Dynamic Core-Satellite Risk-Budgeting
This post is meant as an extension to the posts ALM based Private Wealth Management - Introduction and Asset & Liability based Private Wealth Management 2 – Risk Budgeting that I strongly recommend the reader to review to first.
Posts are located: LDI based Private Wealth Management - Introduction and LDI based Private Wealth Management 2 – Risk Budgeting
The approach of the Dynamic Core-Satellite (DSC) risk-budgeting methodology, is essentially the separation of Assets into several components.
A. The Core Portfolio component, that seek to track a designated benchmark or liability.
B. A more risky Performance oriented component, made up of one or more Satellite portfolios with an absolute return mandate.
The approach is useful both in the context of relative Asset Liability Management, where the aim may be to neutralize Liabilities, and hence is an extension of Liability Driven Investing (LDI).
Or
Absolute Return strategies, where the DSC approach can be used smoothen the ride, and limit drawdowns.
In both cases the Asset Allocation inside does not change, they are so to speak independent of whether the objective is relative or absolute return. The Core portfolio does however change, as it is suppose to mimic the Benchmark as close as possible.
In a Relative Return LDI context, where the objective is to hedge some future Liabilities like Inflation, the Core portfolio is named the “Liability Hedge Portfolio” and is allocated to Assets with a high correlation to Consumer Price Index. Where as in a more absolute return context the Core may be composed of a risk-return optimized portfolio of Beta exposure.
Sometimes we are operating with two extra types of portfolios namely:
A. Completeness portfolios, used tactically to port exposure to or from the combined portfolio, for example in case the Country, Sector or Style exposure deviate unwanted from the Strategic Allocation.
B. A Extreme Risk portfolio, designed to hedge unwanted more regime dependent risks.
Although the weights allocated to the Core and the Satellite can be static, the next step is to let the Satellite allocation be dynamic depending on the current cumulative outperformance of the combined portfolio. There are several options.
In the Constant Proportion Portfolio Insurance (CPPI) variant, total assets are dynamically allocated to Satellite Performance seeking portfolios in proportion to a Multiple of a designated portfolio Cushion. The Cushion being defined the difference between the value of the combined over-all portfolio, and a desired protective floor (For example 90% of resent top), and the Multiple being a numeric value acting so to speak, as a risk gas-pedal between the two portfolios, the higher its numeric value, the higher allocation to the Performance portfolio.
In the Variable Proportion Portfolio Insurance (VPPI) variant the Multiplier is also dynamic and can depend on a whole range on input like P/L, gap-risk, Volatility and Manager views.
Under such allocation strategy the portfolio’s exposure to the risky Satellite portfolio tends to zero as the cushion approaches zero; when the cushion is zero, the portfolio is completely invested in the Core portfolio. Thus, in theory the strategy ensures that the portfolio never falls below the floor; in the event that it touches the floor, the fund is “dead”; that is, it can deliver no performance beyond the guarantee.
The approach should be seen as a structured and hence sustainable form of portfolio management, that allows an investor to effectively truncate the relative-return distribution in such a way as to allocate the probability weights away from severe relative underperformance and towards greater potential outperformance.
In the context of absolute return strategies, it is straightforward to let the Core Portfolio consist of any optimized portfolio, and have a number of Performance seeking Satellite Portfolios compelment it. On can let the multiplier be fixed and simply let allocation to Satellite Portfolio be a function of the set multiplier multiplied by the Cusion, alternativly an investor can also utilize a "Investment view" in a structured fasion, through increasing the multiplier and hence the investment into the Performance Satellite when it is expected to outperform the Core and, conversely reduce the multiplier and allocation to Performance Satellite it when it is expected to underperform. Like standard CPPI, this dynamic allocation technique requires that a floor of potential under-performance is established, and is usually set as a fraction of the benchmark portfolio, say 90%. Investment in the Performance Satellite then provides access to potential outperformance of the benchmark.
The main benefit of the DCS is hence as an on-going structured process that leads to an accumulation of past outperformance and results in an increase in the cushion and hence in the potential for a more aggressive allocation in the future. If the Performance Satellite has underperformed the benchmark, however, the fraction invested in in it, decreases in an attempt to ensure that the relative performance objective will be met.
Mechanics of the Risk Budget
The methodology allows implementation of a wide range of different strategies customized to the risk appetite and investment guidelines of the investor. For example when these strategies are extended from a static to a dynamic portfolio approach, a transaction filters is vital.
How do we determine allocation to each portfolio?Let Pt be the value of the portfolio at date t. The portfolio Pt can then be broken down into a floor Ft and a cushion Ct, according to the relation Pt = Ft + Ct.If we let Bt be a relevant Benchmark, then the floor is given by Ft = kBt, where k is a constant less than one. Finally, let the investment in the Satellite be Et =wSt =mCt =m(Pt -Ft), with m being a constant Multiplier greater than 1 and w the fraction invested in the Satellite. The remainder of the portfolio, Pt - Et = (1-w)Bt, is invested in the benchmark. |
More advanced features also offer the opportunity to remedy potientail weaknesses of the original CPPI, such as the lack of protecting gains, the fixed time horizon and the limited potential to recover from a large drawdown. The guaranteed target level at a fixed time horizon is a feature that may not be necessarily required by an investor as this requirement has also a significant downside: There is little upside potential to take advantage of a market recovery if the risk budget is strongly depleted after a downturn in the risky portfolio.
