Tying Allocation to Selection: the Compound Portfolio Insurance approach Hamza BAHAJI1 Seeyond, Natixis Investment Managers & DRM Finance, University of Paris Dauphine
First draft: January 2015 This version: February 2018
Abstract: Reconciling Allocation and Selection decisions is one of the most challenging issues that stand in the way of core-satellite investing. One aspect lying behind this matter is the fair connection of the downside risk management devices within the core and the satellites. This paper aims to address this issue through Compound Portfolio Insurance (CPI), which is a new approach to core-satellite introduced here. CPI builds on the idea of dynamic core-satellite suggested by Amenc et al. [2004]. It consists in wrapping the core and the satellite in two compound portfolio insurance vehicles so that to nest the downside risk management device of the Selection process inside the one of the Allocation process. We show that CPI broadly outperforms the traditional tracking error-based approach out-of-sample in the US market over the period from 1995 to 2016. Specifically, our approach brings consistent improvements under successful Allocation and Selection decisions. It leads to higher synergy in the generation of alpha within the global portfolio.
Key words: Dynamic Core-Satellite, Allocation, Selection, Portfolio insurance. JEL classification : C60, G11, G24, L10.
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Seeyond, 59 Avenue Pierre-Mendès France, 75013 Paris. DRM Finance, Université Paris-Dauphine, PSL Research University- Mailing address: Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16 FRANCE - Tel: +33 (0) 1 78 40 36 33. Emails:
[email protected],
[email protected]. The author gratefully acknowledges Jean-Guillaume Mémin, Stephane Alloiteau and Alexis Flageollet for valuable comments.
1
Introduction Core-satellite approach to portfolio construction has featured prominently in institutional investment policies over the past decade (Mercer, 2016). Dynamic core-satellite investing breaks down into two processes: Allocation and Selectioni. Allocation is the strategic topdown process that consists in managing the global portfolio allocation between the core and the satellites. The core is mostly the passive component that tracks the benchmark and improves the efficiency of the portfolio. The satellites are the active components that aim to provide diversification and to generate out-performance. Selection is the tactical picking process that aims to bet on single values, sectors, styles or factors which are expected to outperform the related markets. It is mainly operated within the satellites’ asset classes and requires specialist skills (Fahmy, 2015). One of the overwhelming challenges facing core-satellite investing is the reconciliation of Allocation and Selection decisions. Part of this problem lies arguably in the difficulty of connecting the underlying downside risk management processes. A widely spread practice in this regard consists in using nested relative risk budgets which are usually expressed as tracking error targets (TE). As pointed out by Amenc et al. [2004], the exogenous nature of the TE as an allocation criterion leads to restricting the amounts allocated to the satellite in a symmetrical way which, therefore, comes at the cost of forgoing significant outperformance opportunities. This problem can obviously extend to the Selection process within the satellite. A tight Selection TE for instance can be restrictive and, consequently, can prevent potential Selection alpha from being channeled to the global portfolio even through an aggressive allocation (i.e. high exposure to the satellite). Put broadly, this issue restricts the transmission of outcomes from good Selection decisions on the long run. Consequently, Allocation and Selection decisions cannot interact effectively. This paper focuses on this issue and introduces
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a new approach that aims to better reconcile Allocation and Selection decisions within a dynamic core-satellite framework. The ineffectiveness issue of a TE-driven allocation has been addressed by Amenc et al. [2004, 2006] in the context of core-satellite. They have suggested an alternative allocation approach based on formalized risk budgeting with a view to endogenously addressing the downside risk. Their method can be viewed as a natural extension of Constant Proportion Portfolio Insurance (Black and Jones [1987], Perold and Sharpe [1988], Black and Perold [1992]) where the reserve asset is risky. Other authors, including Browne [2000], MantillaGarcia [2014] and Bahaji [2014], have further elaborated on this idea to address closelyrelated portfolio construction problems. Bahaji [2014] focuses for instance on the relevance of this relative portfolio insurance approach to benchmark-driven equity portfolio management. He has elaborated, from a theoretical perspective, on aspects covering riskreward profile, static replication and optimal setting. We build on the idea suggested in this literature to elaborate a new approach that aims to better tie Allocation and Selection together. We introduce the Compound Portfolio Insurance principle (CPI hereafter) which can be viewed as an extension of Constant Proportion Portfolio Insurance to a multi-asset class framework. We then show how it applies to the Allocation-Selection problem. We specifically outline the novel feature of the CPI process which is the “waterfall” asymmetric management of the downside risk. It mainly leads to a higher flexibility in managing relative downside risk and performance and, therefore, to a higher synergy in the generation of alpha within the global core-satellite portfolio. In order to assess the relevance and the robustness of the CPI approach we empirically compare its performance to that of the standard TE approach. Our analysis focuses on the US market over the period from January 1995 to August 2016 and considers most liquid equity and bonds ETFs as building block assets. It consists in forming competing model portfolios 3
based on each approach and then comparing their performance out-of-sample. To do that we introduce an analytical framework that allows to closely examine under several states of the world combining, on the one hand, ex-ante market views underlying the setup of each approaches and, on the other hand, ex-post performance scenarios of the Allocation and the Selection processes. Overall, our results show that the CPI approach broadly improves the performance of a traditional TE-based core-satellite asset allocation process. Specifically, under successful Selection decisions leading to an outperformance of the satellite, the CPI approach adds a strong and consistent improvement. However, our findings suggest that CPI outperforms under prior negative Allocation view only when Selection decisions turn out to be bad later. Moreover, the resilience of our approach to bad Selection decisions tends to vanish with more aggressive Allocation views. For instance, optimistic Allocation and Selection views implemented in CPI lead to a bad performance if the Selection process unexpectedly underperforms. This paper is organized as follows. The first section introduces the CPI approach, elaborates on its principals and shows how it applies to the Allocation-Selection issue within a dynamic core-satellite framework. In the second section we describe the design of the empirical analysis, present the results and discuss the findings. The last section concludes.
