Macro Attribution: Behind the Return Formulae...

One of the challenges for Principles Level students is dealing with the Macro Attribution model.  This model for attribution measures several decisions that a fund sponsor can take to grow its fund.  Because of the number of formulae involved, it seems overwhelming to some candidates.  But, if you look for common themes, the Macro Attribution model is not all that complex, and the return formulae are then easier to memorize.

There are three decisions in the Macro Attribution model that are measured as relative contributions to return; that is to say, a contribution to return in excess to the prior investment decision taken by the fund sponsor.  Those decisions are:

• asset categories
• benchmarks
• investment managers

Recall that the formula for contribution is:

        contribution = weight * return

The return formulae for the three fund sponsor decisions are as follows:

The asset categories return measures how much return is paid by the fund sponsor's decision to invest passively in asset classes (using index funds in the asset classes) in excess of the return paid by the risk-free rate.  Thus, the asset class weight is multiplied by the excess return (broad index fund, or really, the broad index return minus the risk-free rate).

The benchmarks return measures how much return is paid by the fund sponsor's decision to invest passively in investment styles within asset classes using its own policy weights (rather than the implied weights of the broad asset class indexes) in excess of the return paid by the asset class indexes.  thus, the investment style weight is multiplied by the excess return (style index fund, or really, style index return minus the broad asset class index return).

The investment managers return measures how much return is paid by the fund sponsor's decision to invest using active managers in each investment style in excess of the return paid by investing passively in those investment styles.  Thus, the investment style weight is multiplied by the excess return (manager active return minus the investment style index return). 

Hope this helps understand the formulae!