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IAI Actuarial Core Principles · Economic Modelling · Capital Asset Pricing Model (CAPM)

The risk-free rate is 5%, market expected return 11% and market standard deviation 12%. An investor wants an efficient portfolio with an expected return of 8%, and invests Rs 10 lakh in total. What amount is invested in the market portfolio, and what is the portfolio standard deviation?

Rs 5 lakh is invested in the market and the standard deviation is 6%. The weight w solves 5% + 6%w = 8%, so w = 0.5, and risk is 0.5 times the market's 12%, since the risk-free asset has zero variance.

  1. ARs 5 lakh; 6%Correct
  2. BRs 6 lakh; 7.2%
  3. CRs 4 lakh; 4.8%
  4. DRs 5 lakh; 12%
  5. Rs 7.5 lakh; 9%

Explanation

Let w be the market weight: 5% + w × 6% = 8%, so w = 0.5, giving Rs 5 lakh in the market and Rs 5 lakh risk-free. Standard deviation = 0.5 × 12% = 6%. Check on the CML: slope 0.5, 5% + 0.5 × 6% = 8%.

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