- Email: [email protected]
The compensation portfolio
Accepted Manuscript
The Compensation Portfolio Philippe Rohner, Matthias W. Uhl PII: DOI: Reference:
S1544-6123(17)30529-9 10.1016/j.frl.2018.02.023 FRL 876
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
1 September 2017 8 December 2017 22 February 2018
Please cite this article as: Philippe Rohner, Matthias W. Uhl, The Compensation Portfolio, Finance Research Letters (2018), doi: 10.1016/j.frl.2018.02.023
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Highlights • We show how to optimize both for risk and for asset allocation • optimization of individual goals possible
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• Introduction of novel concept of compensation portfolio
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• Bridging Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT)
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Philippe Rohner∗ Matthias W. Uhl† December 2017
Abstract
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The Compensation Portfolio
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We successfully show that it is possible to optimize both for risk and for asset allocation without compromising the optimization of individual goals by introducing the novel concept of a compensation portfolio. Therefore, we solve for the global vs. local optimization paradox by bridging Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT).
Keywords: Optimization, goal-based investing, compensation portfolio Classification: G11, G40, G41
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∗ University of Zurich, Department of Banking and Finance, Plattenstr. Zurich, [email protected] † University of Zurich, Department of Banking and Finance, Plattenstr. Zurich, [email protected]
2
32, CH-8032 32, CH-8032
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1. Portfolio Optimization and Goal-based Invest-
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ing Clients and investment advisors are often confronted with a paradox when they attempt to optimize across their holistic asset allocation and their individ-
ual portfolios: it does not add up. Whether one optimizes a specific portfolio first, and then the next, and so on, or whether one optimizes globally first usually leads to the one inefficiency or the other. The issue typically arises because
AN US
clients need to change risk profiles (and therefore asset allocations) of individual portfolios if they want to optimize across their portfolios holistically. However, breaking up single portfolios usually leads to increased costs, sub-optimal allo-
cations, or not achieving a particular investment goal. In this paper, we attempt to solve this paradox by introducing the so-called compensation portfolio.
M
When Sharpe (1981) introduced the concept of decentralized investment management, the goal was to find a framework how a decentralized manager
ED
can be incentivized to balance a second (passive) portfolio such that the overall portfolio is optimal. Elton and Gruber (2004) extend this idea to multiple decentralized managers. Although these approaches provide valuable insights on
PT
decentralized investment management, they do not directly address behavioral concepts of investing. A key difference to this strand of literature is that our ap-
CE
proach assumes that decentralized managers act independently from each other. Thaler (1985) introduced the concept of mental accounting, which opened a new
AC
stream of literature in the realm of behavioral finance: goal-based investing was born. With the introduction of goal-based investing, a new variable was brought into the equation. However, the equation is still not entirely solved until today, as ample evidence in the literature shows. For instance, a two-step optimization process can result in diversification inefficiencies, as Van Binsbergen et al (2008)
3
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show. Furthermore, Brunel (2006) notes that optimizing one way (traditional) or the other (goal-based behavioral) leads to some form of sub-optimality (even though it may be viewed as trivial). More importantly, Schroeder (2013) shows
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that most wealth managers do not apply any of the proposed theories in practice, as most of the managers focus exclusively on the risk exposure of their
clients’ portfolios. Thus, most managers ignore the need to consider clients’ holistic asset allocation, time horizons as well as planned future income and
expenditures. In this paper, we attempt to present a solution that is feasible
AN US
for practitioners, yet holds within the academic debate.
Let us consider a concrete example. This client is an ultra high-net worth (UHNW) individual who has around USD 200m total wealth.1 One objective of this client is the optimization of his holistic asset allocation. Another objective is to keep track of and arrange his personal goals.2 There are a wide range of
M
goals and each has - by definition - a different time horizon and therefore its own strategic asset allocation (SAA). One can immediately imagine that such
ED
a situation causes one major issue: shall one optimize each goal individually or the holistic portfolio globally?
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2. A Behavioral-based and Holistic Investment Process
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Before we solve this issue, we need to quickly (and roughly for the sake of simplicity) define how to ideally go about the investment process that is able to tackle the above described situation. There are several strains of litera-
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1 The allocation and the total wealth figure are based on real client data. For the sake of anonymity, the data are not specified in more detail. The client’s rough holistic asset allocation consists of the following: 10% cash, 15% hedge funds, 20% private equity, 25% real estate, 5% gold, 9% equities, 13% bonds, and 3% wine. The data used for these allocations are described in more detail in Appendix A.1. 2 The goals of the client are made up as follows: 5% of his assets are for the education of his children, 10% for retirement, 2% for a vacation house, 23% are real estate investments, 3% fun, 5% last resort, 7% general investing, and 45% of his total wealth are undefined in terms of goals.
