Multiple Regression Analysis - Expected ROI Calculation

Very Hard Multiple Regression Analysis Regression Coefficients

A financial analyst has performed a multiple regression analysis to predict the return on investment (ROI) of different portfolios based on independent variables including the market return (MR), the risk-free rate (RF), and the portfolio's beta (B). The regression output yielded the following coefficients:

Intercept: 2.5

Coefficient of MR: 1.2

Coefficient of RF: -0.5

Coefficient of B: 0.8

Given this output, the regression equation can be expressed as:

$$ ext{ROI} = 2.5 + 1.2 imes ext{MR} - 0.5 imes ext{RF} + 0.8 imes B $$

Calculate the expected ROI if the market return is 10%, the risk-free rate is 2%, and the portfolio beta is 1.5. Additionally, interpret the meaning of the coefficient of RF within the context of this regression.

The expected ROI is 10.3%, and the RF coefficient indicates that an increase in the risk-free rate decreases expected ROI.

The expected ROI is 9.6%, and the RF coefficient indicates that an increase in the risk-free rate increases expected ROI.

The expected ROI is 11.0%, and the RF coefficient indicates that an increase in the risk-free rate does not have a significant effect on expected ROI.

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