The traditional issue of Allocation and Selection Most institutional investment policies are bound by benchmarking processes which encompass some constraints based on either market indices or liability-consistent benchmarks. These investment constraints have fueled significant demand for dynamic coresatellite allocation approaches during the last decade, usually including implicit or explicit mandates to maximize the information ratio.
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Dynamic core-satellite investment breaks down into two processes: Allocation and Selection. Allocation is the mainstream process. It consists in managing the global portfolio allocation between the core and the satellites. The core is mostly the passive component that tracks the benchmark and improves the efficiency of the portfolio. The satellites are the active components that aim to provide diversification and to generate out-performance. Selection is the picking process that aims to bet on single values, sectors, styles or factors which are expected to outperform the related benchmark. It is mainly operated within the satellites’ asset classes and requires specialist skills. Both Allocation and Selection processes are bordered by risk budgets which are usually monitored by the CIO and/or the investment and risk committees. Widely used industry practices rely on deviation risk budgets that translate into TE targets. To be more specific, let us consider an illustrative case of a TE-driven core-satellite approach with a single satellite portfolio. Assume that the core is perfectly replicating the Allocation benchmark denoted by . Assume also that the satellite aims to beat a benchmarkii denoted by Selection process that leads to bets on asset S. Let’s denote by
and
through the respectively the
Allocation and the Selection target TEs. Then the global portfolio allocation at time t is as follows:
=1−
= 1−
= where against
× and
and
weights of the core
(1)
×
(2)
(3)
are the global portfolio and the satellite tracking errors assessed respectively at time t. , the satellite’s benchmark
,
) and
are respectively the
and the Selection asset (S).
5
As pointed out by Amenc et al. [2004], the TE-based approach described above relies on exogenous allocation criteria which consist in symmetrically managing relative risk. It therefore leads to disconnecting relative performance monitoring from downside risk management. For instance, restrictions on the amounts allocated to satellites resulting from tight Allocation TE constraints come at the cost of forgoing significant outperformance opportunities from good Selection processes. Tight Selection TE also penalizes an outperforming Selection in the satellite. Conversely, a good Allocation process cannot support a long-term outperforming Selection under restrictive Allocation TE targets. Those examples outline the drawbacksiii of the TE-based approach that ignores synergy benefits from tying together Allocation and Selection relative performance and downside risk management. In the following section we introduce a new approach that aims to address this issue.
The CPI approach Amenc et al. [2004, 2006] have suggested an alternative to the TE-based core-satellite framework. Their solution is a natural extension of CPPI which applies to portfolio relative performance insurance. It allows an endogenous control of relative downside risk that leads to an asymmetric management of the TE. The CPI idea we introduce here can be viewed as a generalization of this approach. It consists in compounding two portfolio insurance vehicles as illustrated in Exhibit 1. The main vehicle aims to endogenously managing the Allocation downside risk through an active rebalancing between the core and the satellite. It allows benefiting from “good” Allocation TE under outperforming satellite scenarios. The subvehicle wraps the satellite. Likewise, it aims to asymmetrically managing the Selection TE so as to make the satellite fully benefit from a good performance of the Selection process while endogenously maintaining the relative downside risk at a specific threshold. The originality of this approach mainly lies in two points. First, the relative downside risk limit of the Selection 6
process is encapsulated in the Allocation risk budget. Therefore, additional risk budget generated by a good Allocation process mechanically translates into extra risk budget in the satellite which provides more latitude to the Selection process. Conversely, a good Selection process can sustain to some extent a “trembling” Allocation process by offsetting the implied diminution of the global downside risk budget. Second, the “waterfall” setup of the CPI approach enables to connect the performance monitoring of the Allocation process to that of the Selection process. This feature leads to higher synergy in the generation of alpha in the global portfolio, specifically under scenarios of jointly outperforming Allocation and Selection processes. In the following subsections we further describe the CPI approach and illustrate the related advantages.
