Scaling an Active Fund to Meet a Portfolio Active Risk Budget

Summary

The document poses an allocation question: how to split capital between an active fund and a passive ETF when the active fund’s risk relative to a benchmark exceeds the investor’s portfolio active-risk budget. It compares two proposed rules: divide the portfolio risk budget by the fund’s active risk to find the active allocation, or use the risk budget itself as the allocation percentage. The passive holding is assumed to have no active risk.

The question highlights that a fund’s active risk and an investor’s portfolio active risk are different quantities: scaling the fund position changes its contribution to portfolio active risk under the stated simplifying assumptions. However, the document contains no answer or worked derivation, so it does not establish which rule is correct beyond presenting the competing calculations. It also gives no discussion of interactions with other holdings, correlated active exposures, or implementation constraints; those details would matter in a more general portfolio calculation.

Key ideas

• The question distinguishes a fund’s active risk from the portfolio’s active-risk budget.
• It presents two competing ways to translate a risk budget into an active allocation.
• The passive ETF is assumed to have zero active risk in the example.
• The document does not resolve the allocation question or analyze correlated active holdings.

Tags

# How do I allocate between passive and active strategy using active risk budget?


# How do I allocate between passive and active strategy using active risk budget?












Lets say I have 100 million dollars. My active risk budget is 5%. I have an active fund that has active risk of 10%. What will be my mix in dollar terms of this active port and passive etf (assume passive ETF has 0 active risk)?

I have 2 answers, 1 says its "Allocation to active fund = Active risk budget / Active risk of active fund" ie in this case will be 5/10 = 50% into active fund.

The other answer is Active Fund Allocation = minimum(Active Fund Active Risk, Active Risk Budget) ie only 5% to Active fund (5 million dollars)

Which one is right? Thank you in advance!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.