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Let R_P be a return of some type on a portfolio and let R_1, ..., R_N be the same type of returns on the assets

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Let R_P be a return of some type on a portfolio and let R_1, ..., R_N be the same type of returns on the assets in this portfolio. Is R_P = w_1R_1 + ... + w_NR_N true if R_P is a net return? Is this equation true if R_P is a gross return? Is it true if R_P is a log return? Justify your answers

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