The arithmetic of CPI To be more explicit on the CPI mechanism, consider that the value of the global portfolio at time t is
. Let’s denote by
and
respectively the cushion and the floor of the
main portfolio insurance vehicle dedicated to managing the Allocation process such as: = 1− =
=
−
0
(4)
(5)
−
(6) and
are the
parameters driving the Allocation process. Specifically, the gearing parameter
acts as a
where
is the amount allocated to the core portfolio
,
cumulative loss limit set as a proportion of the total return of the Allocation benchmark. It 7
therefore allows monitoring the relative downside risk.
is the Allocation leverage
expressed as a multiplier of the Allocation cushion. It determines the amounts invested in the core and the satellite. As stated earlier, the Selection process is managed within an embedded insurance vehicle. In the same way, let’s denote by
and
the related cushion and
floor respectively such as: = 1− =
=
0 −
−
−
−
=
0
(7)
(8)
−
(9) (10)
is the amount invested in the satellite’s core
where
driving the Selection process. Identically, the gearing monitoring the Selection downside risk.
,
and
are the parameters
acts as a cumulative loss limit
is the investment multiplier determining the
amounts invested in the satellite’s core and the Selection asset (S) respectively. Alternatively to the TE-based global allocation stated in (1) to (3), the one implied by the CPI approach comes as follows: !
!
!
=1−
= =
" #
" # $
$
%" #
" # $
(11) (12)
(13)
CPI as a multi-asset dynamic portfolio insurance device 8
The CPI approach can be also displayed differently as a variable proportion portfolio insurance device with variable investment multipliers and where the excess return-generating asset is a portfolio (i.e. the satellite). To show that, let’s restate, after few straightforward developments, the amounts allocated to each asset in equations (6), (9) and (10) as follows: =
∗
=
(14) ∗
(15)
=
−
−
(16)
where: = ∗ ∗
=
=
(17)
−
'1 −
1−
/
)$
$
/
− 1−
∗
%+
* ,
(18)
(19)
The new formulation of the CPI asset allocation mechanism shows that the amounts invested in each asset are determined based on a single cushion and dynamic multipliers. The latter are path-dependent in the sense that they depend on the relative performance of the global portfolio with respect to the Allocation benchmark since inception. The historical simulationiv plot in Exhibit 2 illustrates these patterns. It mainly shows that the Selection multiplier in (18) increases with the global portfolio outperformance while the Allocation multiplier decreases accordingly.
A base case illustration
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In order to better illustrate the process underling the CPI approach, as compared with the TEbased one, let’s use a base case simulation framework based on a frictionless two-period economy with a time step ∆ . Under this economy, asset prices jointly move at each time
period according to three equally-probable scenarios: upward, flat or downward moves (i.e. a trinomial dynamic) such as: . /∆ = 0.
(20)
2 3√5∆ ; upward 0=1 1; flat %3√5∆ ; downward 2
(21)
where . is the asset price at time t, 0 is the move coefficient and B is the asset price return volatility. Consider in addition the following arbitrary setup: = 10%;
= 3%;
= 6%; B
= 5%; B
= 6;
= 4;
= 5%;
= 10%; B = 15%; ∆ = 0.0192 (i.e. a
weekly time step). We perform a comparative analysis of both approaches under the 36 joint asset price scenarios generated under the framework above. Each scenario results from a random combination of the three asset price move scenarios (i.e. up, flat and down) over the two-time step period assuming draws without replacement at each period. We aggregate these scenarios in four homogenous groups. Each group is formed according to states of joint performance of the Selection and the Allocation processes (see table 1). For instance, the good Allocation (+) and bad Selection (-) group includes all joint asset price scenarios where the core of the satellite outperforms both the Allocation benchmark and the Selection asset (i.e.
L and
>L>
>
>
). The analysis then consists in comparing the average performance
generated by each approach under each group of scenarios.
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The results of this comparative analysis are reported in Table 2. Broadly, CPI records higher performance than the TE-based approach. Specifically, under the best case scenarios of outperforming Allocation and Selection CPI delivers significantly higher average return, while it generates comparable performance under the worst case scenarios of underperforming Allocation and Selection. In other words, the asymmetric management of deviation from the benchmark allows better aligning the Allocation process on the Selection one under the CPI approach. Overall, it provides comparable protection against bad Allocation and Selection decisions while allowing to better benefit from good ones.
