The following table contains monthly returns for Cola Co. and Gas Co. for

2010

(the returns are shown in decimal form, i.e., 0.035 is 3.5%). Using this table and the fact that Cola Co. and Gas Co. have a correlation of

0.0969,

calculate the volatility (standard deviation) of a portfolio that is

65%

invested in Cola Co. stock and

35%

invested in Gas Co. stock.

Month Cola Co Gas Co Jan -0.0210 0.0280 Feb 0.0000 -0.0050 Mar -0.0200 -0.0180 Apr 0.0090 0.0280 May -0.0310 0.0840 Jun -0.0840 -0.0460 Jul -0.1190 0.0820 Aug -0.0160 0.0460 Sep 0.0550 0.0300 Oct -0.0110 0.0140 Nov -0.0380 0.0290 Dec -0.0220 0.0740

(Click the icon to view the monthly returns.)

Calculate the volatility by:

a.

Using the formula:

Var left parenthesis Upper R Subscript p right parenthesis equals w Subscript 1 Superscript 2 Baseline SD left parenthesis Upper R 1 right parenthesis squared plus w Subscript 2 Superscript 2 Baseline SD left parenthesis Upper R 2 right parenthesis plus 2 w 1 w 2 Corr left parenthesis Upper R 1 comma Upper R 2 right parenthesis SD left parenthesis Upper R 1 right parenthesis SD left parenthesis Upper R 2 right parenthesisVarRp=w21SDR12+w22SDR2+2w1w2CorrR1,R2SDR1SDR2.

b.

Calculating the monthly returns of the portfolio and computing its volatility directly.

c.

How do your results compare?

a.

Use the formula

Var left parenthesis Upper R Subscript p right parenthesis equals w Subscript 1 Superscript 2 Baseline SD left parenthesis Upper R 1 right parenthesis squared plus w Subscript 2 Superscript 2 Baseline SD left parenthesis Upper R 2 right parenthesis plus 2 w 1 w 2 Corr left parenthesis Upper R 1 comma Upper R 2 right parenthesis SD left parenthesis Upper R 1 right parenthesis SD left parenthesis Upper R 2 right parenthesisVarRp=w21SDR12+w22SDR2+2w1w2CorrR1,R2SDR1SDR2.

The volatility (standard deviation) of the portfolio is

nothing%.

(Round to two decimal places.)