Question

Suppose Johnson​ & Johnson and the Walgreen Company have the expected returns and volatilities shown​ below, with a correlation of

22.8 %22.8%.

	Upper E left bracket Upper R right bracketE [R]	SD left bracket Upper R right bracketSD [R]
Johnson​ & Johnson	6.7 %6.7%	15.1 %15.1%
Walgreen Company	9.9 %9.9%	20.5 %20.5%

For a portfolio that is equally invested in Johnson​ & Johnson's and​ Walgreen's stock,​ calculate:

a. The expected return.

b. The volatility​ (standard deviation).

Answer 1

Ans:- (a) weights for a portfolio that is invested equally in 2 stocks will be 0.50 each.

The expected return is calculated W1*R1+W2*R2....................WN*RN, where W is the weight, and R is the return.

Exp return = 0.50*6.7%+0.50*9.9% = 8.30%

(b) The standard deviation of Portfolio for 2 stocks is calculated by [ W1^2*SD^2+W2^2*SD^2+ 2*W1*W2*SD1*SD2*r]^(1/2), where W is the weights, SD is the Standard deviation and r is the correlation between 1 and 2.

=[ 0.50^2*0.151^2+0.50^2*0.205^2 + 2*0.50*0.50*0.151*0.205*0.228 ]^(1/2) = 0.1405 = 14.05%.

The Portfolio expected return is 8.30% and the Standard deviation is 14.05%.

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