Question

Based on your research, you have already invested 20% of your savings in Stock X, which has a standard deviation of returns of 0.70. You want to diversify your risk and invest the remaining of your savings in one of the two other stocks based on your research: Stock A or Stock B. Standard deviation of the returns for Stock A is 0.83. The covariance of the returns between Stock X and A is –0.75. Whereas returns for Stock B have a standard deviation of 0.91. The covariance of the returns between Stock X and B is –0.61. To diversify, you should invest in _________  and build a two-asset portfolio with Stock X, achieving a variance of __________.

Answer 1

Weight of Stock – X in the two asset portfolio = 0.20

S.D of Stock –X = 0.70

Weight of other Stock in the portfolio = 1-0.20 = 0.80

S.D. of Stock –A = 0.83

Variance of Stock-A = 0.83^2 = 0.6889

Covariance of the returns between Stock X and A = –0.75

S.D of Stock – B = 0.91

Variance of Stock-B = 0.8281

Covariance of the returns between Stock X and B = -0.61

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The variance for a portfolio consisting of two assets is calculated using the following formula:

Where:

• wi – the weight of the ith asset
• σi^2 – the variance of the ith asset
• Cov1,2 – the covariance between assets 1 and 2

Variance of the two asset portfolio of Stock – X & Stock-A = (0.2^2)(0.49^2) + (0.8^2)(0.6889) + 2*0.2*0.8*(-0.75)

= 0.009604 + 0.440896 – 0.2

= 0.2105

=0.21

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Variance of the two asset portfolio of Stock – X & Stock-B = (0.2^2)(0.49^2) + (0.8^2)(0.8281) + 2*0.2*0.8*(-0.61)

= 0.009604 + 0.529984– 0.1952

= 0.344388

=0.34

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High variance in a portfolio is associated with higher risk , So Portfolio of Stock-X & Stock-A has lower risk as it has low variance.(0.21 as compared to 0.34)

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To diversify, you should invest in Stock-A  and build a two-asset portfolio with Stock X, achieving a variance of 0.21 .