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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

horizon, regardless of the performance of equity markets. More formally, it is given

b y F t = A t - 1 2

, where At-12

is the portfolio

value twelve months earlier. Again, by taking F t = B t - 1 2 , f o r e x a m p l e , t h i s c o n s t r a i n t c a be extended to relative risk budgets. n

a piece-wise dynamic allocation strategy, w i t h t h e t h r e s h o l d T t t o e n s u r e s m o o t h pasting. The aforementioned floors (capital guarantee, benchmark protection, maximum drawdown constraint, trailing performance) have equivalents in goals. -

Conventional strategies consider the floor but ignore investment goals. Goal-directed strategies recognise that an investor might have no additional utility gain once a total wealth Gt beyond a given goal is reached. 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 not immediately clear why any investor would want to impose a strict limit on upside potential. But the intuition is that by forgoing performance beyond a certain threshold, where the relative utility of greater wealth is lower, investors benefit from a decrease in the cost of downside protection. In other words, without a performance cap or goal, investors run a higher risk of missing a nearly attained investment goal.

This dynamic risk management approach has a wide variety of applications. Different kinds of floors or the inclusion of goals make possible strategies that meet particular requirements. The inclusion of a maximum drawdown constraint, for example, is of particular interest to open-ended funds, since it lessens the degree to which the investor’s performance for the entire holding period depends on the point at which he entered the fund. Thus, asset managers can use maximum drawdown constraints to satisfy the needs of investors who enter and exit at different times. The trailing performance floor is particularly useful for absolute return products, where the investor expects the probability of losing money over any one-year period to be extremely low. We now turn to the discussion of such absolute return strategies.

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 w e a l t h ( d e n o t e d b y T t ) a t w h i c h t h investor shifts from a goal-oriented focus to a risk-management focus, one obtains e

An EDHEC-Risk Institute Publication

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