Skip to content

CMA Final · Strategic Financial Management · Portfolio Theory and Practice

Under the single-index model, a portfolio holds two shares in equal proportions. Share X has beta 1.2 and residual variance 100 (%²); Share Y has beta 0.8 and residual variance 64 (%²). The market standard deviation is 20%. What is the portfolio's total standard deviation?

The total standard deviation is 21%. Portfolio beta is 1.0, giving systematic variance of 400. Residual risk is diversified with squared weights, so 0.25×100 plus 0.25×64 equals 41. Total variance of 441 has a square root of 21%.

  1. A21.00%Correct
  2. B20.00%
  3. C21.95%
  4. D23.75%

Explanation

Portfolio beta = 0.5×1.2 + 0.5×0.8 = 1.0, so systematic variance = 1.0 × 400 = 400. Residual variance = 0.25×100 + 0.25×64 = 41. Total variance = 441, SD = 21%. Using 0.5 instead of 0.25 for residual weights gives 482 and 21.95%, which is wrong.

Did you get it right without looking?

One question tells you little. A timed set on Portfolio Theory and Practice shows your real accuracy, how long you take and where you lose marks.

Practise Portfolio Theory and PracticeFree diagnostic mock

More Portfolio Theory and Practice questions