How to set CPI? Indeed CPI grants more flexibility than the TE-based approach. However, as a systematic portfolio strategy, its relative performance still depends on its setup. Let’s focus first on the gearing parameters which determine the risk budget and the maximum tolerated underperformance. Beyond the degree of risk tolerance and the assessment of relative downside risk, these parameters should be set based on a risk budgeting exercise that broadly considers expectations on the qualityv of Allocation and Selection. This exercise boils down to assessing the likelihood of each of the main performance scenarios in Table 1 and then calibrating the CPI process accordingly. Furthermore, the same rational should apply to the calibration of the investment multipliers which have to reflect views on the outperformance generating assets and, therefore, the resulting exposures to those assets. A CIO may for instance authorize a range of multiplier values denoting the confidence he has in the potential of the Allocation and the Selection processes to outperform. As a matter of example, figures of the base case illustration are updated in Table 3 using an in-sample adaptive setup under each group of scenarios. For instance, tighter downside risk limits under both bad Allocation
11
and bad Selection scenarios lead to a significant improvement of the relative performance of CPI. Outperformance also improves under positive scenarios when larger gearings are used. Further, the CPI approach can also be set in such a way that reconciles it with the TE-based approach. Using relative portfolio insurance principles, Bahaji et al. [2015] show for instance how a standard TE-driven strategy can be merely adjusted in order to overcome the underlying symmetry issue. By applying the same reasoning, the CPI device can be set based on variable multipliers which depend on target tracking errors as follows: M
M
=
(22)
=
(23)
This adjustment adds a new relative risk control constraint to the global portfolio allocation under CPI and, therefore, leads to a unified approach.
Does CPI better address the Allocation-Selection issue? Research design In this section we compare the performance of the CPI approach and the TE-based approach under several ex-ante market views (i.e. what the processes had expected to deliver) combined with ex-post performance scenarios of the Allocation and the Selection processes (i.e. what they have actually delivered). Our methodological approach aims to comprehensively and reasonably represent a standard dynamic core-satellite allocation framework with merely assembled Allocation and Selection processes. Thus, we restrict ourselves to an investment universe with two traditional asset classes, namely stocks and bonds. Specifically, we assume a standard Allocation process 12
where the core portfolio is allocated to bonds while the satellite is invested in stocks. Moreover, we assume that the Selection process operated within the satellite aims to beat the broad equity market through a systematic style rotation strategy. We consider 3 standard styles: namely value, growth and defensive. The process consists then in ranking 3 related style indices based on their performance over the previous month, then allocating 70% to the top, 25% to the median and 5% to the bottom style indexvi. This strategy can be alternatively viewed as a naïve style momentum strategy. Note here that we implicitly assume that the Selection and the Allocation processes have no predictive ability in the sense that they fully rely on the historical asset returns patterns in formulating investment decisions. Our analyses focus on the US market since it offers a more relevant research ground due to the availability of larger historical asset price time series. We first assume that the Allocation and the Selection benchmarks are represented by the ICE US Treasury 7-10 year Total Return Index
and the S&P 500 Total Return Index
respectively, and consider the following
style indices as underlying assets of the Selection process described previously: Russell 1000 Growth Total Return Index (growth stocks), Russell 1000 Value Total Return Index (value stocks) and MSCI US Minimum volatility Total Return Index (defensive stocks). The main argument behind this choice is the availability of large and liquid ETFs tracking those indices. We then rely on ETF price data in implementing the core-satellite portfolios instead of price data of the underlying indices. We specifically use monthly ETF price returns series over the period from January 1995 to August 2016 from Bloomberg database. Table 4 provides descriptive statistics of this returns data.
The setup of the asset allocation device and the resulting calibration of the risk budget are important components of the global portfolio construction process. This is why investigating the relative performance of CPI under several setups is crucial to the consistency and 13
robustness of the analyses. Furthermore, in order to gauge the resilience of the CPI approach to unexpected market scenarios (i.e. positive views followed by negative investment outcomes), one has to set the underlying processes based on ex-ante market scenarios, as expressed by views representing what the processes were expected to deliver (which translate into risk budgets), then assess their performance based on what they have actually delivered. So we assume that the Allocation and the Selection processes are both set according to 3 exante market views formulated by the CIO or the portfolio managers who are supposed to have no prediction abilities: namely negative, conservative and positive views. When combined together those views lead to 9 portfolio positioning scenarios corresponding each to a specific target global allocation. Consistently, the setup of the Allocation and the Selection processes under each approach is made in such way that meets those target allocationsvii. Negative views for instance imply tighter relative risk budgets leading to narrower TEs under the TEbased approach and lower gearings and multipliers under the CPI approach (see table 5). To be more explicit let’s take the case of the setup scenario under the positive views in table 5. A positive view on the satellite (i.e. allocator’s view) leads to a target allocation of 60% to the core
and 40% to the satellite, which requires setting the target Allocation TE at N =
5.6%. On the other hand, a positive view on the Selection asset (i.e. picker’s view) results in a target asset allocation of 40% to the core of the satellite
and 60% to the Selection asset
(S). In this case the target Selection TE should be set at N = 1.5%. Combined together, those views imply a target global allocation of 60% to
, 16% to
and 24% to S, which is
consistent, on the other hand, with the following setup of the CPI approach:
6;
= 10%;
= 10%.
