FINANCE Corporate financial policy and R and D Management

The portfolio variance is given by the weighted asset variances and
covariances.

(8.1)

whereρ 12 = correlation coefficients of assets 1, 2
σ 12 = covariance of assets 1, 2

let x 2 = 1 – x 1

To minimize the portfolio variance, one should take the first derivative of
the variance with respect to the decision variable, x 1 , and set the function
equal to zero.

(8.2)

(8.2)

Equation (8.2) is the risk-minimizing investment in security one in a two-asset
portfolio. One can compare the portfolio variances of the optimally weighted
portfolio with an equally weighted portfolio, in which x 1 = x 2 = 0.50.

let x 1 = weight of JNJ

x 2 = weight of IBM

The portfolio expected return is a weighted combination of asset expected
returns.

E(Rp) = x 1 E(R 1 ) + x 2 E(R 2 )

= .5(.0852) + .5(.0768) = .0810 (8.3)

σσσσ

σσρσσ

σσρσσρσσ

σ

p

p

xxxx

xxxx

xxxx x

x

2

1

2

1

2

1

2

2

2

1112

1

2

1

2

1

2

2

2

111212

1

2

1

2

112

2

112 1 2 1

2

1212

2

1

2

121

121

11 2 2

=+−+−

=+−+−

=+−−+−

=

() ()

() ()

()()

σσσρσσρσσ

∂σρ

∂

σσσρσσρσσ

σρσσσσρσ

1

2

11

2

2

2

112 1 2 1

2

12 12

2

1

11

2

2

2

12

2

121 2 1 12 12

2

2

1212 1 1

2

12

2

112

12 2 2

2222 4 0

22 2 2 4

+−++−

=−++−=

−=+−

()xx x x

x

xx x

xxx 112

1

2

2

2

12 12 1 2

2

12 12

1

22 121

1

2

2

2

121 2

2

2

σ

σσρσσσρσσ

σσρσ

σσρσσ

()

()

+−=−

=

−

+−

x

x

σσσσ

σρσσ

p xx xx

2

1

2

1

2

2

2

2

2

1112

12 12 1 2

=++− 21

=

()

204 THE USE OF FINANCIAL INFORMATION IN THE RISK AND RETURN OF EQUITY