative to a quantitative model, tailoring solutions to specific circumstances, by considering different levels of each factor shown in Figure 1. The first of three steps in such a move is simulating distributions of potential outcomes based on gross alpha expectations, cost and active risk. The second step is calculating manager risk and performance distribution. The third is assessing the trade-off between net alpha expectation and tolerance for active risk. Figure 2 illustrates the model at a high level. Our active-passive calculations are not an assessment of historical probabilities but, rather, a prospective framework for decision-making.

Figure 2. Active-passive decision flow chart

Figure 2. Active-passive decision flow chart

Source: The Vanguard Group, Inc.

Applying the framework: A case study

To demonstrate the quantitative approach in practice, we applied the four variables in our active-passive decision framework – gross alpha expectation, cost, active risk and active-risk tolerance – in the context of an investor determining a US equity allocation. Although we focus on one asset class, a similar approach could be applied to a wide range of asset classes.

To determine gross alpha expectation – the expectation of selecting outperforming active managers – we subdivided our simulation's population into five skill levels and calibrated them using historical data. We then applied three tranches of cost to determine net alpha expectations. Next we added three levels each of active risk and tolerance for active risk to assess how the combination influences the active-passive decision.

The model yields 135 combinations (5 gross alpha expectation levels x 3 cost levels x 3 active risk levels x 3 active-risk tolerance levels) to which active-passive allocation decisions can be applied. Figure 3 reflects 81 of the 135 combinations. The 54 combinations not shown result in all-index-fund allocations, just as the "neutral gross alpha expectation" combinations do; in each all-index case, the cost of active management overrides gross alpha expectations.

Figure 3. Potential active-passive allocations

Figure 3. Potential active-passive allocationst

Note: This hypothetical illustration does not represent any particular investment. Gross alpha expectation is based on mutual fund data calibrated to history. The active fund data was segmented into very high alpha (top one-third of active fund performance, gross alpha 1.54%), high alpha (top two-thirds, gross alpha 0.85%), neutral alpha (a full universe of active funds, gross alpha 0.16%), low alpha (bottom two-thirds, gross alpha negative –0.42%) and very low alpha (bottom one-third, gross alpha negative –1.28%). The active risk figures represent the median active risk of the associated tertiles of the active fund data. Application of active-risk tolerance uses a utility function with an embedded risk tolerance parameter. Cost levels used were higher cost (median asset-weighted expense ratio plus 0.40%, or 1.19%); moderate cost (median asset-weighted expense ratio of 0.79%); and lower cost (median asset-weighted expense ratio minus 0.40%, or 0.39%).

Source: Calculations by The Vanguard Group, Inc., based on data from Morningstar, Inc., and the Kenneth R. French data library.

Only scenarios where gross alpha expectations were high or very high warranted any allocation to active in the case study depicted in Figure 3. Even a neutral gross alpha expectation, which reflects the full universe of funds represented in the case study, resulted in an all-index portfolio recommendation (just as the not-shown low and very low gross alpha expectations do).

Even for investors with high and very high gross alpha expectations (the expectation that they will select among the top two-thirds or one-third of all active managers), indexing still makes up a sizeable portion of many allocations. Cost remains an influence, as does aversion to active risk. But active allocations predominate when higher assumptions for gross alpha are combined with lower assumptions for cost, active risk and active-risk aversion.


Our simulation analysis identifies three overall conclusions. First, indexing is a valuable starting point for all investors. A lack of conviction in identifying active manager talent leads to an all-indexing solution. Second, the use of active management depends on talent, cost and patience. Third, the array of outcomes for all investor types underscores index funds' ability to mitigate active risk and accommodate a range of investor risk preferences. The preferred trade-off between active and passive funds will vary from investor to investor; there is no one-size-fits-all mix.

1 Making the implicit explicit: A framework for the active-passive decision. Daniel W. Wallick; Brian R. Wimmer, CFA; Christos Tasopoulos; James Balsamo, CFA; and Joshua M. Hirt, The Vanguard Group, Inc., May 2017.

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