4
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ture, such as Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT), which we can draw from in order to define an ideal investment process. Curtis (2004) shows an interesting approach how to combine both theories in
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a constructive way: optimize based on MPT and construct based on BPT. We attempt to follow this idea.
As shown in various studies on risk profiling, in particular by De Giorgi and
Hens (2006), among others,3 who take the initial Prospect Theory of Kahneman and Tversky (1979) further, it is useful to risk profile clients not only based
AN US
on their financial situation (as required by regulators), but also based on their emotions. As shown in these studies, defining utility functions based on client preferences is one of the most efficient ways for obtaining a client’s utility towards potential gains and losses.4 More importantly, risk profiling clients for emotions is a truly holistic approach to risk profiling, as the preferences of a
M
client affect his total wealth and not just isolated individual portfolios. The target state based on a client’s risk profile is then expressed with a holistic strategic
ED
asset allocation (SAA), which are constructed based on principles from MPT.5 If a client has several goals, which make up his holistic allocation, the difficulty becomes obvious: how do we globally optimize the holistic asset alloca-
PT
tion without compromising individual goals (i.e. portfolios)? Chhabra (2005) expands the Markowitz framework with goal-based investing and concludes that
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risk allocation should precede asset allocation. That is why we focus on calculating risk and optimizing for risk first. Nevins (2004) argues along these lines showing how an integrated traditional and behavioral investment approach is
AC
feasible. We therefore follow this route to practically solve this issue.
3 See also Bosch-Domenech and Silvestre (2006), De Giorgi et al (2007), De Giorgi and Hens (2009), and Davies and Brooks (2014). 4 See Appendix A.2 for the specification of the utility function for obtaining a client’s holistic risk profile based on emotions. 5 As example in this study, we distinguish between 12 individual risk profiles, i.e. SAAs, which consist of bonds, equities and cash.
5
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3. The Compensation Portfolio Once we have identified an ideal target state for the client based on a compre-
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hensive risk profiling tool, we need to compare the client’s current holistic asset allocation to the target state. In other words, we need a risk engine that calculates the risk of the current holistic asset allocation of the client and compares it to the defined risk profiles (i.e. SAAs). If there is a difference between the current and the target state, investment advice is necessary to reallocate and
optimize the holistic asset allocation for the target risk profile. We calculate
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the risk score in a straight-forward manner by calculating the volatility of the holistic portfolio.6
In order to solve the issue that arises for our sample client if we want to optimize the client’s holistic asset allocation and align it with the target risk profile without compromising existing goals, we introduce the concept of the
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compensation portfolio. The purpose of the compensation portfolio is thus the following: first, it shall align the client’s current risk profile with the target risk
ED
profile, i.e. we optimize for risk. Second, it shall optimize for the holistic asset allocation. This approach is in line with Chhabra’s (2005) findings. Neverthe-
PT
less, optimizing for one’s holistic asset allocation is a topic that should not be underestimated. For example, the global average UHNW has a cash quote in excess of 35%.7 Optimizing for both the risk and asset allocation by forming
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a compensation portfolio, the assets can ideally be taken from available cash
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positions (if the target risk level is higher than the current risk level).8 Let us consider the concrete example from above. As described above, we
6 As
described in Appendix A.3, we calculate the so-called enhanced volatility, as this measure captures better additional short-term risk measures, such as Value at Risk (VaR), maximum drawdown, and downside deviation. 7 See Wealth X Report (2017), available at http://www.wealthx.com/articles/2017/thewealth-x-world-ultra-wealth-report-2017/, last accessed 30 August 2017. 8 If the target risk level is lower than the current risk level, one would first attempt to re-align the risk of those assets, which do not form a particular goal.
6
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risk profile the client based on an emotional utility function.9 We then calculate the risk score of the client’s current holistic allocation.10 Figure 1 shows the results. In this example, the target client risk profile based on the risk profiling
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should be a 9.11 The current risk score of the client’s holistic allocation is 8.
