Monday, September 13, 2010

The GRAP attribution linking formula

At the Expert Level, CIPM candidates are required to learn a few of the more commonly used linking methodologies for smoothing the attribution effects that come from arithmetic models. The required methodologies include:

  • Cariño

  • Menchero

  • GRAP

Of these methods, the GRAP method is my personal favorite because of it's simplicity... which may not be apparent looking at the formula! Upon first glance, the GRAP formula, which appears above, may seem intimidating for a couple of reasons:

  • It uses three "series" one summation series a two multiplication series.

  • The three series have different indexes (T=1 through N, t = 1 through T-1, and t = T+1 through N).

When teaching the GRAP method, I find that it is easier to explain what it does, effectively, rather than explaining the formula.

Consider a situation where we are linking together monthly attribution effects for the first six months of the calendar year (January through June). Let's consider how we obtain the "G" factor that we will use to smooth the attribution effects for the month of April. Basically, what the GRAP formula tells us is that:

  • The excess return is the sum of the "smoothed" attribution effects

  • We obtain the smoothed attribution effects by multiplying the original attribution effects by the "G" factor

  • The G factor for a particular month is a combination of portfolio returns and benchmark returns for the periods being linked together.

  • In our example, we are smoothing the attribution effects for April. This will be done by multiplying together:
  1. the unitized portfolio returns for the months preceding April (January, February, March)
  2. the unitized benchmark returns for the months coming after April (May, June)

Thus, the following formula yields the G factor that we can use to smooth the April attribution effects:

Thus, the GRAP formula is very easy to remember, and much simpler to use than the Menchero or Cariño methods.