systematic risk

An asset has a beta of 0.9. The variance of the market index is 90. If the variance of the returns on the asset is 120, what proportion of the assets total risk is systematic and what is residual risk? Answer: Systematic risk=0.9^2(90) = 72.9 Thus the portion of total risk that is attributable to market risk is 79.2/120 = 60.75% Can someone explain the logic (or even what is happening) of the first line of the answer. I don’t get it!

total risk = systematic risk + unsystematic risk systematic risk = (beta^2)*market variance

not positive, but I think it’s just a formula that has to be memorized systematic risk = beta^2 x variance of market systematic risk = .9^2 x 90 = 72.9 residual risk (company specific risk) = what’s left where is this q from?

Thanks folks. It’s a CFA EOC question. Stumped me completely. Just been flicking through Treynor-Black… I think I remember someone saying it came up last year for a whole vignette. That’s a bit rough, surely?!

This is a simple market model interpretation. portfolio variance = beta portfolio^2 * variance market covariance between two assets i and j = beta i * beta j * variance market


Thanks, CP. Much appreciated.