That means that we have a discrepancy between the current and the target state
and we need to increase the holistic risk level of this client by one notch. In order
to do this, we form a compensation portfolio, which aligns the risk of the current holistic asset allocation with the target risk of the holistic asset allocation. The
AN US
compensation portfolio is a locally optimized portfolio, which, at the same time,
optimizes the holistic asset allocation. By definition, the compensation portfolio is thus an additional goal within the client’s total wealth. In this particular case, the allocation of the compensation portfolio is determined by two factors: the risk profile and the size of the portfolio. The size of the portfolio is ideally
M
dependent on the available cash quote of the client.
For our example, given that we need to bring the risk level of the client up
ED
one notch (from 8 to 9), we suggest an SAA, which has the highest risk profile (i.e. 12 in this example), so that we can readjust the risk level with the available cash that the client has (10% of allocation available). In order to change the
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holistic risk level of the client from 8 to 9, we suggest to reallocate 5% from cash into the compensation portfolio. Figure 2 shows the new holistic asset
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allocation after compensation, and table 1 shows the goal-based balance sheet including the compensation portfolio as new additional goal. Figure 1 shows that we have successfully aligned the risk level of the holistic asset allocation
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with the target risk profile of the client without breaking up any of the existing goals, yet optimizing for both risk and asset allocation.12 9 See
also Appendix A.2. also Appendix A.3. 11 For this purpose, we distinguish between 12 different risk profiles, which have 12 different underlying SAAs. 1 is the most conservative risk profile, 12 the most aggressive. 12 In practice, a 5% cash allocation is an efficient level within a holistic portfolio. 10 See
7
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Figure 1: Risk score comparison
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This figure shows the risk score of the client’s initial holistic situation, the risk score with compensation portfolio and the target risk profile of the client. The risk scores range from 1 to 12, while 1 being the most conservative and 12 the most aggressive.
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Table 1: Goal-based balance sheet (with compensation portfolio)
This table shows the goal-based balance sheet including the compensation portfolio.
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Figure 2: Holistic asset allocation (with compensation portfolio)
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4. Conclusion
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This figure shows the holistic asset allocation of the sample client including the compensation portfolio.
We successfully show that it is possible to optimize both for risk and for asset allocation without compromising the optimization of individual goals by intro-
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ducing the novel concept of a compensation portfolio. Therefore, we solve for the global vs. local optimization paradox by bridging Modern Portfolio Theory
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(MPT) and Behavioral Portfolio Theory (BPT). These findings have concrete implications for three target groups. First, the fi-
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nancial services industry and in particular client and investment advisors should be aware that clients are best advised if advisors consider their holistic and goalspecific allocation, and not only in terms of optimizing for the asset allocation locally or globally, but also in terms of risk. A best possible solution is what we have described in this paper as the compensation portfolio. Second, regulators
9
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should be aware of the issues that arise between local vs. global optimization in terms of asset allocation and risk, and could therefore evaluate whether it is possible to set a better regulatory framework for tackling this client issue. If
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advisors are required by regulation to check for the necessity of a compensation portfolio, clients would on average be advised better. And, third, economically
speaking, this might decrease high cash allocations of clients, which would be
beneficial for clients by reducing the opportunity cost of holding too much cash in a low-yielding environment, and in turn it would increase potential revenues
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of banks and advisors.
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References [1] Binsbergen, Van, H. J., M. W. Brandt, and R.S.J. Koijen, 2008. Optimal decentralized investment management. The Journal of Finance 63, 18491895.
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[2] Black, F. and R. Litterman, 1992. Global portfolio optimization. Financial Analysts Journal 48, 28-43.
[3] Bosch-Domenech, A. and J. Silvestre, 2006. Reflection on Gains and Losses: A 2 x 2 x 7 Experiment. Journal of Risk and Uncertainty 33, 217-235. [4] Brunel, J.L.P., 2006. How Sub-Optimal - if at all - Is Goal-Based Asset Allocation? Journal of Wealth Management 9, 19-34.
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[5] Chhabra, A.B., 2005. Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors. Journal of Wealth Management 7, 8-34. [6] Curtis, G., 2004. Modern Portfolio Theory and Behavioral Finance. Journal of Wealth Management 7, 16-22.
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[7] Davies, G.B., and P. Brooks, 2014. Risk Tolerance: Essential, Behavioural and Misunderstood. Journal of Risk Management in Financial Institutions 2, 110-113. [8] De Giorgi, E., and T. Hens, 2006. Making prospect theory fit for finance. Financial Markets and Portfolio Management 20, 339-360.
