Active risk vs Benchmark risk

The equation you’ve presented, Var(Portfolio) = Var(active return) + Var(benchmark), is missing a critical term for portfolio variance calculation in CFA Level 2.

The missing term accounts for the covariation between the active return and the benchmark return. This covariation reflects how the active return and the benchmark move together.

@shell shockers online The complete formula for the variance of a portfolio’s return is:

𝑉
𝑎
𝑟
(
𝑃
𝑜
𝑟
𝑡
𝑓
𝑜
𝑙
𝑖
𝑜
)
=
𝑉
𝑎
𝑟
(
𝑎
𝑐
𝑡
𝑖
𝑣
𝑒
𝑟
𝑒
𝑡
𝑢
𝑟
𝑛
)
+
𝑉
𝑎
𝑟
(
𝑏
𝑒
𝑛
𝑐
ℎ
𝑚
𝑎
𝑟
𝑘
)
−
2
∗
𝑊
𝑒
𝑖
𝑔
ℎ
𝑡
𝑝
𝑜
𝑟
𝑡
𝑓
𝑜
𝑙
𝑖
𝑜
∗
𝐶
𝑜
𝑣
(
𝑎
𝑐
𝑡
𝑖
𝑣
𝑒
𝑟
𝑒
𝑡
𝑢
𝑟
𝑛
,
𝑏
𝑒
𝑛
𝑐
ℎ
𝑚
𝑎
𝑟
𝑘
)
Var(Portfolio)=Var(activereturn)+Var(benchmark)−2∗Weight
p
​
ortfolio∗Cov(activereturn,benchmark)