Question

1. You are given the following information about the stocks in a two-stock portfolio

Stock	Return	Portfolio Weight	Standard Deviation
Blue Hotel Inc.	22%	45%	9%
Joys Food Inc.	25%	55%	11%

The correlation coefficient between the two stocks is 0.5.

Using the information above, calculate the following:

1. The expected return of the portfolio,
2. The variance of the portfolio,
3. The standard deviation of the portfolio.

Answer 1

a)Expected return of the portfolio = Wb * Rb + Wj * Rj

Expected return of the portfolio = 0.45 * 22% + 0.55 * 25% = 23.65%

Where

Wb = Weights of Blue Hotel Inc.

Wj = Weights of Joys Food Inc.

Rb = Return of Blue Hotel Inc.

Rj = Return of Joys Food Inc.

b)

Variance of the portfolio = (Wb^2*SD^2 + Wj^2*SD^2 + 2*Wb*Wj*Correlation*SD*SD)

Variance of the portfolio = 0.45^2 *9^2 + 0.55^2 * 11^2 + 2*0.45*0.55*9*11*0.50

Variance of the portfolio = 16.4025 + 36.6025 + 24.5025

Variance of the portfolio = 77.51%

c)

Standard deviation of the portfolio = Square root of Variance of portfolio

Standard deviation of the portfolio =8.80%

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Wb = Weights of Blue Hotel Inc.

Wj = Weights of Joys Food Inc.

SD = Standard Deviation of Blue Hotel Inc.

SD = Standard Deviation of Joys Food Inc.