The index model for stock B has been estimated with the following result:R_B = 0.01 + 1.1R_M + e_B.If σ_M = 0.20 and R²_B = 0.50, the standard deviation of the return on stock B is A) 0.1111. B) 0.2111. C) 0.3111. D) 0.4111.

Question

Quizplus · Accepted Answer

The standard deviation of stock B, σ_B, can be calculated using the formula: σ_B = √(β²σ_M² + σ_e²). Given R²_B = 0.50, we know that β²σ_M² accounts for 50% of the variance of B. Therefore, σ_e² also accounts for 50% of the variance. Since β = 1.1 and σ_M = 0.20, β²σ_M² = (1.1)²(0.20)² = 0.0484. Thus, σ_e² = 0.0484. Therefore, σ_B = √(0.0484 + 0.0484) = √0.0968 ≈ 0.3111.

The Index Model for Stock B Has Been Estimated with the Following