FRM Part I · FRM Exam Part I · Modern Portfolio Theory (MPT) and the Capital Asset Pricing Model (CAPM)
Asset X has volatility 30% and Asset Y has volatility 10%. A risk manager forms a portfolio of X and Y with the aim of minimizing portfolio variance when the correlation is zero. What weight in X minimizes variance?
The variance-minimizing weight in Asset X is 10%. With zero correlation, the weight in X equals the variance of Y divided by the sum of both variances, which is 0.01 divided by 0.10. The riskier asset therefore receives the smaller weight.
- A10%Correct
- B25%
- C50%
- D90%
Explanation
For zero correlation, the weight in X is σY²/(σX²+σY²) = 0.01/(0.09+0.01) = 0.10. The 90% option reverses the weights. The 25% option uses an incorrect ratio of volatilities rather than variances.
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