= 4;
=
We use the methodology discussed above to form two competing portfolios under each scenario in table 5: one is formed based on the TE approach, the other relies on the CPI 14
approach. Recall that both portfolios have a similar starting global allocation. We apply a monthly rebalancing. TEs are estimated based on the annualized standard deviation of monthly excess returns over the 12-month period prior to the date of rebalancing. Moreover, we assume that the management of the portfolios is subject to frictions. These are mainly comprised of transaction (i.e. brokerage) commissions associated to the ETFs tracking the benchmarks considered. Average transaction commissions are set at 0.10% per traded dollarviii. Finally, we perform an out-of-sample comparative analysis of portfolios performance over 3-year sliding historical periods. To be more specific, the performance of the portfolios set at a given time point (within the historical period covered in the sample) is assessed over the subsequent 3-year period. Each of those periods is considered as a historical scenario in the sample. Results and discussion Table 6 reports descriptive statistics of the performance of the Selection process. It mainly shows that the underlying style rotation strategy exhibits a negative skewness in that gains from scenarios of outperformance (+), although slightly more frequent, tend to be offset on average by extreme losses under some underperformance scenarios (-). Overall, the process yields a neutral performance with a barely positive average return and an immaterial information ratio. Those features are relevant to our comparative analysis for mainly two reasons. First, extreme drawdowns in the Selection strategy allow comparing the robustness of the downside risk management device of each approach. Second, potential biases due to sample representativeness are avoided thanks to the neutrality of the average performance of the strategy. A predominance of outperformance scenarios for example would’ve been, by construction, favorable to the CPI approach.
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Table 7 provides comparative statistics of the performance of both approaches under the setups described earlier (see table 5). The figures show that the CPI portfolios have significantly higher returns on average compared to the TE-based ones. They bear however significantly higher realized TE which penalizes their information ratios. The latter are still, in spite of that, slightly above those of the other competing portfolios. The CPI portfolios also display significantly higher turnover. The active management of the downside risk under the CPI approach is therefore more costly, specifically under “optimistic” setups. It follows that the implementation of this approach in a low-liquidity market environment, for instance, would be very challenging with regards to the turnover matter. Moreover, as expected, positive setups are the most favorable to the CPI portfolios, in particular the one combining positive views of both Allocation and Selection. More specifically, the higher risk budgets along with the aggressive investment multipliers implied by those views leave more room for the CPI approach to benefit from outperformance scenarios of the satellite. In the same vein, tighter relative risk budgets and reduced investment leverage under negative views, implying cautious target allocation profiles, reduce substantially the turnover and the realized TE of the CPI portfolios which still outperform on average. For instance, under the setups resulting from a negative view of the Allocation process, those portfolios outperform the TE-based ones and have comparable turnovers and realized TEs. This preliminary result suggests that the CPI approach provides, on average, a protection against the relative downside risk as effectively as the TE-based approach. This protection doesn’t come at zero cost however. Severe and frequent relative drawdowns may trigger the stop-loss device embedded in the CPI structure (i.e. cushions ran out) and, therefore, exit the strategy. Although the setups assumed in our analyses lead to no exit scenario, one should apprehend exit as a specific risk that can potentially materialize in a CPI portfolio. 16
The analysis reported in Exhibit 3 compares the performance of the simulated portfolios under another perspective. It consists in breaking down the sample generated under each setup into 4 subsamples. Each of these represents one of the 4 scenarios of joint performance of Allocation and Selection as described earlier in table 1. The main benefit of this framework is allowing a comparison of the competing approaches under several states combining ex ante views underlying the setup of the Allocation and the Selection processes with their subsequent (ex post) performance configurations. The outputs of the analysis are represented in a grid comprised of 36 scores. The latter are based on t-statistics of the spreads between the portfolios excess returns under each scenario. The statistical significance is highlighted with a color contrast strip as described in the legend of Exhibit 3. The darker the scenario cell in the grid, the more significant is the underperformance of the CPI portfolio and the poorer the relative performance of the approach. Conversely, the brighter the cell the more significant is the performance of the CPI approach. For sake of clarity, we develop an aggregate metric that broadly gauges the relative performance of CPI across all scenarios in this grid. It therefore provides to some extent an assessment of the overall improvement the CPI approach adds to the core-satellite process. We will refer to this metric as the “Improvement Ratio”: U,V OP," = ∑PSY+ RS ∑" XY+ W"
T
ZS,X
3; _ ` S,X > 0 `ab Rc`de2S,X ≤ 1% ^ 2; _ ` S,X > 0 `ab 1% < Rc`de2S,X ≤ 5% \ \ ⋮ = 0; Rc`de2S,X > 10% ] \ ⋮ \ −3; _ ` S,X < 0 `ab Rc`de2S,X ≤ 1% [
(24)
(25)
where a = 4 is the number of joint performance scenarios (see table 1), and RS the historical probability of scenario i determined from the sample;
= 9 is the number of setups; ZS,X is a
dummy variable corresponding to the level of performance of CPI under scenario (i,j). It
17
ranges from -3 to +3 according to the p-value/t-statistic value scale given in the legend of Exhibit 3.