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[9] De Giorgi, E., and T. Hens, 2009. Prospect theory and mean-variance analysis: Does it make a difference in wealth management? Investment Management and Financial Innovations 6, 122-129.
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[10] De Giorgi, E. G., T. Hens, and J. Mayer, 2007. Computational Aspects of Prospect Theory with Asset Pricing Applications. Computational Economics 29, 267-281.
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[11] Elton, E.J., and M.J. Gruber, 2004. Optimum centralized portfolio construction with decentralized portfolio management. Journal of Financial and Quantitative Analysis 39, 481-494.
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[12] Kahneman, D., and A. Tversky, 1979. Prospect Theory: An Analysis of Decisions under Risk. Econometrica 47, 263-291. [13] Nevins, D., 2004. Goals-Based Investing - Integrating Traditional and Behavioral Finance. Journal of Wealth Management 6, 8-23. [14] Schroeder, D, 2013. Asset allocation in private wealth management: Theory versus practice. Journal of Asset Management 14, 162-181.
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[15] Sharpe, W., 1981. Decentralized Investment Management. Journal of Finance 36, 217-234. [16] Stein, D.M., and G. McIntire, 2003. Overlay Portfolio Management in a Multi-Manager Account. Journal of Wealth Management 5, 57-71.
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[17] Thaler, R., 1985. Mental accounting and consumer choice. Marketing Science 4, 199-214.
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Appendix
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A.1 Data The data are obtained from Thomson Reuters Datastream and include the fol-
lowing indices for the example that is shown: UBS ETF HFRX Global Hedge Fund Index (proxy for hedge funds), S&P Listed Private Equity USD Price In-
dex (proxy for private equity), IShares Global Real Estate Index ETF (proxy
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for real estate), MSCI World USD Total Return Index (proxy for equities), Bar-
clays US Treasury Total Return Index (proxy for bonds), Liv-ex Fine Wine 50 Price Index (proxy for wine), and JP Morgan US 3mth cash index (proxy for cash). In order to calculate the risk (volatility) of the client’s portfolio, we use a time window of the last 250 working days.
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A.2 Emotional Risk Profiling
We risk profile our sample client emotionally as described based on Prospect
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Theory by Kahneman and Tversky (1979) and the further work by De Giorgi and Hens (2006), De Giorgi and Hens (2009), and De Giorgi et al (2007). To describe a client’s preferences towards risk in this realm, four components are
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important to calculate a client’s emotional risk profile: the reference point RPW , ˜ T − RPW ˜ − RPW , loss aversion, which we capture by υ − W = −βυ W
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˜ T ≥ RPW and β ≥ 1, investment temperament Whl , and uncertainty where W
aversion α, capturing the aversion of clients to fluctuations in their level of
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wealth. To describe the four components above we use the following value ˜T: function defined on terminal wealth W ˜ T − RPW = υ W
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˜ T − RPW > if W
W0 2α ,
W0 α
2 ˜ T − RPW , ˜ T − RPW − α W if 0 ≤ W˜T − RPW ≤ Wα0 W 2W0 ˜ T − RPW , ˜ T ≤ RPW β W if Whl ≤ W ˜ T − RPW + β (1 − ) (Whl − RPW ) , ˜ T < Whl , β W if W
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=
(1)
where α ≥ 0, β ≥ 1, and ≥ 1 capture the attitude to uncertainty to gains,
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the attitude to losses, and the investment temperament, respectively. W0 is the initial wealth, RPW is the target wealth or reference point, and Whl indicates the level for high losses. These parameters are client-specific and are calibrated
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using a questionnaire.
A.3 Risk Calculation
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The risk calculation is done on the following risk measure, namely volatility, with an enhancement approach in order to account for various risk scenarios
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(which are aligned with the emotional risk profiling that we describe above):
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s
where the enhancement factor fi = 1 −
1 N
N P
i=1
(2)
σenh,i = σi,t ∗ fi
2
V aR+M axDD+DDev 3
∗ ρ , σi,t =
(xi − µ) , V aR is a short-term value at risk measure, M axDD refers to
a short-term maximum drawdown, and DDev to short-term downside deviation,
and ρ is a specific weight given to these risk measures, which determines the degree to which the enhancement factor impacts the standard deviation.
