Skip to content

FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)

The risk-free rate is 2%. Risky asset A has an expected return of 8% and volatility of 10%. Risky asset B has an expected return of 14% and volatility of 20%. The correlation between A and B is zero. What is the expected return of the tangency (maximum Sharpe ratio) portfolio of A and B?

The tangency portfolio's expected return is 10.0%. With zero correlation, weights are proportional to excess return divided by variance, giving 600 for A and 300 for B, so 2/3 in A and 1/3 in B. The weighted expected return is 8% × 2/3 plus 14% × 1/3, which equals 10%.

  1. A10.0%Correct
  2. B11.0%
  3. C12.0%
  4. D9.2%

Explanation

With zero correlation, optimal weights are proportional to excess return divided by variance. For A: 6/0.01 = 600. For B: 12/0.04 = 300. So wA = 2/3 and wB = 1/3. Expected return = (2/3)(8%) + (1/3)(14%) = 10%. The 12% option weights by excess return alone, ignoring variance. The 9.2% option weights by inverse variance, ignoring excess return.

Did you get it right without looking?

One question tells you little. A timed set on Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM) shows your real accuracy, how long you take and where you lose marks.

Practise Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)Free diagnostic mock

More Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM) questions