Question

Stock beta=1.2, SD of returns iis 32%, SD of return on market portfolio is 15%, what proportion of the total risk is due to firm-specific factor?

Answer 1

Given,

Beta of Stock =1.2

Standard Deviation of Stock = 0.32

Standard Deviation of Market = 0.15

As, there are two kinds of risk Systematic which is related to market and Unsystematic which is related to firm,

Total Variance = Systematic Variance + Unsystematic Variance

or, (Total Standard Deviation of the Stock)² = (Systematic Risk)² + (Unsystematic Risk)²

or, (0.32)² = (Beta x Standard Deviation of market)² + (Unsystematic Risk)²

or, 0.1024 = (1.2 x 0.15)² + (Unsystematic Risk)²

or, 0.1024 = (0.18) ² + (Unsystematic Risk)²

or, 0.1024 = 0.0324 + (Unsystematic Risk)²

or, (0.1024-0.0324) = (Unsystematic Risk)²

or, 0.07 = (Unsystematic Risk)²

So, Unsystematic Risk = √0.07   = 0.2646   = 26.46%

Therefore, 26.46% of total risk is due to firm-specific factor.