Both in CFAI 2016 book, reading 54, example, question 4 as well in Schweser Notes the combined portfolios excess return calculation doesn’t include the weight of active portfoio and benchmark portfolio.

For example in CFAI book they did below

“Note that at the 6.5% optimal level of active risk, Fund III has an expected active return of 0.20(6.5%) = 1.3%, a total expected excess return of 7.2% + 1.3% = 8.5%”.

Here they calculated excess return on active portfolio as IR * Active Risk i.e. 0.2 * 0.065 = 0.013 ~ 1.3% and then added it to 7.2 which is nothing but Sharpe Ratio (Benchmark) * Benchmark Risk i.e. 0.47 * 0.152 = 0.07144 ~ 7.2%

So 1.3% + 7.2% = 8.5% is combined portfolio’s excess return.

In overall calculation they haven’t catered for weight of active portfolio and weight of benchmark portfolio before coming with return calculation. In question 3 they determined that active portfolio to be longed 1.3 times and benchmark to be shorted 0.3 times.

Wondering why weight of portfolio is not used in coming up with excess return calculation. Can anyone shed light on this?

I know how to calculate the expected active return over the benchmark, but I don’t understand how the ‘‘total excess return’’ is calculated:

Here they calculated excess return on active portfolio as IR * Active Risk i.e. 0.2 * 0.065 = 0.013 ~ 1.3% and then added it to 7.2 which is nothing but Sharpe Ratio (Benchmark) * Benchmark Risk i.e. 0.47 * 0.152 = 0.07144 ~ 7.2%

okay I finally figured it out after being stuck on this for an hour fml

Total excess return should equal to (Rp-Rb)+(Rb-Rf)
The calculation of excess active return on active portfolio should be IR* active risk which equals to excess return on active portfolio. (Rp-Rb)
The sharpe ratio*benchmark standard dev. would equal to excess return on benchmark portfolio. (Rb-Rf).