Why does low correlated asset increase active risk

CFA Level III
#1

Well my question says it all. Just wanted to know rationale as to why adding cash in a portfolio, increases active risk.

#2

What’s the definition of active risk?

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#3

More like tracking error. = Volatility of active returns = can be decomposed into variance due to factor exposure or idiosyncratic.

#4

Exactly like tracking error; that’s the definition of active risk.

So . . . what does adding cash do to your tracking error?

#5

Mathematically it made sense. Thanks.

But, also if a pair of stock has low correlation and added to portfolio as long short = active risk increases= is it due to the exposure of these stocks are not yet cancelled by each other?

Please assume pair of stock with low corr is from two diff sectors.

#6

Low correlation with each other, or with the portfolio?

#7

Meant with each other. Like underweight a stock relative to bench but overweight a stock in different sector.

#8

In that case, you cannot say for certain whether how it will change the tracking error.

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