Relative/Active Risk Attribution

Hello! New here on this forum…

Super stuck on this section under equities (Active Equity investing - portfolio construction - Reading 29, Book 4)

In Exhibit 12 (page 478) - the example works out the relative risk attribution by changing the original benchmarks weights of 50% in both Index A and B _ to _ 40% each of Index A and B and adding a 20% allocation to cash.

How did they work out the variance of active returns attribution for index A and B after the weight change is 14.3%, -14.3% respectively and all the risk (i.e. 100%) of the active risk is attributed to cash?

Would appreciate help!

I was also looking at this and racking my brains for a long time on this, before I realised that they don’t give any co-variances in order to use the formula, neither Schweser or the CFAI books give a worked example of using a formula :confused:

Guessing that the key takeaways are the important points mentioned after.

Would still be good to see a worked example given that they give us the formula like we’re expected to be able to use it.

Don’t want to create another thread so adding to this.

Anyone has this figured out? It seems the double summation formula for relative portfolio return variance does not work for the exhibit provided. I’m probably missing something.

How can I summon S2000magician…

I did this spreadsheet a while back for my students.

Link: https://drive.google.com/file/d/1Kn1tqckCeNJKho3xq1VcIk5CEyubk0bS/view?usp=sharing

Column Q and R shows two ways of calculating the CAV. Column S is the % that you want to derive. Formulae in blue font.

Thank you so much!