14
The Compensation Portfolio Philippe Rohner, Matthias W. Uhl PII: DOI: Reference:
S1544-6123(17)30529-9 10.1016/j.frl.2018.02.023 FRL 876
To appear in:
Finance Research Letters
Received date: Revised date: Accepted date:
1 September 2017 8 December 2017 22 February 2018
Please cite this article as: Philippe Rohner, Matthias W. Uhl, The Compensation Portfolio, Finance Research Letters (2018), doi: 10.1016/j.frl.2018.02.023
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
ACCEPTED MANUSCRIPT
Highlights • We show how to optimize both for risk and for asset allocation • optimization of individual goals possible
CR IP T
• Introduction of novel concept of compensation portfolio
AC
CE
PT
ED
M
AN US
• Bridging Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT)
1
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Philippe Rohner∗ Matthias W. Uhl† December 2017
Abstract
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The Compensation Portfolio
ED
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We successfully show that it is possible to optimize both for risk and for asset allocation without compromising the optimization of individual goals by introducing the novel concept of a compensation portfolio. Therefore, we solve for the global vs. local optimization paradox by bridging Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT).
Keywords: Optimization, goal-based investing, compensation portfolio Classification: G11, G40, G41
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∗ University of Zurich, Department of Banking and Finance, Plattenstr. Zurich, [email protected] † University of Zurich, Department of Banking and Finance, Plattenstr. Zurich, [email protected]
2
32, CH-8032 32, CH-8032
ACCEPTED MANUSCRIPT
1. Portfolio Optimization and Goal-based Invest-
CR IP T
ing Clients and investment advisors are often confronted with a paradox when they attempt to optimize across their holistic asset allocation and their individ-
ual portfolios: it does not add up. Whether one optimizes a specific portfolio first, and then the next, and so on, or whether one optimizes globally first usually leads to the one inefficiency or the other. The issue typically arises because
AN US
clients need to change risk profiles (and therefore asset allocations) of individual portfolios if they want to optimize across their portfolios holistically. However, breaking up single portfolios usually leads to increased costs, sub-optimal allo-
cations, or not achieving a particular investment goal. In this paper, we attempt to solve this paradox by introducing the so-called compensation portfolio.
M
When Sharpe (1981) introduced the concept of decentralized investment management, the goal was to find a framework how a decentralized manager
ED
can be incentivized to balance a second (passive) portfolio such that the overall portfolio is optimal. Elton and Gruber (2004) extend this idea to multiple decentralized managers. Although these approaches provide valuable insights on
PT
decentralized investment management, they do not directly address behavioral concepts of investing. A key difference to this strand of literature is that our ap-
CE
proach assumes that decentralized managers act independently from each other. Thaler (1985) introduced the concept of mental accounting, which opened a new
AC
stream of literature in the realm of behavioral finance: goal-based investing was born. With the introduction of goal-based investing, a new variable was brought into the equation. However, the equation is still not entirely solved until today, as ample evidence in the literature shows. For instance, a two-step optimization process can result in diversification inefficiencies, as Van Binsbergen et al (2008)
3
ACCEPTED MANUSCRIPT
show. Furthermore, Brunel (2006) notes that optimizing one way (traditional) or the other (goal-based behavioral) leads to some form of sub-optimality (even though it may be viewed as trivial). More importantly, Schroeder (2013) shows
CR IP T
that most wealth managers do not apply any of the proposed theories in practice, as most of the managers focus exclusively on the risk exposure of their
clients’ portfolios. Thus, most managers ignore the need to consider clients’ holistic asset allocation, time horizons as well as planned future income and
expenditures. In this paper, we attempt to present a solution that is feasible
AN US
for practitioners, yet holds within the academic debate.
Let us consider a concrete example. This client is an ultra high-net worth (UHNW) individual who has around USD 200m total wealth.1 One objective of this client is the optimization of his holistic asset allocation. Another objective is to keep track of and arrange his personal goals.2 There are a wide range of
M
goals and each has - by definition - a different time horizon and therefore its own strategic asset allocation (SAA). One can immediately imagine that such
ED
a situation causes one major issue: shall one optimize each goal individually or the holistic portfolio globally?
PT
2. A Behavioral-based and Holistic Investment Process
CE
Before we solve this issue, we need to quickly (and roughly for the sake of simplicity) define how to ideally go about the investment process that is able to tackle the above described situation. There are several strains of litera-
AC
1 The allocation and the total wealth figure are based on real client data. For the sake of anonymity, the data are not specified in more detail. The client’s rough holistic asset allocation consists of the following: 10% cash, 15% hedge funds, 20% private equity, 25% real estate, 5% gold, 9% equities, 13% bonds, and 3% wine. The data used for these allocations are described in more detail in Appendix A.1. 2 The goals of the client are made up as follows: 5% of his assets are for the education of his children, 10% for retirement, 2% for a vacation house, 23% are real estate investments, 3% fun, 5% last resort, 7% general investing, and 45% of his total wealth are undefined in terms of goals.
