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Risk Control through Dynamic Core-Satellite Portfolios of ETFs: Applications to Absolute Return Funds and Tactical Asset Allocation — January 2010

1. Method: Dynamic Risk Budgeting

however, the fraction invested in the satellite decreases in an attempt to ensure that the relative performance objective will be met.

1.2. Extensions 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.

In the standard case presented above, the floor is a constant fraction of the benchmark v a l u e F t = k B t . H o w e v e r , d e p e n d i n g o n t h 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. e

Capital guarantee floor: this is the most basic expression of a risk budget given by F t = k e - r ( T - t ) A 0 , w h e r e r i s t h e r i s k - f r e e r a t (here assumed to be a constant), k a constant <1, and A0 the initial amount of wealth. e

The capital guarantee floor is what is usually used in CPPI.

Benchmark protection floor: this is the basic dynamic core-satellite structure; it protects k% of the value of any given s t o c h a s t i c b e n c h m a r k : F t = k B t . I n a s s e 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, t s o A t F t = k B t i s a m i n i m u m f u n d i n g r a constraint (Martellini and Milhau 2009). t i o

Maximum drawdown floor: extensions of the standard dynamic asset allocation strategy can accommodate various forms of time-varying multipliers and floors. Grossman and Zhou (1996), for example, consider a “drawdown constraint” that r e q u i r e s t h e a s s e t v a l u e A t a t a l l t i m e s t o s a t i s f y A t > α M t , w h e r e M t i s t h e m a x i m asset value reached between date 0 and date u m t : m a x ( A s ) s < t . I n o t h e r w o r d s , o n l y p o r t 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 labelled them “time invariant portfolio protection strategies” (TIPP), and later formalised by Grossman and Zhou (1993) and Cvitanic and Karatzas (1995). This maximum drawdown floor was originally described for absolute f o l i o s r i s k m a n a g e m e n t , b u t b y t a k i n g A t / B t > α m a x ( A s / B s ) s < t , w h e r e B t i s t benchmark, it can also be used for relative risk management. h e v a l u e o f a n y

Trailing performance floor: this floor prevents a portfolio from posting negative performance over a twelve-month trailing

An EDHEC-Risk Institute Publication

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