Alex and Kay Are Two Retail Property Investment Managers Hired

Essay

Alex and Kay are two retail property investment managers hired one year ago by two different investors. In both cases the managers were free to use their own judgment regarding geographical allocation between properties in the East versus West of the country. Kay allocated her capital equally between the two regions, while Alex placed 65% of his capital in the Western region. After one year their respective total returns were as depicted in the table below. As you can see, Kay beat Alex by 60 basis-points in her total portfolio performance for the year.
$\begin{array}{lrr} \text{Alex \& Kay's returns realized for clients:}\\\hline Weights: & Alex & Kay \\East & 35 \% & 50 \% \\West & 65 \% & 50 \% \\\hline Returns: & Alex & Kay \\Total~ Portfolio & 6.65 \% & 7.25 \% \\East & 6.00 \% & 6.50 \% \\West & 7.00 \% & 8.00 \% \end{array}$ How would you attribute this 60 basis-point differential between pure allocation performance, pure selection performance, and a combined interaction effect, if you wanted to compute an unconditional performance attribution that was independent of the order of computation? Note: This is equivalent to taking Alex as the benchmark against which Kay's performance is being compared.)