4
ACCEPTED MANUSCRIPT
ture, such as Modern Portfolio Theory (MPT) and Behavioral Portfolio Theory (BPT), which we can draw from in order to define an ideal investment process. Curtis (2004) shows an interesting approach how to combine both theories in
CR IP T
a constructive way: optimize based on MPT and construct based on BPT. We attempt to follow this idea.
As shown in various studies on risk profiling, in particular by De Giorgi and
Hens (2006), among others,3 who take the initial Prospect Theory of Kahneman and Tversky (1979) further, it is useful to risk profile clients not only based
AN US
on their financial situation (as required by regulators), but also based on their emotions. As shown in these studies, defining utility functions based on client preferences is one of the most efficient ways for obtaining a client’s utility towards potential gains and losses.4 More importantly, risk profiling clients for emotions is a truly holistic approach to risk profiling, as the preferences of a
M
client affect his total wealth and not just isolated individual portfolios. The target state based on a client’s risk profile is then expressed with a holistic strategic
ED
asset allocation (SAA), which are constructed based on principles from MPT.5 If a client has several goals, which make up his holistic allocation, the difficulty becomes obvious: how do we globally optimize the holistic asset alloca-
PT
tion without compromising individual goals (i.e. portfolios)? Chhabra (2005) expands the Markowitz framework with goal-based investing and concludes that
CE
risk allocation should precede asset allocation. That is why we focus on calculating risk and optimizing for risk first. Nevins (2004) argues along these lines showing how an integrated traditional and behavioral investment approach is
AC
feasible. We therefore follow this route to practically solve this issue.
3 See also Bosch-Domenech and Silvestre (2006), De Giorgi et al (2007), De Giorgi and Hens (2009), and Davies and Brooks (2014). 4 See Appendix A.2 for the specification of the utility function for obtaining a client’s holistic risk profile based on emotions. 5 As example in this study, we distinguish between 12 individual risk profiles, i.e. SAAs, which consist of bonds, equities and cash.
5
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3. The Compensation Portfolio Once we have identified an ideal target state for the client based on a compre-
CR IP T
hensive risk profiling tool, we need to compare the client’s current holistic asset allocation to the target state. In other words, we need a risk engine that calculates the risk of the current holistic asset allocation of the client and compares it to the defined risk profiles (i.e. SAAs). If there is a difference between the current and the target state, investment advice is necessary to reallocate and
optimize the holistic asset allocation for the target risk profile. We calculate
AN US
the risk score in a straight-forward manner by calculating the volatility of the holistic portfolio.6
In order to solve the issue that arises for our sample client if we want to optimize the client’s holistic asset allocation and align it with the target risk profile without compromising existing goals, we introduce the concept of the
M
compensation portfolio. The purpose of the compensation portfolio is thus the following: first, it shall align the client’s current risk profile with the target risk
ED
profile, i.e. we optimize for risk. Second, it shall optimize for the holistic asset allocation. This approach is in line with Chhabra’s (2005) findings. Neverthe-
PT
less, optimizing for one’s holistic asset allocation is a topic that should not be underestimated. For example, the global average UHNW has a cash quote in excess of 35%.7 Optimizing for both the risk and asset allocation by forming
CE
a compensation portfolio, the assets can ideally be taken from available cash
AC
positions (if the target risk level is higher than the current risk level).8 Let us consider the concrete example from above. As described above, we
6 As
described in Appendix A.3, we calculate the so-called enhanced volatility, as this measure captures better additional short-term risk measures, such as Value at Risk (VaR), maximum drawdown, and downside deviation. 7 See Wealth X Report (2017), available at http://www.wealthx.com/articles/2017/thewealth-x-world-ultra-wealth-report-2017/, last accessed 30 August 2017. 8 If the target risk level is lower than the current risk level, one would first attempt to re-align the risk of those assets, which do not form a particular goal.
6
ACCEPTED MANUSCRIPT
risk profile the client based on an emotional utility function.9 We then calculate the risk score of the client’s current holistic allocation.10 Figure 1 shows the results. In this example, the target client risk profile based on the risk profiling
CR IP T
should be a 9.11 The current risk score of the client’s holistic allocation is 8.