As we can see from the formula in (24) above, the Improvement Ratio may interpret as a weighted average of dummy variables ranging from -3 to +3 depending on the value and the significance of the corresponding t-statistic in the grid. The ratio is normalized in the sense that it ranges from -100% to +100%; the higher the value, the better the relative performance of the CPI approach. A +100% means that CPI outperforms under all scenarios. Conversely, 100% means that CPI has lessen the performance of the core-satellite process in all cases. The reported results beg several comments. First, the resulting empirical Improvement Ratio of 37.9% is significantix at the 1% level. This means that, empirically, the CPI approach significantly improves the performance of a traditional TE-based core-satellite asset allocation process. As expected, under outperformance scenarios of the satellite, and specifically those with successful Selection decisions (see cells representing (+,+) scenarios), the CPI approach adds a strong and consistent improvement. However, when Selection decisions turn out to be wrong (see cell with (+,-)), our approach only outperforms under tight Allocation risk budget setups (i.e. negative Allocation view). In such cases the good performance of the satellite allows to better resorb the underperformance of the Selection process. The more conservative the Allocation view, the better the resilience of the CPI approach to bad Selection outcomes. This finding conveys one of the key features of the CPI device outlined earlier in this paper which is the asymmetric management of relative risk budget allowing a better sustainability of the Selection process. Furthermore, resilience to bad Selection decisions tends to vanish, however, with more aggressive Allocation views. Both optimistic Allocation and Selection views, for instance, lead to a bad performance of CPI if the Selection process unexpectedly underdelivers (see the (+,-) scenario). Last but not least, 18
scenarios where both Allocation and Selection underperform (i.e. (-,-)), specifically when the underperformance is unexpected (i.e. positive views and negative outcomes), show a significant underperformance of CPI. It follows that our approach may have lower resilience to joint bad scenarios than the standard TE-based approach. This finding is to be tempered, however, in the sense that underperformance is in lower depth in this case than the outperformance generated under other scenarios and specifically favorable ones as outlined before.
Conclusion The performance of a core-satellite portfolio depends on how the inner Allocation and Selection processes fit together. One may think of reconciling them by tying together the underlying downside risk control devices. This is the idea developed in this paper. The contributions therein are twofold. First, we introduce CPT, a new approach to dynamic coresatellite investing elaborated from relative portfolio insurance principles as suggested in a previous literature. We mainly show that CPT allows better flexibility in managing relative downside risk and performance and, therefore, leads to higher synergy in the generation of excess returns in the global portfolio. Second, we suggest a general analytical framework to assess the relative performance of a benchmarked investment strategy. The empirical findings from this framework show that CPT has broadly outperformed the traditional TE-based approach on the long run in the US market. This study bears some limitations that should be outlined. As previously mentioned, the major drawback of CPT is the high amount of turnover it generates, which makes it hardly implementable to asset classes with questionable liquidity. Adding constraints based on rotation control devices or tighter re-allocation time scales are potential solutions to be investigated in this regard. Other practical implementation aspects should be also revisited, 19
including for instance exposure and leverage limits. Adding such constraints may affect the performance profile of the CPT approach. We leave those issues to future investigations.