The situation is worse if this happens in the early stage of the strategy, since the risk budget is used. One possibility to remedy this weakness is the minimum exposure CPPI. Here, the allocation in the risky portfolio is held at a minimum guaranteed level. This ensures participation over the complete lifetime of the strategy.
In the standard case presented above, the floor is a constant fraction of the benchmark value Ft = kBt. However, depending on the investment purpose, different floors might be used to exploit the benefits of core-satellite management. Indeed, the core-satellite approach can be extended in a number of directions, allowing the introduction of more complex floors or of so-called investment goals. Instead of imposing a lower limit on total portfolio value, a goal (or cap) restricts the upside potential of the portfolio. It can also be extended to account for a state- dependent risk budget, as opposed to the constant expenditure of the risk budget implied by the basic dynamic core-satellite strategy. We list below several possible floor designs, and we then discuss the option of making a goal part of the investment process. Setting the floor is the key to dynamic core-satellite management, since it ensures asymmetric risk management of the overall portfolio. If the difference between the floor and the total portfolio value increases, that is, if the cushion becomes larger, more of the assets are allocated to the risky satellite. By contrast, if the cushion becomes smaller, investment in the satellite decreases.
Conventional strategies consider the floor but ignore investment goals. Goal-directed strategies recognize that an investor might have no additional utility gain once a total wealth gets beyond a give treshold. This goal, or investment cap, may be constant; it may also be a deterministic or stochastic function of time. Goal-directed strategies involve optimal switching at some suitably defined threshold above which hope becomes fear (Browne 2000).
It is may not be immediately clear why any investor would want to impose a strict limit on upside potential. But the intuition is that investor may prefer forgoing additional performance beyond a certain threshold, where the relative utility of greater wealth is lower, and rather benefit from a reduced probability and cost of downside protection. In other words, without a performance cap, investors run a higher risk of missing a nearly attained investment goal.
Such a goal can be accommodated by a strategy in which the fraction invested in the performance-seeking satellite is a multiple m2 of the distance to the goal, whereas a floor can be accommodated by a strategy in which the fraction invested in the performance-seeking satellite is a multiple m1 of the distance to the floor. If, in addition, one defines the threshold wealth (denoted by Tt) at which the investor shifts from a goal-oriented focus to a risk-management focus, one obtains a funding state-dependent dynamic allocation strategy, with the threshold Tt to ensure a smooth transition. A few basic strategies and extensions worth highlighting.
Capital guarantee floor
This is the basic dynamic Core-Satellite structure; it protects k% of the value of any given stochastic benchmark: Ft = kBt. In asset management, the benchmark can be any given target (e.g., a stock index). In asset/ liability management, the benchmark will be given by the liability value, so At ≥ Ft = kBt is a minimum funding ratio constraint.
Benchmark protection floor
This is the basic dynamic Core-Satellite structure; it protects k% of the value of any given stochastic benchmark: Ft = kBt. In asset management, the benchmark can be any given target (e.g., a stock index). In asset/ liability management, the benchmark will be given by the liability value, so At ≥ Ft = kBt is a minimum funding ratio constraint.
Trailing performance floor
This floor prevents a portfolio from posting negative performance over a twelve-month trailing horizon, regardless of the performance of equity markets. More formally, it is given by Ft = At-12, where At-12 is the portfolio value twelve months earlier. Again, by taking Ft = Bt-12, for example, this constraint can be extended to relative risk budgets.
Maximum drawdown floor
Extensions of the standard dynamic asset allocation strategy can also accommodate various forms of time-varying multipliers and floors. As an example, consider a “drawdown constraint” that requires the asset value At at all times to satisfy At > αMt, where Mt is the maximum asset value reached between date 0 and date t: max(As)s<t. In other words, only portfolios that never fall below 100α% of their maximum-to-date value are admitted, for some given constant α. The interpretation is that any drawdown must always be smaller than 1-α. These strategies were introduced by Estep and Kritzman (1988), who labeled them “time invariant portfolio protection strategies” (TIPP), and later formalized by Grossman and Zhou (1993) and Cvitanic and Karatzas (1995). This maximum drawdown floor was originally described for absolute risk management, but by taking At/Bt > α max(As/Bs) s<t, where Bt is the value of any benchmark, it can also be used for relative risk management.
The cost of absolutely protecting especially a TIPP based investment floor can be high. This is particularly true in cases where there is erratic movement in the underlying and risk-free returns are low. There are several approaches to help mitigate such cost:
- Exposure to the underlying risky Performance Portfolio can be adjusted to a minimum level if the asset falls, the implication being that there can be a temporary “break” in the floor.
- Exposure to the underlying can be resumed on the basis of an additional annual risk budget. This resumption, which is achieved by lowering the floor, is assessed at fixed intervals, or conditionally based on the risky underlying, or on a discretionary basis; charging management fees to the floor so that they do not affect management of the exposure.
These approaches, whether implemented individually or in combination, increase the ability to participate in upward movements in the underlying. The objective is shifted away from protection of an absolute investment floor which can only be adjusted upwards, to the generation of investments with real asymmetric return profiles.
Moreover, the greater the participation in rising markets, the higher the upward adjustment over time to the floor. Lowering protection costs, therefore, does not necessarily mean less protection, at least in the longer term.
Fortunately investors don’t need to construct these algorithms themselves. Companies exist that specialize in Portfolio Insurance. Cranberger will continue to expand the coverage of these strategies and their practical implementations. Please find below a Companies that specialize in Portfolio Insurance.