Question

Asset A has an expected volatility of 8%. Asset B has an expected volatility of 25%....

  1. Asset A has an expected volatility of 8%. Asset B has an expected volatility of 25%. Their covariance is -0.200. If 10% of your wealth is in Asset A and 90% is in Asset B, the expected volatility of your portfolio is _____%.
  1. 8.00
  2. 10.00
  3. 11.13
  4. 12.12
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Answer #1

Weight of asset A in the portfolio = wA = 10%

Weight of asset B in the portfolio = wB = 90%

Volatility or standard deviation of asset A = σA = 8%

Volatility or standard deviation of asset B = σB = 25%

Covariance between A and B = Cov(A,B) = -0.2

Variance of the portfolio is calculated suing the formula:

Portfolio Variance = σP2 = wA2*σA2 + wB2*σB2 + 2*wA*wB*Cov(A,B) = (10%)2*(8%)2 + (90%)2*(25%)2 + 2*10%*90%*(-0.2) = 0.000064 + 0.050625 + (-0.036) = 0.014689

The volatility or standard deviation of the portfolio is square-root of its variance

Volatility or standard deviation of portfolio = σP = (0.014689)1/2 = 0.121198184804889 ~ 12.12% (Rounded to two decimals)

Answer -> 12.12 (option d)

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