References Amenc, Noel, Philippe Malaise, and Lionel Martellini. 2004. “Revisiting core satellite investing.” The Journal of Portfolio Management 31, no.1: 64−75. Amenc, Noel, Philippe Malaise, and Lionel Martellini. 2006. “From delivering to packaging of alpha.” The Journal of Portfolio Management 32, no.2: 90−98. Bahaji, Hamza. 2014. “Equity portfolio insurance against a benchmark: setting, replication and optimality.” Economic Modelling 40: 382–391. https://doi.org/10.1016/ j.econmod.2013.11.031 Bahaji, Hamza, Emmanuel Bourdeix, and Stephanie Ridon. 2015. “Expanding the benchmarked equity portfolio management paradigm.” Insurance Risk Magazine, January, 2015. Black, Fischer and Robert W. Jones. 1987. “Simplifying portfolio insurance.” The Journal of Portfolio Management 14, no.1: 48−51. Black, Fischer and André F. Perold. 1992. “Theory of constant proportion portfolio insurance.” Journal of Economic Dynamics and Control 16: 403-426. https: //doi.org/ 10.1016/0165-1889(92)90043-E Browne, Sid. 2000. “Risk-constrained dynamic active portfolio management.” Management Science 46, no.9: 1188–1199. Fahmy, Hany. 2015. “Asset Allocation and Security Selection in Theory & in Practice: A Literature Survey from a Practitioner’s Perspective.” Applied Finance and Accounting 1, no.2: 10−37. Giese, Guido. 2012. “Optimal design of volatility-driven algo-alpha trading strategies.” Risk 25, no.6: 68−73. Perold, André F. and William, Sharpe. 1988. “Dynamic strategies for asset allocation.” Financial Analysts Journal 51, no.1: 149−160. Mercer. 2016. “European Asset Allocation Survey.” https://www.uk.mercer.com/ourthinking/2016-european-asset-allocation-survey.html.
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Appendix Exhibit 1: Dynamic core-satellite CPI process
Allocation cushion (Ca)
Step-3: Terminal CPI allocation
Step-2: Selection setup
Satellite
Setp-1: Allocation setup
Selection cushion (Cs)
Selection asset (S)
Selection floor (Fs)
Allocation floor (Fa)
Core portfolio
Bs = Ca x ma -S
Selection benchmark (Bs)
Allocation benchmark (Ba)
Allocation benchmark (Ba)
Ba=Fa +Ca x(1- ma ) ma: allocation multiple
ms: selection multiple
Exhibit 2: Historical illustration of CPI dynamic investment multipliers.
21
Exhibit 3: Comparative performance scorecard of CPI and TE-based approaches. Notes: Scores in the grid are t-statistics of the spreads between CPI and TE portfolios excess returns. Significance is highlighted according to the color scheme in the legend.
Table 1. Scenarios representing the joint performance of Allocation and Selection. Allocation
+
>
Selection
L> > >L>
-
-
>L
+ L>
>
> >L >L>
Notes: “A>B” indicates that asset A outperforms asset B.
Table 2. Average excess-returns of simulated TE and CPI core-satellite approaches.
-
Selection
+
Allocation
-
+
CPI
-0.33%
1.26%
TE
-0.33%
0.87%
CPI-TE
0.00% (0.00)
0.39%* (1.55)
CPI
-0.81%
0.10%
TE
-0.88%
0.26%
0.07% -0.16% CPI-TE (0.29) (-0.69) Notes: = 6; = 4; = 5%; = 10%; N = 3%; N = 6%; t-statistics are in parentheses. “*”, “**” and “***” indicate significance at the 10%, the 5% and the 1% level respectively.
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Table 3. Average excess-returns of simulated in-sample adaptive CPI approach.
+ (αa = 20%)
+
(αs = 10%)
-0.17%
5.06%
-
-0.25%
1.99%
Selection
(αa = 2.5%)
(αs = 2.5%)
Allocation
Notes: = 6; = 4; αa and αs are set based on the expected performance of the Allocation and the Selection processes respectively.
Table 4. Data sample descriptive statistics. Mean Std. Dev. Skewness Ex Kurtosis Correlations Core Bonds Core Stocks Growth Stocks Value Stocks Defensive Stocks
Core Bonds 0.38% 1.97% 0.185 2.204
Core Stocks 0.75% 4.36% -0.858 1.675
Growth Stocks 0.70% 5.01% -0.914 1.795
Value Stocks 0.78% 4.34% -0.975 2.612
Defensive Stocks 0.81% 3.39% -0.896 2.252
1.000 -0.212 -0.209 -0.206 -0.088
1.000 0.952 0.941 0.926
1.000 0.802 0.824
1.000 0.934
1.000
Table 5. Setup of CPI and TE-based devices. Allocation Conservative
N = 1.45% TA: 90-10
N = 3.50% TA: 75-25
Negative
N = 1.5% TA: 40-60
Selection
Positive
N = 1% TA: 60-40
Conservative
CPI parameters TA
90-4-6
CPI parameters TA
ma
2
αa ms
N = 5.60% TA: 60-40
Positive
75-10-15
CPI parameters TA
60-16-24
ma
3.53
ma
4
5%
αa
7%
αa
10%
6
ms
6
ms
6
Setup
Setup
Setup
αs
10%
αs
10%
αs
10%
TA
90-6-4
TA
75-15-10
TA
60-24-16
ma
2
ma
3.53
ma
4
αa
5%
αa
7%
αa
10%
ms
5.1
ms
5.5
ms
5.72
αs
7%
αs
7%
αs
7%
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TA N = 0.5% TA: 80-20
Negative
90-8-2
TA
75-20-5
TA
60-32-8
ma
2
ma
3.53
ma
4
αa
5%
αa
7%
αa
10%
ms
4
ms
4
ms
4
αs
5%
αs
5%
αs
5%
TA: Target asset allocation.
