FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
Two assets each have a standard deviation of 20%. They are combined 50/50 in a portfolio, and their correlation is 0.5. What is the portfolio standard deviation (to two decimals)?
The portfolio standard deviation is 17.32%. With equal 50% weights, 20% volatilities and correlation 0.5, portfolio variance is 0.01 plus 0.01 plus 0.01, which is 0.03. Taking the square root gives about 17.32%, below 20% because correlation is less than one.
- A15.00%
- B17.32%Correct
- C20.00%
- D10.00%
Explanation
Variance = 0.25×0.04 + 0.25×0.04 + 2×0.25×0.5×0.04 = 0.01 + 0.01 + 0.01 = 0.03. The square root is 17.32%. The 15% figure comes from the wrong step of using correlation 0.0 in a misapplied form; 20% would require correlation of 1.
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