Number of stocks in portfolio 20 30 1,000 Variance - loxepompe t on noes Portfol

Question

Number of stocks in portfolio 20 30 1,000 Variance - loxepompe t on noes Portfolio risk is measured by the standard deviation, which is the variance. The following steps are used to measure portfolio variance square root of portfolico Let i 1,2...S is the number of scenario Compute the portfolio return for each scenario i " 4() = w,r, (i) j-1 Where, N is the number of assets in the portfolio, and w, : Weight of asset j in the portflio; r,(0): Return of asset,/ in scenario Compute the expected portfolio return using the same formula as for an individual asset r,, :2p(i)rp(i) Where, p(i) s the probability ofscenario i Compute the portfolio variance and standard deviation using the same formula as for an individual asset. .

Explanation / Answer

Answer to Example 2:

Asset A:

Expected Return = 0.40 * 30% + 0.60 * (-10%)
Expected Return = 6%

Variance = 0.40 * (0.30 - 0.06)^2 + 0.60 * (-0.10 - 0.06)^2
Variance = 0.0384

Standard Deviation = (0.0384)^(1/2)
Standard Deviation = 0.1960 or 19.60%

Asset B:

Expected Return = 0.40 * (-5%) + 0.60 * 25%
Expected Return = 13%

Variance = 0.40 * (-0.05 - 0.13)^2 + 0.60 * (0.25 - 0.13)^2
Variance = 0.0216

Standard Deviation = (0.0216)^(1/2)
Standard Deviation = 0.1470 or 14.70%

Portfolio:

Boom:

Expected Return = 50% * 30% + 50% * (-5%)
Expected Return = 12.50%

Bust:

Expected Return = 50% * (-10%) + 50% * 25%
Expected Return = 7.50%

Expected Return on Portfolio = 0.40 * 12.50% + 0.60 * 7.50%
Expected Return on Portfolio = 9.50%

Variance = 0.40 * (0.125 - 0.095)^2 + 0.60 * (0.075 - 0.095)^2
Variance = 0.0006

Standard Deviation = (0.0006)^(1/2)
Standard Deviation = 0.0245 or 2.45%

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