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!

Principles Level: Macro Attribution (risk-free rate)

I received an email from a candidate that requested a repeat explanation of the answer to a question from our recent CIPM Q&A webinar, and I thought the answer is worth sharing with everyone here, as I would hate to see candidates waste their time with this particular item.

The question:

Macro Attirbution – Risk Free – how do we come up w/ fund value of 187,944,879 or 575,474 if none of below #s multiplied by .31% give # $575,474????

Exhibit 1-6

Michigan Endowment for the Performing Arts

Monthly Performance Attribution

June 20xx

Decision-Making Level (Investment Alternative)	Fund Value	Incremental Return Contribution	Incremental Value Contribution
Beginning Value	$186,419,405	—	—
Net Contributions	187,369,405	0.00%	950,000
Risk-Free Asset	187,944,879	0.31%	575,474
Asset Category	194,217,537	3.36%	6,272,658
Benchmarks	194,720,526	0.27%	502,989
Investment Managers	194,746,106	0.01%	25,580
Allocation Effects	194,816,599	0.04%	70,494
Total Fund	194,816,599	3.99%	8,397,194

The answer is: you don't. Or, rather, you can't. The reading that CFA Institute provides does not give you adequate information to calculate their value metric for the "risk-free asset" decision.

I refer you to the footnote at the bottom of page 35 in the "Evaluating Portfolio Performance" reading. The footnote indicates that the value metric of $575,474 "cannot be replicated... because the $950,000 net contribution... was not a single, beginning-of-the-month cash flow."

In other words, there was more than external cash flow and some of them did not occur at the start of the month, thus they did not grow at the risk-free rate of 0.31% for the entire month. They do not, unfortunately, give you all of the details of the external cash flows - they simply give you the answer; i.e., the value metric for the risk-free rate decision.

In our prep class, for simplicity, the example and exercise we cover assumes all cash flows occur at the end of the month, which enables candidates to calculate the metric themselves (and, presumably, gives them some comfort level that they understand this particular item.

A follow-up question that is often asked in our classes is what should the candidate do if presented with a problem with cash flows that do not occur at the start of the month. My answer is that you should prorate the growth at the risk-free rate accordingly. For example, assuming a 30 day month, if a cash flow occurred at the end of the 10th day, then the cash flow would grow at the risk-free rate for 2/3 of the month.