The monthly standard deviation of the equally weighted JNJ and IBM
portfolio is .0045 (.45 percent), as its corresponding monthly standard de-
viation is 6.71 percent. The annualized standard deviation of the equally
weighted portfolio is 23.24 percent. The annualized expected return of the
equally weighted Johnson & Johnson and IBM portfolio is 8.10 percent,
and its standard deviation is 23.24 percent. The portfolio returns should
fall within the –15.14 to 31.34 percent range approximately 68 percent of
the time.
If we use equation (8.2) to calculate the optimal security investments
to minimize risk:

The optimally weighted JNJ and IBM portfolio return is 8.29 percent.

The optimally weighted JNJ and IBM portfolio, composed of 71.8 percent
JNJ and 28.2 percent IBM, has a monthly standard deviation of 6.05 per-
cent and an annualized standard deviation of 20.96 percent. Note that the
optimally weighted portfolio has a slightly higher expected return (in this
particular case), but a lower standard deviation. Markowitz’s mean-variance
analysis seeks to minimize risk, holding expected return constant.

σ

σ

p

p

(^2222271807102821107) 2 718 282 0184 071 1107
0026 0010 0001 0037
0605
=++
=++=

(. ) (. ) (. ) (. ) (. )(. )(. )(. )(. )
....
.

xx

x

x

xx

ER

JNJ

IBM

p

1 22

1

1

2

1107 1107 0184 0710

0710 1107 2 0184 0710 1107

0123 0001

0050 0123 0003

0122

0170

718

282

718 8 52 282 7 68 6 12 2 17 8 29

==

−

+−

=

−

+−

==

==

=+=+=

. [.. (. )]

(. ) (. ) (. )(. )(. )

..

...

.

.

.

.

(). (.). (.)...

σ

σ

σ

p

p

p

22 22 2

2

5 0710 5 1107 2 5 5 0184 0710 1107

0013 0031 0001

0045

0671

=++

=++

=

=

(. ) (. ) (. ) (. ) (. )(. )(. )(. )(. )

...

.

.

The Use of Financial Information in the Risk and Return of Equity 205