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 5%, and the market portfolio has expected return 11% and standard deviation 18%. An investor wants an expected return of 14% using only the risk-free asset and the market portfolio. What weight must be invested in the market portfolio, and what is the resulting standard deviation?

The investor must hold 150% in the market portfolio, borrowing 50% at the risk-free rate, and the standard deviation is 27%. The weight solves 5% + w×6% = 14%, and volatility scales with the market weight: 1.5×18%.

  1. A150% and 27%Correct
  2. B150% and 18%
  3. C127% and 27%
  4. D133% and 24%

Explanation

Weight w solves 5% + w×(11%-5%) = 14%, so w = 9/6 = 1.5. This means borrowing 50% at the risk-free rate. Standard deviation = 1.5 × 18% = 27%. Check via CML: slope 6/18 = 1/3; 5% + 27%/3 = 14%.

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