Question

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

21.2 %21.2%.

	Upper E left bracket Upper R right bracketE [R]	SD left bracket Upper R right bracketSD [R]
Johnson​ & Johnson	7.3 %7.3%	16.1 %16.1%
Walgreen Company	10.8 %10.8%	19.8 %19.8%

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

Given

E(RJ) Expected return for Johnson & Johnson = 7.3%

E(RW) Expected return for Walgreen Company = 10.8%

Standard deviation SDJ = 16.1%

Standard deviation SDW = 19.8%

Weights of each Jonson and Johnson and Walgreen = 50%

a) E(RP) expected return of portfolio = wJ * E(RJ) + wW * E(RW)

E(RP) = 0.50 * 0.073 + 0.50 * 0.108

E(RP) = 9.05%

Expected return of portfolio is 9.05%

b) Standard deviation of portfolio = sqrt ( wJ² * SDJ² + wW² * SDW² +2* wJ * wW * correlation * SDJ * SDW )

Standard deviation = sqrt ( 0.5² * 0.161² + 0.5² * 0.198² + 2* 0.5 * 0.5 * 0.212* 0.161 * 0.198 )

Standard deviation = sqrt ( 0.01966)

Standard deviation = 14.02%

The volatility of SD is 14.02%