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What is the point/benefit of using a dollar-neutral strategy in addition to a Beta-neutral strategy? What exactly does a dollar-neutral strategy buy the investor? What's useful about balancing long and short positions?

Using the notation in Qian et al.'s book, in the mean-variance optimization problem, why would an investor force:

$w\cdot I = 0 $ in addition to $w \cdot B = 0 $ ?

with

  • $w$ being the portfolio weights
  • $B$ being the exposure matrix
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    $\begingroup$ Marketing wise, perhaps dollar neutral is easier for investors to understand and to check, while beta neutral is more obscure and subjective (different data services give different values for Beta). So "we give you both MN and BN" sounds like a good advertising line. $\endgroup$ – noob2 May 31 '16 at 18:02
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Imagine a scenario where a beta neutral portfolio comprised being long one very high beta stock and short many low beta stocks. Such a portfolio clearly has extreme concentration of risk. Additionally imposing a 'dollar neutral' constraint, would help to spread the weights more evenly over all the stocks.

A further observation is that measuring true 'beta' is fraught with difficulty, and the underlying true value is likely anyway dynamic (due to cyclical and structural changes at both the corporate and market wide level). Knowing this, imposing a dollar neutral constraint on the portfolio can be done in a precise way, and in this sense might give some added sense of security (that 'market' risk is being minimised).

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