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Correlated Factors - Quant question

Let’s say you have a Fund that has a Beta of:
0.20 to the HY Market
0.40 to the US Equity Market
0.35 to the International Equity Market
I don’t believe you can calculate expected return for the Fund as:
= RFR + B(HY Risk Premium) + B(US Equity Risk Premium) + B(Int’l Equity RIsk Premium)
…because the three markets are correlated.  How do you get around this issue?

looks like you are describing the APT? each of the 3 funds could be expressed as Rf + betas * risk premiums. in the total portfolio you would weight each fund and calc the portoflio beta for each risk premium.

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