That means that we have a discrepancy between the current and the target state
and we need to increase the holistic risk level of this client by one notch. In order
to do this, we form a compensation portfolio, which aligns the risk of the current holistic asset allocation with the target risk of the holistic asset allocation. The
AN US
compensation portfolio is a locally optimized portfolio, which, at the same time,
optimizes the holistic asset allocation. By definition, the compensation portfolio is thus an additional goal within the client’s total wealth. In this particular case, the allocation of the compensation portfolio is determined by two factors: the risk profile and the size of the portfolio. The size of the portfolio is ideally
M
dependent on the available cash quote of the client.
For our example, given that we need to bring the risk level of the client up
ED
one notch (from 8 to 9), we suggest an SAA, which has the highest risk profile (i.e. 12 in this example), so that we can readjust the risk level with the available cash that the client has (10% of allocation available). In order to change the
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holistic risk level of the client from 8 to 9, we suggest to reallocate 5% from cash into the compensation portfolio. Figure 2 shows the new holistic asset
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allocation after compensation, and table 1 shows the goal-based balance sheet including the compensation portfolio as new additional goal. Figure 1 shows that we have successfully aligned the risk level of the holistic asset allocation
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with the target risk profile of the client without breaking up any of the existing goals, yet optimizing for both risk and asset allocation.12 9 See
also Appendix A.2. also Appendix A.3. 11 For this purpose, we distinguish between 12 different risk profiles, which have 12 different underlying SAAs. 1 is the most conservative risk profile, 12 the most aggressive. 12 In practice, a 5% cash allocation is an efficient level within a holistic portfolio. 10 See
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Figure 1: Risk score comparison
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This figure shows the risk score of the client’s initial holistic situation, the risk score with compensation portfolio and the target risk profile of the client. The risk scores range from 1 to 12, while 1 being the most conservative and 12 the most aggressive.
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Table 1: Goal-based balance sheet (with compensation portfolio)
This table shows the goal-based balance sheet including the compensation portfolio.
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Figure 2: Holistic asset allocation (with compensation portfolio)
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4. Conclusion
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This figure shows the holistic asset allocation of the sample client including the compensation portfolio.
We successfully show that it is possible to optimize both for risk and for asset allocation without compromising the optimization of individual goals by intro-
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ducing the novel concept of a compensation portfolio. Therefore, we solve for the global vs. local optimization paradox by bridging Modern Portfolio Theory
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(MPT) and Behavioral Portfolio Theory (BPT). These findings have concrete implications for three target groups. First, the fi-
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nancial services industry and in particular client and investment advisors should be aware that clients are best advised if advisors consider their holistic and goalspecific allocation, and not only in terms of optimizing for the asset allocation locally or globally, but also in terms of risk. A best possible solution is what we have described in this paper as the compensation portfolio. Second, regulators
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should be aware of the issues that arise between local vs. global optimization in terms of asset allocation and risk, and could therefore evaluate whether it is possible to set a better regulatory framework for tackling this client issue. If
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advisors are required by regulation to check for the necessity of a compensation portfolio, clients would on average be advised better. And, third, economically
speaking, this might decrease high cash allocations of clients, which would be
beneficial for clients by reducing the opportunity cost of holding too much cash in a low-yielding environment, and in turn it would increase potential revenues
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of banks and advisors.
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References [1] Binsbergen, Van, H. J., M. W. Brandt, and R.S.J. Koijen, 2008. Optimal decentralized investment management. The Journal of Finance 63, 18491895.
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[2] Black, F. and R. Litterman, 1992. Global portfolio optimization. Financial Analysts Journal 48, 28-43.
[3] Bosch-Domenech, A. and J. Silvestre, 2006. Reflection on Gains and Losses: A 2 x 2 x 7 Experiment. Journal of Risk and Uncertainty 33, 217-235. [4] Brunel, J.L.P., 2006. How Sub-Optimal - if at all - Is Goal-Based Asset Allocation? Journal of Wealth Management 9, 19-34.
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[5] Chhabra, A.B., 2005. Beyond Markowitz: A Comprehensive Wealth Allocation Framework for Individual Investors. Journal of Wealth Management 7, 8-34. [6] Curtis, G., 2004. Modern Portfolio Theory and Behavioral Finance. Journal of Wealth Management 7, 16-22.