Table 6. Descriptive statistics of the Selection process performance.
Annual Turnover Frequency Max Annualized Ex Return Average Annualized Ex Return Min Annualized Ex Return Information Ratio N/A: not applicable
Overall 36%
+ N/A
N/A
100%
51.38%
48.62%
338.40%
338.40%
-0.19%
0.79%
38.08%
-28.28%
-84.77%
0.05%
-84.73%
0.059
4.76
-3.48
Table 7. Performance analysis of CPI and TE-based approaches. Allocation Negative TE
Positive
Annualized Ex-Return
Information Ratio Exit Frequency
Conservative
Annualized Ex-Return
0.80%
Conservative TE CPI 1.43%
0.19%* (1.629) 1.61%
2.06%
Positive TE 2.21%
0.63%** (2.045) 1.92%
3.90%
0.38
0.42
N/A
0.00%
CPI 3.05% 0.84%** (1.704)
5.34%
6.24%
8.60%
0.37
0.39
0.35
0.35
N/A
0.00%
N/A
0.00%
0.32
0.75
0.60
3.41
1.38
5.96
0.58%
0.74%
1.37%
2.05%
2.12%
3.03%
0.16%* (1.309)
0.68%** (2.166)
0.91%** (1.842)
Tracking Error
1.63%
1.89%
3.93%
5.31%
6.30%
8.56%
Information Ratio
0.36
0.39
0.35
0.39
0.34
0.35
Exit Frequency
N/A
0.00%
N/A
0.00%
N/A
0.00%
Annual Turnover
0.30
0.63
0.53
3.27
0.81
5.85
0.69%
1.32%
1.92%
2.03%
Annualized Ex-Return
Negative
Selection
0.61%
Tracking Error
Annual Turnover
CPI
0.56% 0.13% (1.059)
Tracking Error
1.65%
Information Ratio Exit Frequency
0.60%** (1.956) 1.88%
3.98%
0.34
0.37
N/A
0.00%
2.86% 0.83%** (1.698)
5.20%
6.37%
8.41%
0.33
0.37
0.32
0.34
N/A
0.00%
N/A
0.00%
Annual Turnover 0.28 0.50 0.48 2.60 0.73 4.75 Notes: Figures in italic are the spreads between CPI and TE excess returns and those in parentheses are the related t-statistics. “*”, “**” and “***” indicate significance at the 10%, the 5% and the 1% level respectively. N/A means that the statistic is not applicable.
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i
To avoid confusion, uppercase letters will be used to designate “Allocation” and “Selection” as the portfolio construction processes comprising the core-satellite approach. ii Satellites are usually assimilated to high-alpha portfolios pursuing absolute performance strategies, like hedge funds. Even if those portfolios are not explicitly benchmarked, in practice their target performance is compared to a benchmark representing the asset class they operate in (e.g. equity, credit indexes), the type of their strategies (e.g. hedge funds indices) or the risk-free asset (e.g. a money market index). iii The structural issues of the TE-based approach are further depicted by Bahaji et al. [2015]. iv Historical simulations performed over the period from January 1995 to August 2016 based on the following assumptions: := “ICE US Treasury 7-10 year TR Index”; := “S&P 500 TR Index”; S:= “Style rotation strategy described in §3”; = = 2; = = 10%; 0 = 0 = 0 = S(0) =100. v The skills and the track records of the global allocators and the satellite managers are for instance relevant assessment criteria in this regard. vi The subsequent empirical results are robust with respect to this setup. The author can provide robustness analyses based on alternative setups upon request. vii For seek of comparability both approaches are set in order to yield the same starting global allocation as reported in table 5. Note also that those target allocations correspond to standard profiles usually seen in practice. viii We consider these assumptions to be roughly conservative given the actually practiced fee level in the ETFs market. ix Roughly assuming that ZS,X are i.i.d and follow a Normal distribution, then OP," follows a Normal distribution i with zero mean and a variance ∑PSY+ RS5 . j"
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