# Calculate unsystematic-risk of a firm in a regression with SD or R2?

i'm studying for a finance exam and i can't answer this question. It is asking me to calculate the unsystematic risk of firm A and i have the following information:

Return firm A: 0,1% + 1,2Returnstockexchange

R² = 0,15

SD of regression = 0,38

Risk free rate = 5%

Market rate = 8%

I know that the SD is the total risk of the firm A, but how can i find the unsystematic risk from this?

Some post in the internet says that the Unsystematic risk is (1-R²) but i coudn't find anything solid about this subject, does someone here can answer this?

• regarding (1-R^2): please note that $R^2 = cov(R_m, R_i)/(\sigma_m \sigma_i)$. Thus the relation between $R^2$ and B is given by: $B = cov(R_m, R_i) / \sigma_m ^2 = R^2 *\frac{\sigma_i}{\sigma_m}$. So (1-R^2) = $1 - \frac{\sigma_m^2 B^2}{\sigma_i ^2}$. simplifying results into $(1-R^2) = \frac{(\sigma_\epsilon)^2}{(\sigma_m)^2}$. Where $\sigma_\epsilon$ is the residual risk. So, asuming i did not mess up my maths it looks like (1-R^2) gives you the ratio between residual risk and market risk (squared) – mbison Nov 19 '18 at 19:05
• Assuming that you are given the value of R2, and assuming you know the variance of the market portfolio, you can isolate the residual risk $\sigma_\epsilon$. (The next link gives you the same result, but derives it in a different way win-vector.com/blog/2011/11/correlation-and-r-squared) – mbison Nov 19 '18 at 19:15