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[7] Davies, G.B., and P. Brooks, 2014. Risk Tolerance: Essential, Behavioural and Misunderstood. Journal of Risk Management in Financial Institutions 2, 110-113. [8] De Giorgi, E., and T. Hens, 2006. Making prospect theory fit for finance. Financial Markets and Portfolio Management 20, 339-360.
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[9] De Giorgi, E., and T. Hens, 2009. Prospect theory and mean-variance analysis: Does it make a difference in wealth management? Investment Management and Financial Innovations 6, 122-129.
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[10] De Giorgi, E. G., T. Hens, and J. Mayer, 2007. Computational Aspects of Prospect Theory with Asset Pricing Applications. Computational Economics 29, 267-281.
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[11] Elton, E.J., and M.J. Gruber, 2004. Optimum centralized portfolio construction with decentralized portfolio management. Journal of Financial and Quantitative Analysis 39, 481-494.
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[12] Kahneman, D., and A. Tversky, 1979. Prospect Theory: An Analysis of Decisions under Risk. Econometrica 47, 263-291. [13] Nevins, D., 2004. Goals-Based Investing - Integrating Traditional and Behavioral Finance. Journal of Wealth Management 6, 8-23. [14] Schroeder, D, 2013. Asset allocation in private wealth management: Theory versus practice. Journal of Asset Management 14, 162-181.
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[15] Sharpe, W., 1981. Decentralized Investment Management. Journal of Finance 36, 217-234. [16] Stein, D.M., and G. McIntire, 2003. Overlay Portfolio Management in a Multi-Manager Account. Journal of Wealth Management 5, 57-71.
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[17] Thaler, R., 1985. Mental accounting and consumer choice. Marketing Science 4, 199-214.
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Appendix
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A.1 Data The data are obtained from Thomson Reuters Datastream and include the fol-
lowing indices for the example that is shown: UBS ETF HFRX Global Hedge Fund Index (proxy for hedge funds), S&P Listed Private Equity USD Price In-
dex (proxy for private equity), IShares Global Real Estate Index ETF (proxy
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for real estate), MSCI World USD Total Return Index (proxy for equities), Bar-
clays US Treasury Total Return Index (proxy for bonds), Liv-ex Fine Wine 50 Price Index (proxy for wine), and JP Morgan US 3mth cash index (proxy for cash). In order to calculate the risk (volatility) of the client’s portfolio, we use a time window of the last 250 working days.
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A.2 Emotional Risk Profiling
We risk profile our sample client emotionally as described based on Prospect
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Theory by Kahneman and Tversky (1979) and the further work by De Giorgi and Hens (2006), De Giorgi and Hens (2009), and De Giorgi et al (2007). To describe a client’s preferences towards risk in this realm, four components are
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important to calculate a client’s emotional risk profile: the reference point RPW , ˜ T − RPW ˜ − RPW , loss aversion, which we capture by υ − W = −βυ W
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˜ T ≥ RPW and β ≥ 1, investment temperament Whl , and uncertainty where W
aversion α, capturing the aversion of clients to fluctuations in their level of
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wealth. To describe the four components above we use the following value ˜T: function defined on terminal wealth W ˜ T − RPW = υ W
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˜ T − RPW > if W
W0 2α ,
W0 α
2 ˜ T − RPW , ˜ T − RPW − α W if 0 ≤ W˜T − RPW ≤ Wα0 W 2W0 ˜ T − RPW , ˜ T ≤ RPW β W if Whl ≤ W ˜ T − RPW + β (1 − ) (Whl − RPW ) , ˜ T < Whl , β W if W
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=
(1)
where α ≥ 0, β ≥ 1, and ≥ 1 capture the attitude to uncertainty to gains,
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the attitude to losses, and the investment temperament, respectively. W0 is the initial wealth, RPW is the target wealth or reference point, and Whl indicates the level for high losses. These parameters are client-specific and are calibrated
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using a questionnaire.
A.3 Risk Calculation
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The risk calculation is done on the following risk measure, namely volatility, with an enhancement approach in order to account for various risk scenarios
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(which are aligned with the emotional risk profiling that we describe above):
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where the enhancement factor fi = 1 −
1 N
N P
i=1
(2)
σenh,i = σi,t ∗ fi
2
V aR+M axDD+DDev 3
∗ ρ , σi,t =
(xi − µ) , V aR is a short-term value at risk measure, M axDD refers to
a short-term maximum drawdown, and DDev to short-term downside deviation,
and ρ is a specific weight given to these risk measures, which determines the degree to which the enhancement factor impacts the standard deviation.
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